News and updates, April 2009

Apr 30, 2009 (5th)

By Ignacio Santos / GGNFS, Msieve / Apr 30, 2009
(53·10¹⁶³-17)/9 = 5(8)₁₆₂7_<164> = 3 · 19 · 34765350967304163312833_<23> · C140
C140 = P53 · P87
P53 = 62622882318570911412650973707031773485945464667516361_<53>
P87 = 474546564403968967469298671548430514892021736391287023805749850667560421046179684788407_<87>

Number: 58887_163 N=29717473657351880511406397184182422265767672183342114852866813048791098856416018648200989323953206454366254829764036411860857577932495626927 ( 140 digits) SNFS difficulty: 166 digits. Divisors found: r1=62622882318570911412650973707031773485945464667516361 (pp53) r2=474546564403968967469298671548430514892021736391287023805749850667560421046179684788407 (pp87) Version: Msieve-1.39 Total time: 50.02 hours. Scaled time: 128.54 units (timescale=2.570). Factorization parameters were as follows: n: 29717473657351880511406397184182422265767672183342114852866813048791098856416018648200989323953206454366254829764036411860857577932495626927 m: 500000000000000000000000000000000 deg: 5 c5: 424 c0: -425 skew: 1.00 type: snfs lss: 1 rlim: 4100000 alim: 4100000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 4100000/4100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [2050000, 4650001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 766824 x 767072 Total sieving time: 50.02 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000 total time: 50.02 hours. --------- CPU info (if available) ----------

(55·10¹⁵⁴+17)/9 = 6(1)₁₅₃3_<155> = 3³ · 13 · C153
C153 = P58 · P96
P58 = 1232654391467284570396223070468890151373701148611847251467_<58>
P96 = 141244562033352471422960766465762608824220881553425132457487800547462661060496451035078688975589_<96>

Number: 61113_154 N=174105729661285216840772396327951883507439062994618550174105729661285216840772396327951883507439062994618550174105729661285216840772396327951883507439063 ( 153 digits) SNFS difficulty: 156 digits. Divisors found: r1=1232654391467284570396223070468890151373701148611847251467 (pp58) r2=141244562033352471422960766465762608824220881553425132457487800547462661060496451035078688975589 (pp96) Version: Msieve-1.39 Total time: 17.35 hours. Scaled time: 44.60 units (timescale=2.571). Factorization parameters were as follows: n: 174105729661285216840772396327951883507439062994618550174105729661285216840772396327951883507439062994618550174105729661285216840772396327951883507439063 m: 10000000000000000000000000000000 deg: 5 c5: 11 c0: 34 skew: 1.25 type: snfs lss: 1 rlim: 2800000 alim: 2800000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1400000, 2300001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 445869 x 446117 Total sieving time: 17.35 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000 total time: 17.35 hours. --------- CPU info (if available) ----------

(55·10¹²⁷+17)/9 = 6(1)₁₂₆3_<128> = 3³ · 7 · 191599 · C121
C121 = P40 · P81
P40 = 4682653728534234711143308235969476153633_<40>
P81 = 360390300507760405496205851150786683695433826066308510126793078082183441435140851_<81>

Number: 61113_127 N=1687582984400237563818213450460429248882679688106067622082261453494543901533963532663363502192978802402071254669070361683 ( 121 digits) SNFS difficulty: 130 digits. Divisors found: r1=4682653728534234711143308235969476153633 (pp40) r2=360390300507760405496205851150786683695433826066308510126793078082183441435140851 (pp81) Version: Msieve-1.39 Total time: 2.48 hours. Scaled time: 6.39 units (timescale=2.571). Factorization parameters were as follows: n: 1687582984400237563818213450460429248882679688106067622082261453494543901533963532663363502192978802402071254669070361683 m: 50000000000000000000000000 deg: 5 c5: 44 c0: 425 skew: 1.57 type: snfs lss: 1 rlim: 1030000 alim: 1030000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1030000/1030000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [515000, 965001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 155761 x 155992 Total sieving time: 2.48 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,130,5,0,0,0,0,0,0,0,0,1030000,1030000,26,26,47,47,2.3,2.3,50000 total time: 2.48 hours. --------- CPU info (if available) ----------

(55·10¹⁵⁸+17)/9 = 6(1)₁₅₇3_<159> = 331 · C157
C157 = P51 · P106
P51 = 473827959932100290692183934041550493799062394539511_<51>
P106 = 3896471482034884541768779423085832074586818741605048169360830630153978031461284856168107994452562187584093_<106>

Number: 61113_158 N=1846257133266196710305471634776770728432359852299429338704263175562269217858341725411211816045652903658945955018462571332661967103054716347767707284323598523 ( 157 digits) SNFS difficulty: 160 digits. Divisors found: r1=473827959932100290692183934041550493799062394539511 (pp51) r2=3896471482034884541768779423085832074586818741605048169360830630153978031461284856168107994452562187584093 (pp106) Version: Msieve-1.39 Total time: 28.19 hours. Scaled time: 49.02 units (timescale=1.739). Factorization parameters were as follows: n: 1846257133266196710305471634776770728432359852299429338704263175562269217858341725411211816045652903658945955018462571332661967103054716347767707284323598523 m: 50000000000000000000000000000000 deg: 5 c5: 88 c0: 85 skew: 0.99 type: snfs lss: 1 rlim: 3300000 alim: 3300000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 3300000/3300000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1650000, 3150001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 608868 x 609116 Total sieving time: 28.19 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,3300000,3300000,27,27,51,51,2.4,2.4,100000 total time: 28.19 hours. --------- CPU info (if available) ----------

(55·10¹³⁸+17)/9 = 6(1)₁₃₇3_<139> = 59 · 1657 · 37137218441_<11> · 15147010896290711_<17> · C108
C108 = P43 · P65
P43 = 1187288381940462130868009909981206026936967_<43>
P65 = 93595104147558747071446841923837021201891200362881632886909849003_<65>

Number: 61113_118 N=111124379760904060998273023772063612247139489669364432832383286955350483631183018958061606008642952568793901 ( 108 digits) SNFS difficulty: 140 digits. Divisors found: r1=1187288381940462130868009909981206026936967 (pp43) r2=93595104147558747071446841923837021201891200362881632886909849003 (pp65) Version: Msieve-1.39 Total time: 5.36 hours. Scaled time: 13.78 units (timescale=2.571). Factorization parameters were as follows: n: 111124379760904060998273023772063612247139489669364432832383286955350483631183018958061606008642952568793901 m: 5000000000000000000000000000 deg: 5 c5: 88 c0: 85 skew: 0.99 type: snfs lss: 1 rlim: 1530000 alim: 1530000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1530000/1530000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [765000, 1665001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 239127 x 239362 Total sieving time: 5.36 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,140,5,0,0,0,0,0,0,0,0,1530000,1530000,26,26,48,48,2.3,2.3,75000 total time: 5.36 hours. --------- CPU info (if available) ----------

(55·10¹⁴⁰+17)/9 = 6(1)₁₃₉3_<141> = 61 · 89 · 30738941020813527919_<20> · C118
C118 = P44 · P75
P44 = 10615121701713873642054896444448927095209397_<44>
P75 = 344974075185369880980187433999848289501839524696372984170815766498887686079_<75>

Number: 61113_140 N=3661941792028893320771674453906461398736845292068741409358102612764247173984037287722223413240085681776284995306884363 ( 118 digits) SNFS difficulty: 141 digits. Divisors found: r1=10615121701713873642054896444448927095209397 (pp44) r2=344974075185369880980187433999848289501839524696372984170815766498887686079 (pp75) Version: Msieve-1.39 Total time: 4.88 hours. Scaled time: 12.50 units (timescale=2.560). Factorization parameters were as follows: n: 3661941792028893320771674453906461398736845292068741409358102612764247173984037287722223413240085681776284995306884363 m: 10000000000000000000000000000 deg: 5 c5: 55 c0: 17 skew: 0.79 type: snfs lss: 1 rlim: 1610000 alim: 1610000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1610000/1610000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [805000, 1605001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 248771 x 249007 Total sieving time: 4.88 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,141,5,0,0,0,0,0,0,0,0,1610000,1610000,26,26,48,48,2.3,2.3,100000 total time: 4.88 hours. --------- CPU info (if available) ----------

(55·10¹⁴³+17)/9 = 6(1)₁₄₂3_<144> = 10273 · 397115083203972041_<18> · C123
C123 = P53 · P70
P53 = 60340823343326933516766372625551502784610350942842391_<53>
P70 = 2482534413113388832724548281270442360749001612536624017335879644836551_<70>

Number: 61113_143 N=149798170465404801889673648353571477390630741370430580041195733866328662659834965071847732868899781815670187328774549033441 ( 123 digits) SNFS difficulty: 145 digits. Divisors found: r1=60340823343326933516766372625551502784610350942842391 (pp53) r2=2482534413113388832724548281270442360749001612536624017335879644836551 (pp70) Version: Msieve-1.39 Total time: 8.00 hours. Scaled time: 20.60 units (timescale=2.576). Factorization parameters were as follows: n: 149798170465404801889673648353571477390630741370430580041195733866328662659834965071847732868899781815670187328774549033441 m: 50000000000000000000000000000 deg: 5 c5: 88 c0: 85 skew: 0.99 type: snfs lss: 1 rlim: 1860000 alim: 1860000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1860000/1860000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [930000, 2230001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 318333 x 318562 Total sieving time: 8.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,1860000,1860000,26,26,49,49,2.3,2.3,100000 total time: 8.00 hours. --------- CPU info (if available) ----------

Apr 30, 2009 (4th)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / Apr 30, 2009
(53·10¹⁶⁷+1)/9 = 5(8)₁₆₆9_<168> = 7 · 31 · 5801 · 2171422861_<10> · C153
C153 = P42 · P112
P42 = 135266161385821144300657096869448610669383_<42>
P112 = 1592711769493037551738175961976900809985538358919210031942464262455167074834538118938696628704611091433213992059_<112>

Number: n N=215440007253341983299390084531258679074808434912488229449321198057364616718462923193195079761680811761040513937707338780162671744395500109087669636429597 ( 153 digits) SNFS difficulty: 170 digits. Divisors found: Thu Apr 30 12:02:04 2009 prp42 factor: 135266161385821144300657096869448610669383 Thu Apr 30 12:02:04 2009 prp112 factor: 1592711769493037551738175961976900809985538358919210031942464262455167074834538118938696628704611091433213992059 Thu Apr 30 12:02:04 2009 elapsed time 01:21:52 (Msieve 1.39 - dependency 3) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 43.70 hours. Scaled time: 116.72 units (timescale=2.671). Factorization parameters were as follows: name: KA_5_8_166_9 n: 215440007253341983299390084531258679074808434912488229449321198057364616718462923193195079761680811761040513937707338780162671744395500109087669636429597 m: 5000000000000000000000000000000000 deg: 5 c5: 212 c0: 125 skew: 0.90 type: snfs lss: 1 rlim: 4900000 alim: 4900000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4900000/4900000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2450000, 4902193) Primes: RFBsize:341992, AFBsize:341903, largePrimes:16344668 encountered Relations: rels:15617764, finalFF:725294 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1679045 hash collisions in 17282749 relations Msieve: matrix is 834325 x 834573 (223.6 MB) Total sieving time: 43.13 hours. Total relation processing time: 0.57 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,4900000,4900000,28,28,56,56,2.4,2.4,100000 total time: 43.70 hours. --------- CPU info (if available) ----------

(55·10¹⁰²+17)/9 = 6(1)₁₀₁3_<103> = 411583 · C98
C98 = P35 · P63
P35 = 32358778405965305440492935854465363_<35>
P63 = 458849891881505688703834082750529184484557904436360837193089997_<63>

Number: n N=14847821972994781395517091597833513801860405097176295209255754273405634127529832648848740378273911 ( 98 digits) SNFS difficulty: 103 digits. Divisors found: r1=32358778405965305440492935854465363 (pp35) r2=458849891881505688703834082750529184484557904436360837193089997 (pp63) Version: GGNFS-0.77.1-VC8(Wed Total time: 0.79 hours. Scaled time: 0.98 units (timescale=1.243). Factorization parameters were as follows: name: KA_6_1_101_3 n: 14847821972994781395517091597833513801860405097176295209255754273405634127529832648848740378273911 m: 100000000000000000000 deg: 5 c5:5500 c0: 17 skew: 0.18 type: snfs rlim: 400000 alim: 400000 lpbr: 26 lpba: 26 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 qintsize: 10000 Factor base limits: 400000/400000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 52/52 Sieved algebraic special-q in [200000, 260001) Primes: RFBsize:33860, AFBsize:33824, largePrimes:1890853 encountered Relations: rels:1727952, finalFF:90219 Max relations in full relation-set: 28 Initial matrix: 67751 x 90219 with sparse part having weight 7022083. Pruned matrix : 61776 x 62178 with weight 3504147. Total sieving time: 0.68 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.04 hours. Total square root time: 0.03 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,103,5,0,0,0,0,0,0,0,0,400000,400000,26,26,52,52,2.4,2.4,20000 total time: 0.79 hours. --------- CPU info (if available) ----------

(55·10¹³⁹+17)/9 = 6(1)₁₃₈3_<140> = 3 · 7 · 43 · 383833 · 144778732945720361_<18> · C115
C115 = P32 · P40 · P43
P32 = 81763899605527921358782677567481_<32>
P40 = 4069370006867177330397707858452514611997_<40>
P43 = 3660130512500783146450462819085092132451731_<43>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM] Input number is 1217826297265224073102082739938273395751150789544672150731742120357286571820237935321180590087550810674361752653167 (115 digits) Using B1=1372000, B2=1426564240, polynomial Dickson(6), sigma=3773204362 Step 1 took 13509ms Step 2 took 5117ms ********** Factor found in step 2: 81763899605527921358782677567481 Found probable prime factor of 32 digits: 81763899605527921358782677567481 Composite cofactor 14894425328790077194413442180434380837484123126965525964547625497245590385796016807 has 83 digits Thu Apr 30 19:21:58 2009 Thu Apr 30 19:21:58 2009 Thu Apr 30 19:21:58 2009 Msieve v. 1.39 Thu Apr 30 19:21:58 2009 random seeds: 891a2560 10e6359e Thu Apr 30 19:21:58 2009 factoring 14894425328790077194413442180434380837484123126965525964547625497245590385796016807 (83 digits) Thu Apr 30 19:21:58 2009 searching for 15-digit factors Thu Apr 30 19:21:59 2009 commencing quadratic sieve (83-digit input) Thu Apr 30 19:21:59 2009 using multiplier of 3 Thu Apr 30 19:21:59 2009 using 32kb Intel Core sieve core Thu Apr 30 19:21:59 2009 sieve interval: 12 blocks of size 32768 Thu Apr 30 19:21:59 2009 processing polynomials in batches of 17 Thu Apr 30 19:21:59 2009 using a sieve bound of 1355089 (52059 primes) Thu Apr 30 19:21:59 2009 using large prime bound of 124668188 (26 bits) Thu Apr 30 19:21:59 2009 using trial factoring cutoff of 27 bits Thu Apr 30 19:21:59 2009 polynomial 'A' values have 11 factors Thu Apr 30 19:39:42 2009 52241 relations (26351 full + 25890 combined from 281262 partial), need 52155 Thu Apr 30 19:39:42 2009 begin with 307613 relations Thu Apr 30 19:39:42 2009 reduce to 74928 relations in 2 passes Thu Apr 30 19:39:42 2009 attempting to read 74928 relations Thu Apr 30 19:39:43 2009 recovered 74928 relations Thu Apr 30 19:39:43 2009 recovered 68440 polynomials Thu Apr 30 19:39:43 2009 attempting to build 52241 cycles Thu Apr 30 19:39:43 2009 found 52241 cycles in 1 passes Thu Apr 30 19:39:43 2009 distribution of cycle lengths: Thu Apr 30 19:39:43 2009 length 1 : 26351 Thu Apr 30 19:39:43 2009 length 2 : 25890 Thu Apr 30 19:39:43 2009 largest cycle: 2 relations Thu Apr 30 19:39:43 2009 matrix is 52059 x 52241 (7.1 MB) with weight 1660494 (31.79/col) Thu Apr 30 19:39:43 2009 sparse part has weight 1660494 (31.79/col) Thu Apr 30 19:39:43 2009 filtering completed in 3 passes Thu Apr 30 19:39:43 2009 matrix is 38003 x 38067 (5.7 MB) with weight 1338402 (35.16/col) Thu Apr 30 19:39:43 2009 sparse part has weight 1338402 (35.16/col) Thu Apr 30 19:39:43 2009 saving the first 48 matrix rows for later Thu Apr 30 19:39:43 2009 matrix is 37955 x 38067 (3.6 MB) with weight 1010804 (26.55/col) Thu Apr 30 19:39:43 2009 sparse part has weight 719314 (18.90/col) Thu Apr 30 19:39:43 2009 matrix includes 64 packed rows Thu Apr 30 19:39:43 2009 using block size 15226 for processor cache size 6144 kB Thu Apr 30 19:39:44 2009 commencing Lanczos iteration Thu Apr 30 19:39:44 2009 memory use: 4.2 MB Thu Apr 30 19:39:47 2009 lanczos halted after 602 iterations (dim = 37953) Thu Apr 30 19:39:47 2009 recovered 17 nontrivial dependencies Thu Apr 30 19:39:47 2009 prp40 factor: 4069370006867177330397707858452514611997 Thu Apr 30 19:39:47 2009 prp43 factor: 3660130512500783146450462819085092132451731 Thu Apr 30 19:39:47 2009 elapsed time 00:17:49

Apr 30, 2009 (3rd)

By Sinkiti Sibata / Msieve / Apr 30, 2009
(55·10¹²⁰+17)/9 = 6(1)₁₁₉3_<121> = 23² · 29 · 14885411 · 4444147626799_<13> · C97
C97 = P38 · P59
P38 = 98307462555318089826526950770199792763_<38>
P59 = 61253472778706241794870926147499037925858616278305839202899_<59>

Thu Apr 30 07:44:49 2009 Msieve v. 1.41 Thu Apr 30 07:44:49 2009 random seeds: bf780874 d93eee60 Thu Apr 30 07:44:49 2009 factoring 6021673481575859773124401532919227792673004029510249607602079740999815999962637314855610908819937 (97 digits) Thu Apr 30 07:44:51 2009 searching for 15-digit factors Thu Apr 30 07:44:52 2009 commencing quadratic sieve (97-digit input) Thu Apr 30 07:44:53 2009 using multiplier of 17 Thu Apr 30 07:44:53 2009 using 32kb Intel Core sieve core Thu Apr 30 07:44:53 2009 sieve interval: 36 blocks of size 32768 Thu Apr 30 07:44:53 2009 processing polynomials in batches of 6 Thu Apr 30 07:44:53 2009 using a sieve bound of 2404033 (88123 primes) Thu Apr 30 07:44:53 2009 using large prime bound of 360604950 (28 bits) Thu Apr 30 07:44:53 2009 using double large prime bound of 2527301234494800 (43-52 bits) Thu Apr 30 07:44:53 2009 using trial factoring cutoff of 52 bits Thu Apr 30 07:44:53 2009 polynomial 'A' values have 13 factors Thu Apr 30 13:48:31 2009 88458 relations (21528 full + 66930 combined from 1321428 partial), need 88219 Thu Apr 30 13:48:35 2009 begin with 1342956 relations Thu Apr 30 13:48:36 2009 reduce to 231324 relations in 11 passes Thu Apr 30 13:48:36 2009 attempting to read 231324 relations Thu Apr 30 13:48:40 2009 recovered 231324 relations Thu Apr 30 13:48:40 2009 recovered 218564 polynomials Thu Apr 30 13:48:41 2009 attempting to build 88458 cycles Thu Apr 30 13:48:41 2009 found 88458 cycles in 6 passes Thu Apr 30 13:48:41 2009 distribution of cycle lengths: Thu Apr 30 13:48:41 2009 length 1 : 21528 Thu Apr 30 13:48:41 2009 length 2 : 15366 Thu Apr 30 13:48:41 2009 length 3 : 14830 Thu Apr 30 13:48:41 2009 length 4 : 12274 Thu Apr 30 13:48:41 2009 length 5 : 8982 Thu Apr 30 13:48:41 2009 length 6 : 6220 Thu Apr 30 13:48:41 2009 length 7 : 3944 Thu Apr 30 13:48:41 2009 length 9+: 5314 Thu Apr 30 13:48:41 2009 largest cycle: 22 relations Thu Apr 30 13:48:41 2009 matrix is 88123 x 88458 (23.7 MB) with weight 5867152 (66.33/col) Thu Apr 30 13:48:41 2009 sparse part has weight 5867152 (66.33/col) Thu Apr 30 13:48:43 2009 filtering completed in 3 passes Thu Apr 30 13:48:43 2009 matrix is 84104 x 84167 (22.7 MB) with weight 5602479 (66.56/col) Thu Apr 30 13:48:43 2009 sparse part has weight 5602479 (66.56/col) Thu Apr 30 13:48:43 2009 saving the first 48 matrix rows for later Thu Apr 30 13:48:43 2009 matrix is 84056 x 84167 (13.7 MB) with weight 4362940 (51.84/col) Thu Apr 30 13:48:43 2009 sparse part has weight 3088177 (36.69/col) Thu Apr 30 13:48:43 2009 matrix includes 64 packed rows Thu Apr 30 13:48:43 2009 using block size 33666 for processor cache size 1024 kB Thu Apr 30 13:48:44 2009 commencing Lanczos iteration Thu Apr 30 13:48:44 2009 memory use: 13.5 MB Thu Apr 30 13:49:34 2009 lanczos halted after 1331 iterations (dim = 84054) Thu Apr 30 13:49:34 2009 recovered 17 nontrivial dependencies Thu Apr 30 13:49:35 2009 prp38 factor: 98307462555318089826526950770199792763 Thu Apr 30 13:49:35 2009 prp59 factor: 61253472778706241794870926147499037925858616278305839202899 Thu Apr 30 13:49:35 2009 elapsed time 06:04:46

(55·10¹³⁵+17)/9 = 6(1)₁₃₄3_<136> = 19 · 3638454243911_<13> · 342126911555309500721535304267_<30> · C93
C93 = P47 · P47
P47 = 13042718211587829831766097413915690329339148483_<47>
P47 = 19810448732557328228341823177874542870780022037_<47>

Thu Apr 30 14:57:37 2009 Msieve v. 1.41 Thu Apr 30 14:57:37 2009 random seeds: 9171f740 959a443a Thu Apr 30 14:57:37 2009 factoring 258382100463852506230968335487805430257100969220134618900431126539928243525631289673555119871 (93 digits) Thu Apr 30 14:57:37 2009 searching for 15-digit factors Thu Apr 30 14:57:39 2009 commencing quadratic sieve (93-digit input) Thu Apr 30 14:57:39 2009 using multiplier of 1 Thu Apr 30 14:57:39 2009 using 32kb Intel Core sieve core Thu Apr 30 14:57:39 2009 sieve interval: 36 blocks of size 32768 Thu Apr 30 14:57:39 2009 processing polynomials in batches of 6 Thu Apr 30 14:57:39 2009 using a sieve bound of 1889131 (70449 primes) Thu Apr 30 14:57:39 2009 using large prime bound of 221028327 (27 bits) Thu Apr 30 14:57:39 2009 using double large prime bound of 1047143580966873 (42-50 bits) Thu Apr 30 14:57:39 2009 using trial factoring cutoff of 50 bits Thu Apr 30 14:57:39 2009 polynomial 'A' values have 12 factors Thu Apr 30 16:54:56 2009 70670 relations (18405 full + 52265 combined from 916226 partial), need 70545 Thu Apr 30 16:54:57 2009 begin with 934631 relations Thu Apr 30 16:54:58 2009 reduce to 177805 relations in 13 passes Thu Apr 30 16:54:58 2009 attempting to read 177805 relations Thu Apr 30 16:55:00 2009 recovered 177805 relations Thu Apr 30 16:55:00 2009 recovered 156794 polynomials Thu Apr 30 16:55:01 2009 attempting to build 70670 cycles Thu Apr 30 16:55:01 2009 found 70670 cycles in 6 passes Thu Apr 30 16:55:01 2009 distribution of cycle lengths: Thu Apr 30 16:55:01 2009 length 1 : 18405 Thu Apr 30 16:55:01 2009 length 2 : 13040 Thu Apr 30 16:55:01 2009 length 3 : 12090 Thu Apr 30 16:55:01 2009 length 4 : 9445 Thu Apr 30 16:55:01 2009 length 5 : 6860 Thu Apr 30 16:55:01 2009 length 6 : 4372 Thu Apr 30 16:55:01 2009 length 7 : 2799 Thu Apr 30 16:55:01 2009 length 9+: 3659 Thu Apr 30 16:55:01 2009 largest cycle: 18 relations Thu Apr 30 16:55:01 2009 matrix is 70449 x 70670 (17.6 MB) with weight 4333606 (61.32/col) Thu Apr 30 16:55:01 2009 sparse part has weight 4333606 (61.32/col) Thu Apr 30 16:55:02 2009 filtering completed in 3 passes Thu Apr 30 16:55:02 2009 matrix is 66349 x 66413 (16.7 MB) with weight 4101622 (61.76/col) Thu Apr 30 16:55:02 2009 sparse part has weight 4101622 (61.76/col) Thu Apr 30 16:55:02 2009 saving the first 48 matrix rows for later Thu Apr 30 16:55:02 2009 matrix is 66301 x 66413 (10.0 MB) with weight 3166149 (47.67/col) Thu Apr 30 16:55:02 2009 sparse part has weight 2210961 (33.29/col) Thu Apr 30 16:55:02 2009 matrix includes 64 packed rows Thu Apr 30 16:55:02 2009 using block size 26565 for processor cache size 1024 kB Thu Apr 30 16:55:03 2009 commencing Lanczos iteration Thu Apr 30 16:55:03 2009 memory use: 10.0 MB Thu Apr 30 16:55:30 2009 lanczos halted after 1050 iterations (dim = 66297) Thu Apr 30 16:55:30 2009 recovered 15 nontrivial dependencies Thu Apr 30 16:55:31 2009 prp47 factor: 13042718211587829831766097413915690329339148483 Thu Apr 30 16:55:31 2009 prp47 factor: 19810448732557328228341823177874542870780022037 Thu Apr 30 16:55:31 2009 elapsed time 01:57:54

(55·10¹⁵⁰+17)/9 = 6(1)₁₄₉3_<151> = 19690979640099324919_<20> · 860104955775585341543623128989_<30> · C102
C102 = P43 · P59
P43 = 8420887143370657565490007495995287668142801_<43>
P59 = 42849283068676424463551912087229682013357069256594047052443_<59>

Number: 61113_150 N=360828976895667299737562769774660717483559074368529041201510988550692299042274113620704153686059912843 ( 102 digits) Divisors found: r1=8420887143370657565490007495995287668142801 (pp43) r2=42849283068676424463551912087229682013357069256594047052443 (pp59) Version: Msieve-1.40 Total time: 4.78 hours. Scaled time: 12.22 units (timescale=2.554). Factorization parameters were as follows: name: 61113_150 # Murphy_E = 3.043745e-09, selected by Jeff Gilchrist n: 360828976895667299737562769774660717483559074368529041201510988550692299042274113620704153686059912843 Y0: -44113535318694843826 Y1: 24303255677 c0: 465157296557827797222705 c1: 268644217472380387089 c2: 16241102223304477 c3: -1397388248401 c4: -105304494 c5: 2160 skew: 16337.53 type: gnfs # selected mechanically rlim: 1670000 alim: 1670000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.4 alambda: 2.4 Factor base limits: 1670000/1670000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [835000, 1435001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 220727 x 220975 Total sieving time: 4.78 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,101,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1670000,1670000,26,26,48,48,2.4,2.4,100000 total time: 4.78 hours. --------- CPU info (if available) ----------

Apr 30, 2009 (2nd)

By Serge Batalov / GMP-ECM 6.2.2 / Apr 30, 2009
(55·10¹⁵¹+17)/9 = 6(1)₁₅₀3_<152> = 3 · 7 · 83 · 1429 · 2417 · C143
C143 = P31 · P112
P31 = 3308092725448856055133083186613_<31>
P112 = 3068571445944642173555566328749439194505144924727462058149060519333716290496346376102747785291468715529594477999_<112>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1070043456 Step 1 took 7665ms Step 2 took 8164ms ********** Factor found in step 2: 3308092725448856055133083186613 Found probable prime factor of 31 digits: 3308092725448856055133083186613 Probable prime cofactor has 112 digits

(55·10¹¹⁹+17)/9 = 6(1)₁₁₈3_<120> = C120
C120 = P31 · C90
P31 = 1619798646167707926668253111679_<31>
C90 = [377275973502597272706476705893861400303860757026705314272481031102839141493245455438961847_<90>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=905747387 Step 1 took 6385ms Step 2 took 7264ms ********** Factor found in step 2: 1619798646167707926668253111679 Found probable prime factor of 31 digits: 1619798646167707926668253111679 Composite cofactor has 90 digits

Apr 30, 2009

By Markus Tervooren / Ggnfs (64bit/asm). msieve 1.41 for postprocessing / Apr 30, 2009
(5·10¹⁹⁰+31)/9 = (5)₁₈₉9_<190> = 3² · 19 · 1289 · C185
C185 = P63 · P122
P63 = 596490706585371570344324760800537294958709584946084830273397247_<63>
P122 = 42254676923334035495094749677381553294665771130138374934168106601251727561083274480199497819607561303592623938582818320563_<122>

Msieve v. 1.41 Wed Apr 29 14:52:14 2009 random seeds: edf8ec04 782fc9ce factoring 25204522094536113291302272288484910808757664065055896068649052738446121049254172986700581871597074460711443004258051962650930979432605880416640832031519767150543081837570969633087690061 (185 digits) searching for 15-digit factors commencing number field sieve (185-digit input) R0: -100000000000000000000000000000000000000 R1: 1 A0: 31 A1: 0 A2: 0 A3: 0 A4: 0 A5: 5 skew 1.44, size 3.598405e-13, alpha 1.058678, combined = 4.358459e-11 commencing relation filtering commencing duplicate removal, pass 1 found 2765388 hash collisions in 21909200 relations added 2008 free relations commencing duplicate removal, pass 2 found 2395885 duplicates and 19515323 unique relations memory use: 98.6 MB reading rational ideals above 10551296 reading algebraic ideals above 10551296 commencing singleton removal, pass 1 relations with 0 large ideals: 276562 relations with 1 large ideals: 1803867 relations with 2 large ideals: 5315527 relations with 3 large ideals: 7329666 relations with 4 large ideals: 4050810 relations with 5 large ideals: 56111 relations with 6 large ideals: 682780 relations with 7+ large ideals: 0 19515323 relations and about 18790045 large ideals commencing singleton removal, pass 2 found 6777251 singletons current dataset: 12738072 relations and about 10470759 large ideals commencing singleton removal, pass 3 found 1852958 singletons current dataset: 10885114 relations and about 8502586 large ideals commencing singleton removal, pass 4 found 526086 singletons current dataset: 10359028 relations and about 7965610 large ideals commencing singleton removal, pass 5 found 160949 singletons current dataset: 10198079 relations and about 7803602 large ideals commencing singleton removal, final pass memory use: 176.4 MB commencing in-memory singleton removal begin with 10198079 relations and 8686922 unique ideals reduce to 8126643 relations and 6547174 ideals in 20 passes max relations containing the same ideal: 52 reading rational ideals above 720000 reading algebraic ideals above 720000 commencing singleton removal, final pass keeping 7164674 ideals with weight <= 20, new excess is 791838 memory use: 250.5 MB commencing in-memory singleton removal begin with 8128654 relations and 7164674 unique ideals reduce to 8125274 relations and 7151386 ideals in 9 passes max relations containing the same ideal: 20 removing 402438 relations and 374760 ideals in 27678 cliques commencing in-memory singleton removal begin with 7722836 relations and 7151386 unique ideals reduce to 7706040 relations and 6759735 ideals in 8 passes max relations containing the same ideal: 20 removing 289505 relations and 261827 ideals in 27678 cliques commencing in-memory singleton removal begin with 7416535 relations and 6759735 unique ideals reduce to 7407787 relations and 6489121 ideals in 8 passes max relations containing the same ideal: 20 relations with 0 large ideals: 63990 relations with 1 large ideals: 431150 relations with 2 large ideals: 1396533 relations with 3 large ideals: 2324416 relations with 4 large ideals: 2038853 relations with 5 large ideals: 878401 relations with 6 large ideals: 252051 relations with 7+ large ideals: 22393 commencing 2-way merge reduce to 4358946 relation sets and 3440280 unique ideals commencing full merge memory use: 311.5 MB found 2107420 cycles, need 1990480 weight of 1990480 cycles is about 139461325 (70.06/cycle) distribution of cycle lengths: 1 relations: 259851 2 relations: 243805 3 relations: 238556 4 relations: 210119 5 relations: 188648 6 relations: 157800 7 relations: 135361 8 relations: 114188 9 relations: 95544 10+ relations: 346608 heaviest cycle: 20 relations commencing cycle optimization start with 11200236 relations pruned 262711 relations memory use: 383.6 MB distribution of cycle lengths: 1 relations: 259851 2 relations: 249376 3 relations: 247493 4 relations: 215226 5 relations: 192636 6 relations: 159411 7 relations: 136102 8 relations: 113416 9 relations: 94468 10+ relations: 322501 heaviest cycle: 20 relations RelProcTime: 875 commencing linear algebra read 1990480 cycles cycles contain 6522097 unique relations read 6522097 relations using 20 quadratic characters above 268435034 building initial matrix memory use: 797.2 MB read 1990480 cycles matrix is 1989699 x 1990480 (596.7 MB) with weight 176041428 (88.44/col) sparse part has weight 134521867 (67.58/col) filtering completed in 3 passes matrix is 1962834 x 1963034 (591.7 MB) with weight 174425357 (88.85/col) sparse part has weight 133519598 (68.02/col) read 1963034 cycles matrix is 1962834 x 1963034 (591.7 MB) with weight 174425357 (88.85/col) sparse part has weight 133519598 (68.02/col) saving the first 48 matrix rows for later matrix is 1962786 x 1963034 (560.2 MB) with weight 138173302 (70.39/col) sparse part has weight 127216851 (64.81/col) matrix includes 64 packed rows using block size 65536 for processor cache size 4096 kB commencing Lanczos iteration (4 threads) memory use: 585.2 MB linear algebra completed 1962681 of 1963034 dimensions (100.0%, ETA 0h 0m) lanczos halted after 31043 iterations (dim = 1962785) recovered 35 nontrivial dependencies BLanczosTime: 18268 commencing square root phase reading relations for dependency 1 read 981558 cycles cycles contain 3931062 unique relations read 3931062 relations multiplying 3243788 relations multiply complete, coefficients have about 84.11 million bits initial square root is modulo 1090381 reading relations for dependency 2 read 982286 cycles cycles contain 3935792 unique relations read 3935792 relations multiplying 3247420 relations multiply complete, coefficients have about 84.21 million bits initial square root is modulo 1107721 sqrtTime: 1133 prp63 factor: 596490706585371570344324760800537294958709584946084830273397247 prp122 factor: 42254676923334035495094749677381553294665771130138374934168106601251727561083274480199497819607561303592623938582818320563 elapsed time 05:38:12 Sieving took ~ 151hours on one core (Q6700@3.3Ghz)

(55·10¹⁰⁵+17)/9 = 6(1)₁₀₄3_<106> = 683 · 1445241877_<10> · C94
C94 = P38 · P56
P38 = 81029967971957752955713055836047647693_<38>
P56 = 76403503205391551231527775810749279533656827067863897451_<56>

Number: k1 N=6190973417678248911826496973321001897506450037367806314609001941975686201499624743187528730543 ( 94 digits) SNFS difficulty: 107 digits. Divisors found: r1=81029967971957752955713055836047647693 (pp38) r2=76403503205391551231527775810749279533656827067863897451 (pp56) Version: Msieve-1.39 Total time: 0.20 hours. Scaled time: 0.50 units (timescale=2.472). Factorization parameters were as follows: n: 6190973417678248911826496973321001897506450037367806314609001941975686201499624743187528730543 m: 200000000000000000000000000 deg: 4 c4: 275 c0: 136 skew: 0.84 type: snfs lss: 1 rlim: 440000 alim: 440000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 Factor base limits: 440000/440000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [220000, 300001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 38956 x 39183 Total sieving time: 0.19 hours. Total relation processing time: 0.01 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,107,4,0,0,0,0,0,0,0,0,440000,440000,25,25,44,44,2.2,2.2,40000 total time: 0.20 hours. --------- CPU info (if available) ---------- [ 0.140008] CPU0: Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b [ 0.232014] CPU1: Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b [ 0.327367] CPU2: Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b [ 0.424240] CPU3: Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b [ 0.004000] Memory: 8198000k/10485760k available (2226k kernel code, 189836k reserved, 1082k data, 392k init) [ 0.083992] Calibrating delay using timer specific routine.. 6404.32 BogoMIPS (lpj=12808640) [ 0.152009] Calibrating delay using timer specific routine.. 6400.07 BogoMIPS (lpj=12800150) [ 0.244015] Calibrating delay using timer specific routine.. 6400.09 BogoMIPS (lpj=12800199) [ 0.343793] Calibrating delay using timer specific routine.. 6400.09 BogoMIPS (lpj=12800187) [ 0.428765] Total of 4 processors activated (25604.58 BogoMIPS).

Apr 29, 2009 (5th)

By Robert Backstrom / GGNFS, Msieve / Apr 29, 2009
(53·10¹⁷⁰+1)/9 = 5(8)₁₆₉9_<171> = 1559 · 2903 · 370723 · 33658580232709090033_<20> · 67871489825328151030318753_<26> · C114
C114 = P50 · P64
P50 = 15878422731457635314161599067107119872220986892417_<50>
P64 = 9676095432618857994298840083734799477765342988159463785324899923_<64>

Number: n N=153641133669048676609099915708201614219856303269170854973086875495889780066889209852193311327532571098675292583891 ( 114 digits) Divisors found: Wed Apr 29 23:25:18 2009 prp50 factor: 15878422731457635314161599067107119872220986892417 Wed Apr 29 23:25:18 2009 prp64 factor: 9676095432618857994298840083734799477765342988159463785324899923 Wed Apr 29 23:25:18 2009 elapsed time 00:59:50 (Msieve 1.39 - dependency 3) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 18.46 hours. Scaled time: 49.31 units (timescale=2.671). Factorization parameters were as follows: name: KA_5_8_169_9 n: 153641133669048676609099915708201614219856303269170854973086875495889780066889209852193311327532571098675292583891 Y0: -8973732757865968818489 Y1: 1655113373459 c0: 6530038059463148739514985720 c1: -505049272014818434778864 c2: -6938797053941142849 c3: 242228848255076 c4: 1249680886 c5: 2640 skew: 50592.33 type: gnfs rlim: 3500000 alim: 3500080 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 3500000/3500080 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [1750040, 2600177) Primes: RFBsize:250150, AFBsize:249214, largePrimes:16960803 encountered Relations: rels:14902027, finalFF:531448 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 952641 hash collisions in 15494590 relations Msieve: matrix is 583643 x 583891 (164.2 MB) Total sieving time: 17.90 hours. Total relation processing time: 0.57 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500080,28,28,56,56,2.6,2.6,100000 total time: 18.46 hours. --------- CPU info (if available) ----------

Apr 29, 2009 (4th)

By Ignacio Santos / GGNFS, Msieve / Apr 29, 2009
(32·10¹⁸¹+13)/9 = 3(5)₁₈₀7_<182> = 23² · 37 · 97 · C176
C176 = P66 · P110
P66 = 187800281843242246319283489339418659405151754020076889041478011149_<66>
P110 = 99719960730962349469939681299619260059373306342828270295826680925337086911707248717062806086045272017174413653_<110>

Number: 35557_181 N=18727436730671778320522303528559253229414786914835635432755071053358037163310680742910392316975444058249585114122365890923566366436594254106385535068325004598463565976671817297 ( 176 digits) SNFS difficulty: 182 digits. Divisors found: r1=187800281843242246319283489339418659405151754020076889041478011149 (pp66) r2=99719960730962349469939681299619260059373306342828270295826680925337086911707248717062806086045272017174413653 (pp110) Version: Msieve-1.39 Total time: 137.88 hours. Scaled time: 239.22 units (timescale=1.735). Factorization parameters were as follows: n: 18727436730671778320522303528559253229414786914835635432755071053358037163310680742910392316975444058249585114122365890923566366436594254106385535068325004598463565976671817297 m: 2000000000000000000000000000000000000 deg: 5 c5: 10 c0: 13 skew: 1.05 type: snfs lss: 1 rlim: 7700000 alim: 7700000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 7700000/7700000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3850000, 6150001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1475073 x 1475319 Total sieving time: 137.88 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,182,5,0,0,0,0,0,0,0,0,7700000,7700000,28,28,53,53,2.5,2.5,100000 total time: 137.88 hours. --------- CPU info (if available) ----------

(38·10¹⁷⁰+43)/9 = 4(2)₁₆₉7_<171> = 7 · 17 · 2895407 · 52481041 · C155
C155 = P51 · P105
P51 = 159420766227975595294803856574498124726059142719287_<51>
P105 = 146466118542925818385076619853708085471450289535066254778571014685940595834245664133461216599012397408957_<105>

Number: 42227_170 N=23349740844550738413468620796920875678681831018675493539509566502420110283104445553529638281716803731915120107180379989058300534100274710632172829990453659 ( 155 digits) SNFS difficulty: 171 digits. Divisors found: r1=159420766227975595294803856574498124726059142719287 (pp51) r2=146466118542925818385076619853708085471450289535066254778571014685940595834245664133461216599012397408957 (pp105) Version: Msieve-1.39 Total time: 72.39 hours. Scaled time: 185.32 units (timescale=2.560). Factorization parameters were as follows: n: 23349740844550738413468620796920875678681831018675493539509566502420110283104445553529638281716803731915120107180379989058300534100274710632172829990453659 m: 10000000000000000000000000000000000 deg: 5 c5: 38 c0: 43 skew: 1.03 type: snfs lss: 1 rlim: 5100000 alim: 5100000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4Factor base limits: 5100000/5100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2550000, 6150001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1013018 x 1013266 Total sieving time: 72.39 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,5100000,5100000,27,27,52,52,2.4,2.4,100000 total time: 72.39 hours. --------- CPU info (if available) ----------

Apr 29, 2009 (3rd)

By Wataru Sakai / GMP-ECM 6.2.1 / Apr 29, 2009
6·10²⁰²+1 = 6(0)₂₀₁1_<203> = 113761 · 244393 · 660429923798209_<15> · 135180804513951511904761_<24> · 5164634473621039289825138497_<28> · C127
C127 = P40 · P88
P40 = 1664792180982452240067957261454638056603_<40>
P88 = 2811432753405739343413857814027793980466733704390188713337746638191403396481943299125843_<88>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2090088941 Step 1 took 39950ms Step 2 took 13878ms ********** Factor found in step 2: 1664792180982452240067957261454638056603 Found probable prime factor of 40 digits: 1664792180982452240067957261454638056603 Probable prime cofactor 2811432753405739343413857814027793980466733704390188713337746638191403396481943299125843 has 88 digits

Apr 29, 2009 (2nd)

By matsui / GGNFS / Apr 29, 2009
6·10¹⁷³-7 = 5(9)₁₇₂3_<174> = 13413022373_<11> · C164
C164 = P63 · P102
P63 = 254106107960663411887642298189807618950496854389331792179242251_<63>
P102 = 176039244907150995933870857374771574815002400239328663586454894500763717483116064141859499252833070191_<102>

N=44732647371690177676556686975116849751041565641321994088050866177437636038751129875566338175972264890219757780761885559854944409552577729082119380134429900275839941 ( 164 digits) SNFS difficulty: 175 digits. Divisors found: r1=254106107960663411887642298189807618950496854389331792179242251 (pp63) r2=176039244907150995933870857374771574815002400239328663586454894500763717483116064141859499252833070191 (pp102) Version: GGNFS-0.77.1-20060722-nocona

Apr 29, 2009

Factorizations of 611...113 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Apr 28, 2009 (4th)

By Robert Backstrom / GMP-ECM / Apr 28, 2009
(17·10¹⁹⁵-11)/3 = 5(6)₁₉₄3_<196> = 7² · C195
C195 = P30 · P31 · P135
P30 = 414958074700194542917848678779_<30>
P31 = 2262764706204964092765220058089_<31>
P135 = 123165186981656208756429892828244296154398570791072162187495203445595219090684605813054472085211731050735511770532990502679306295915277_<135>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 115646258503401360544217687074829931972789115646258503401360544217687074829931972789115646258503401360544217687074829931972789115646258503401360544217687074829931972789115646258503401360544217687 (195 digits) Using B1=256000, B2=128992510, polynomial Dickson(3), sigma=2791982785 Step 1 took 4578ms Step 2 took 1922ms ********** Factor found in step 2: 414958074700194542917848678779 Found probable prime factor of 30 digits: 414958074700194542917848678779 Composite cofactor 278693838135226779409771569075683326071205809800631128168413521983821959681026143781812575882484316995296990661338781612806612800609366574896864133131995689362525653 has 165 digits GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 278693838135226779409771569075683326071205809800631128168413521983821959681026143781812575882484316995296990661338781612806612800609366574896864133131995689362525653 (165 digits) Using B1=582000, B2=522330282, polynomial Dickson(3), sigma=2912169454 Step 1 took 8203ms Step 2 took 3687ms ********** Factor found in step 2: 2262764706204964092765220058089 Found probable prime factor of 31 digits: 2262764706204964092765220058089 Probable prime cofactor 123165186981656208756429892828244296154398570791072162187495203445595219090684605813054472085211731050735511770532990502679306295915277 has 135 digits

Apr 28, 2009 (3rd)

By Ignacio Santos / GGNFS, Msieve / Apr 28, 2009
(37·10¹⁹⁴+71)/9 = 4(1)₁₉₃9_<195> = 116269 · 575551 · 474471463 · 16349135082988589810249_<23> · 7590690876337436335686621759791_<31> · C123
C123 = P50 · P73
P50 = 12689133514263467130577716351690146927441657627153_<50>
P73 = 8222299893729791483441854911572970421842011419673633184844616755425556501_<73>

Number: 41119_194 N=104333861145851641332524267483514811395721107982807617312384858364100696592011759800416745004248697924636939449966193271653 ( 123 digits) Divisors found: r1=12689133514263467130577716351690146927441657627153 (pp50) r2=8222299893729791483441854911572970421842011419673633184844616755425556501 (pp73) Version: Msieve-1.39 Total time: 52.43 hours. Scaled time: 134.81 units (timescale=2.571). Factorization parameters were as follows: # Murphy_E = 2.261027e-10, selected by Jeff Gilchrist n: 104333861145851641332524267483514811395721107982807617312384858364100696592011759800416745004248697924636939449966193271653 Y0: -358902855847175299483599 Y1: 12722330017853 c0: -67487540322810138587241212720 c1: -1928877254811875151103060 c2: 9917690775179473736 c3: -365384477507579 c4: 7519778430 c5: 17520 skew: 108467.52 type: gnfs # selected mechanically rlim: 6000000 alim: 6000000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved algebraic special-q in [3000000, 5460001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 872357 x 872605 Total sieving time: 52.43 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,122,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,6000000,6000000,27,27,52,52,2.5,2.5,60000 total time: 52.43 hours. --------- CPU info (if available) ----------

Apr 28, 2009 (2nd)

By Sinkiti Sibata / Msieve / Apr 28, 2009
(53·10¹⁵¹+1)/9 = 5(8)₁₅₀9_<152> = C152
C152 = P41 · P112
P41 = 11005133755709399739846139646663420523079_<41>
P112 = 5351037997001869599349449652602850650625326819936478162439626755570976783012160572839424777050332270827075435391_<112>

Number: 58889_151 N=58888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889 ( 152 digits) SNFS difficulty: 153 digits. Divisors found: r1=11005133755709399739846139646663420523079 (pp41) r2=5351037997001869599349449652602850650625326819936478162439626755570976783012160572839424777050332270827075435391 (pp112) Version: Msieve-1.40 Total time: 17.28 hours. Scaled time: 44.13 units (timescale=2.554). Factorization parameters were as follows: name: 58889_151 n: 58888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889 m: 2000000000000000000000000000000 deg: 5 c5: 265 c0: 16 skew: 0.57 type: snfs lss: 1 rlim: 2600000 alim: 2600000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2600000/2600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1300000, 2100001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 417672 x 417920 Total sieving time: 17.28 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,153.000,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000 total time: 17.28 hours. --------- CPU info (if available) ----------

Apr 28, 2009

By Erik Branger / GGNFS, Msieve / Apr 28, 2009
(53·10¹⁵⁹+1)/9 = 5(8)₁₅₈9_<160> = 3² · 13 · 47 · 61 · 543172787 · 146740646009623_<15> · C132
C132 = P35 · P98
P35 = 10377904187206720222921982134102753_<35>
P98 = 21223730306600451520506577284963975239844497432815229537295512873899546101677447590414810139556667_<98>

Number: 58889_159 N=220257839617014993830972198331986848532988764441820703907772064964369436808103896076625018003186857576871201553751260640857244204251 ( 132 digits) SNFS difficulty: 161 digits. Divisors found: r1=10377904187206720222921982134102753 r2=21223730306600451520506577284963975239844497432815229537295512873899546101677447590414810139556667 Version: Total time: 35.62 hours. Scaled time: 13.04 units (timescale=0.366). Factorization parameters were as follows: n: 220257839617014993830972198331986848532988764441820703907772064964369436808103896076625018003186857576871201553751260640857244204251 m: 100000000000000000000000000000000 deg: 5 c5: 53 c0: 10 skew: 0.72 type: snfs lss: 1 rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1750000, 2950001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 552981 x 553229 Total sieving time: 35.62 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,51,51,2.4,2.4,100000 total time: 35.62 hours. --------- CPU info (if available) ----------

(53·10¹⁵⁸+1)/9 = 5(8)₁₅₇9_<159> = 17 · 89803869709_<11> · C147
C147 = P44 · P104
P44 = 19946527811963839934482153629736138114375201_<44>
P104 = 19338468652164063844346333500613745540736302026055121157305398505959820677361605766269700887682845416813_<104>

Number: 58889_158 N=385735302811181373164720709392959043285994687825358692003531655890684490008848014445034506438029630727378434344317104001017539262422756993915654413 ( 147 digits) SNFS difficulty: 161 digits. Divisors found: r1=19946527811963839934482153629736138114375201 r2=19338468652164063844346333500613745540736302026055121157305398505959820677361605766269700887682845416813 Version: Total time: 49.58 hours. Scaled time: 38.92 units (timescale=0.785). Factorization parameters were as follows: n: 385735302811181373164720709392959043285994687825358692003531655890684490008848014445034506438029630727378434344317104001017539262422756993915654413 m: 100000000000000000000000000000000 deg: 5 c5: 53 c0: 100 skew: 1.14 type: snfs lss: 1 rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1750000, 3150001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 652164 x 652412 Total sieving time: 49.58 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,51,51,2.4,2.4,100000 total time: 49.58 hours. --------- CPU info (if available) ----------

Apr 27, 2009 (7th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Apr 27, 2009
(8·10¹⁹⁶+1)/9 = (8)₁₉₅9_<196> = 3 · 1049 · 19963 · 41551177 · 17551912671521_<14> · C168
C168 = P84 · P84
P84 = 421129308634456116834768473972139562323863312499765456942425930345152305882854016787_<84>
P84 = 460682463707263415511160506455196986916514178796229063957358489523887114186474351731_<84>

Number: 88889_196 N=194006887441057763765515995169149538695667950334540943575287725969382691109491784798555200805367453309820823386266387230890825153146947270793405098814003126465216508297 ( 168 digits) SNFS difficulty: 197 digits. Divisors found: r1=421129308634456116834768473972139562323863312499765456942425930345152305882854016787 r2=460682463707263415511160506455196986916514178796229063957358489523887114186474351731 Version: Total time: 229.06 hours. Scaled time: 547.23 units (timescale=2.389). Factorization parameters were as follows: n: 194006887441057763765515995169149538695667950334540943575287725969382691109491784798555200805367453309820823386266387230890825153146947270793405098814003126465216508297 m: 2000000000000000000000000000000000000000 deg: 5 c5: 5 c0: 2 skew: 0.83 type: snfs lss: 1 rlim: 14000000 alim: 14000000 lpbr: 29 lpba: 29 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5 Factor base limits: 14000000/14000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 55/55 Sieved rational special-q in [7000000, 12300001) Primes: rational ideals reading, algebraic ideals reading, Relations: 33667751 Max relations in full relation-set: Initial matrix: Pruned matrix : 2463371 x 2463619 Total sieving time: 202.13 hours. Total relation processing time: 9.13 hours. Matrix solve time: 17.44 hours. Time per square root: 0.36 hours. Prototype def-par.txt line would be: snfs,197,5,0,0,0,0,0,0,0,0,14000000,14000000,29,29,55,55,2.5,2.5,100000 total time: 229.06 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673787) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672338) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)

Apr 27, 2009 (6th)

By Ignacio Santos / GGNFS, Msieve / Apr 27, 2009
(53·10¹⁵³-17)/9 = 5(8)₁₅₂7_<154> = 7³ · 523 · 23831 · 229108109084325281_<18> · C127
C127 = P37 · P91
P37 = 1259429971180200006189700716076596071_<37>
P91 = 4773982244934065198215618554300837516932709210804279640544817629668719303310081359797913443_<91>

Number: 58887_153 N=6012496321152096259587445596313959195882890027045872444206377914501626152518858072335323398759172848423407980293982711731882453 ( 127 digits) SNFS difficulty: 156 digits. Divisors found: r1=1259429971180200006189700716076596071 (pp37) r2=4773982244934065198215618554300837516932709210804279640544817629668719303310081359797913443 (pp91) Version: Msieve-1.39 Total time: 22.23 hours. Scaled time: 57.14 units (timescale=2.571). Factorization parameters were as follows: n: 6012496321152096259587445596313959195882890027045872444206377914501626152518858072335323398759172848423407980293982711731882453 m: 5000000000000000000000000000000 deg: 5 c5: 424 c0: -425 skew: 1.00 type: snfs lss: 1 rlim: 2800000 alim: 2800000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1400000, 2600001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 520131 x 520379 Total sieving time: 22.23 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000 total time: 22.23 hours. --------- CPU info (if available) ----------

(53·10¹⁵⁴+1)/9 = 5(8)₁₅₃9_<155> = 37971697959006556067063120880293_<32> · C124
C124 = P56 · P68
P56 = 26750290160545884056238066771927664782732542089391686301_<56>
P68 = 57975545719181940975342922884870737353678736928569607670017493537673_<68>

Number: 58889_154 N=1550862670204110724982219118634479678512243171560765368957625011087319684805930920674488261437103400564207360267959541517573 ( 124 digits) SNFS difficulty: 156 digits. Divisors found: r1=26750290160545884056238066771927664782732542089391686301 (pp56) r2=57975545719181940975342922884870737353678736928569607670017493537673 (pp68) Version: Msieve-1.39 Total time: 15.78 hours. Scaled time: 27.44 units (timescale=1.739). Factorization parameters were as follows: n: 1550862670204110724982219118634479678512243171560765368957625011087319684805930920674488261437103400564207360267959541517573 m: 10000000000000000000000000000000 deg: 5 c5: 53 c0: 10 skew: 0.72 type: snfs lss: 1 rlim: 2900000 alim: 2900000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2900000/2900000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1450000, 2350001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 450588 x 450836 Total sieving time: 15.78 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,2900000,2900000,27,27,50,50,2.4,2.4,100000 total time: 15.78 hours. --------- CPU info (if available) ----------

(53·10¹⁶⁹-17)/9 = 5(8)₁₆₈7_<170> = 3 · 10289 · C166
C166 = P53 · P114
P53 = 10349469969241347631837446124602660629190655792332907_<53>
P114 = 184340529031864544303987400282044404412493423618646133662587944074027945204887635621848468895056963952913120131623_<114>

Number: 58887_169 N=1907826769329344895483490099099001810635594288038646090934943107165869339064012987620724038257326234777882168299118440045643855537917157122133310295425175394074218061 ( 166 digits) SNFS difficulty: 171 digits. Divisors found: r1=10349469969241347631837446124602660629190655792332907 (pp53) r2=184340529031864544303987400282044404412493423618646133662587944074027945204887635621848468895056963952913120131623 (pp114) Version: Msieve-1.39 Total time: 72.50 hours. Scaled time: 186.41 units (timescale=2.571). Factorization parameters were as follows: n: 1907826769329344895483490099099001810635594288038646090934943107165869339064012987620724038257326234777882168299118440045643855537917157122133310295425175394074218061 m: 10000000000000000000000000000000000 deg: 5 c5: 53 c0: -170 skew: 1.26 type: snfs lss: 1 rlim: 5100000 alim: 5100000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 5100000/5100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2550000, 6150001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1038042 x 1038289 Total sieving time: 72.50 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,5100000,5100000,27,27,52,52,2.4,2.4,100000 total time: 72.50 hours. --------- CPU info (if available) ----------

Apr 27, 2009 (5th)

By Wataru Sakai / GMP-ECM 6.2.1, Msieve / Apr 27, 2009
(10²¹²-7)/3 = (3)₂₁₁1_<212> = 31 · 1093 · 100741 · 10606483 · 31419071 · 50412367 · 160369474887919636204031018406084819503_<39> · C142
C142 = P44 · P99
P44 = 25944778565180928052792910166261047114212759_<44>
P99 = 139706665555714048450456121278199435970156709083690111782361972187434491639694660431695110194802271_<99>

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=4244805371 Step 1 took 162657ms Step 2 took 52038ms ********** Factor found in step 2: 25944778565180928052792910166261047114212759 Found probable prime factor of 44 digits: 25944778565180928052792910166261047114212759 Probable prime cofactor 139706665555714048450456121278199435970156709083690111782361972187434491639694660431695110194802271 has 99 digits

(14·10¹⁹⁴-11)/3 = 4(6)₁₉₃3_<195> = 23 · 1487 · C191
C191 = P44 · P68 · P80
P44 = 19918602523557170046661811204547110828816287_<44>
P68 = 38002400406508649071698524483443108152436953406221425871715619951251_<68>
P80 = 18025946657480442016359745430074112476927580274403990407522607197025714289498299_<80>

Number: 46663_194 N=13644825200042883736342991920314220831749558979756927185364950342582575558219545237468689999317758739997855813182850403984288958412522051012153640731752482870871222089022738126565500034112063 ( 191 digits) SNFS difficulty: 195 digits. Divisors found: r1=19918602523557170046661811204547110828816287 r2=38002400406508649071698524483443108152436953406221425871715619951251 r3=18025946657480442016359745430074112476927580274403990407522607197025714289498299 Version: Total time: 581.92 hours. Scaled time: 1161.52 units (timescale=1.996). Factorization parameters were as follows: n: 13644825200042883736342991920314220831749558979756927185364950342582575558219545237468689999317758739997855813182850403984288958412522051012153640731752482870871222089022738126565500034112063 m: 1000000000000000000000000000000000000000 deg: 5 c5: 7 c0: -55 skew: 1.51 type: snfs lss: 1 rlim: 12900000 alim: 12900000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5 Factor base limits: 12900000/12900000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [6450000, 12150001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1950698 x 1950946 Total sieving time: 581.92 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,195,5,0,0,0,0,0,0,0,0,12900000,12900000,28,28,55,55,2.5,2.5,100000 total time: 581.92 hours. --------- CPU info (if available) ----------

Apr 27, 2009 (4th)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / Apr 27, 2009
(53·10¹⁵⁵-17)/9 = 5(8)₁₅₄7_<156> = 13 · 12659042761_<11> · C145
C145 = P67 · P78
P67 = 4922032361863921654624733150235114276655806509234915061421645406483_<67>
P78 = 727017184113077927619676603072589808158867829035481257917742796614728442684473_<78>

Number: n N=3578402107835750531698448482643947610984702739732320519120106422645908869862545312176728426906934381208959970689773175902877349108209185797638459 ( 145 digits) SNFS difficulty: 156 digits. Divisors found: r1=4922032361863921654624733150235114276655806509234915061421645406483 (pp67) r2=727017184113077927619676603072589808158867829035481257917742796614728442684473 (pp78) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 19.09 hours. Scaled time: 48.76 units (timescale=2.554). Factorization parameters were as follows: name: KA_5_8_154_7 n: 3578402107835750531698448482643947610984702739732320519120106422645908869862545312176728426906934381208959970689773175902877349108209185797638459 m: 10000000000000000000000000000000 deg: 5 c5: 53 c0: -17 skew: 0.80 type: snfs lss: 1 rlim: 2900000 alim: 2900000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 2900000/2900000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved rational special-q in [1450000, 2550001) Primes: RFBsize:210109, AFBsize:209174, largePrimes:13191696 encountered Relations: rels:12964330, finalFF:660670 Max relations in full relation-set: 28 Initial matrix: 419348 x 660670 with sparse part having weight 77279116. Pruned matrix : 341602 x 343762 with weight 40442152. Total sieving time: 17.68 hours. Total relation processing time: 0.27 hours. Matrix solve time: 0.70 hours. Total square root time: 0.44 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,2900000,2900000,28,28,56,56,2.4,2.4,100000 total time: 19.09 hours. --------- CPU info (if available) ----------

(53·10¹⁵⁵+1)/9 = 5(8)₁₅₄9_<156> = 7 · 1792927 · 3543577 · C143
C143 = P67 · P76
P67 = 2443577634254454687137637845111973397935401399897115454809979896223_<67>
P76 = 5418819651805614652357594463326606111851486150836128615586608425053563039831_<76>

Number: n N=13241306505210711739279184521760332252149425240510002368729844950310950047876697791013586060711032376595753767593684056758030112492701795458313 ( 143 digits) SNFS difficulty: 156 digits. Divisors found: Mon Apr 27 18:10:44 2009 prp67 factor: 2443577634254454687137637845111973397935401399897115454809979896223 Mon Apr 27 18:10:44 2009 prp76 factor: 5418819651805614652357594463326606111851486150836128615586608425053563039831 Mon Apr 27 18:10:44 2009 elapsed time 00:34:11 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 15.04 hours. Scaled time: 39.84 units (timescale=2.649). Factorization parameters were as follows: name: KA_5_8_154_9 n: 13241306505210711739279184521760332252149425240510002368729844950310950047876697791013586060711032376595753767593684056758030112492701795458313 m: 10000000000000000000000000000000 deg: 5 c5: 53 c0: 1 skew: 0.45 type: snfs lss: 1 rlim: 2900000 alim: 2900000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 2900000/2900000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [1450000, 2361467) Primes: RFBsize:210109, AFBsize:210189, largePrimes:12185451 encountered Relations: rels:11340683, finalFF:370663 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 907702 hash collisions in 12192549 relations Msieve: matrix is 486333 x 486581 (129.7 MB) Total sieving time: 14.81 hours. Total relation processing time: 0.23 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,2900000,2900000,28,28,56,56,2.4,2.4,100000 total time: 15.04 hours. --------- CPU info (if available) ----------

(53·10¹⁶¹-17)/9 = 5(8)₁₆₀7_<162> = 13 · 301013 · C156
C156 = P38 · P55 · P63
P38 = 40079032860800981034271182219977895493_<38>
P55 = 3845042550038572909061181163224247339297802581922082119_<55>
P63 = 976531759921969567716202456727446938275394815869598707738421069_<63>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM] Input number is 150488999807799992509622990698558863388953783720787139244149406501198616489318219808265088701481814071635773688508952434430736032327990150409780126769094023 (156 digits) Using B1=1398000, B2=2139965110, polynomial Dickson(6), sigma=2643783734 Step 1 took 23821ms Step 2 took 9563ms ********** Factor found in step 2: 40079032860800981034271182219977895493 Found probable prime factor of 38 digits: 40079032860800981034271182219977895493 Composite cofactor 3754806168364025338444730098765301182030827656499506159990711901017869567305316246258327391762206262324084086017765211 has 118 digits Number: n N=3754806168364025338444730098765301182030827656499506159990711901017869567305316246258327391762206262324084086017765211 ( 118 digits) Divisors found: Mon Apr 27 18:53:56 2009 prp55 factor: 3845042550038572909061181163224247339297802581922082119 Mon Apr 27 18:53:56 2009 prp63 factor: 976531759921969567716202456727446938275394815869598707738421069 Mon Apr 27 18:53:56 2009 elapsed time 00:56:10 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 27.34 hours. Scaled time: 72.15 units (timescale=2.639). Factorization parameters were as follows: name: KA_5_8_160_7 n: 3754806168364025338444730098765301182030827656499506159990711901017869567305316246258327391762206262324084086017765211 Y0: -46560131168840686478827 Y1: 3378042388439 c0: 81517691767964263443146531760 c1: 2433157487496539211369302 c2: -4257028842031457161 c3: -501233010921252 c4: -401084884 c5: 17160 skew: 94782.03 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 50000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2250000, 3750001) Primes: RFBsize:315948, AFBsize:316419, largePrimes:14325298 encountered Relations: rels:13552992, finalFF:777281 Max relations in full relation-set: 28 Initial matrix: 632452 x 777281 with sparse part having weight 74821822. Pruned matrix : Msieve: found 1227986 hash collisions in 14513606 relations Msieve: matrix is 580380 x 580628 (160.7 MB) Total sieving time: 26.66 hours. Total relation processing time: 0.68 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,28,28,56,56,2.4,2.4,60000 total time: 27.34 hours. --------- CPU info (if available) ----------

(53·10¹⁷²+1)/9 = 5(8)₁₇₁9_<173> = 807379 · 603812754341_<12> · 28759572858649_<14> · 9993027152629419597904559069_<28> · C114
C114 = P38 · P77
P38 = 35301764274656969995635746440541350381_<38>
P77 = 11906324612627081905737388568432204863860375854067088525617352372196014894391_<77>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM] Input number is 420314264852507707333627373820020436227707521394433722129394296927603797534587440177074834216240620687800242612971 (114 digits) Using B1=1172000, B2=1426247560, polynomial Dickson(6), sigma=1695054277 Step 1 took 11700ms Step 2 took 5070ms ********** Factor found in step 2: 35301764274656969995635746440541350381 Found probable prime factor of 38 digits: 35301764274656969995635746440541350381 Probable prime cofactor 11906324612627081905737388568432204863860375854067088525617352372196014894391 has 77 digits

Apr 27, 2009 (3rd)

By Serge Batalov / GMP-ECM 6.2.2 / Apr 27, 2009
6·10²¹⁶+1 = 6(0)₂₁₅1_<217> = 7³ · 3559 · 4057 · 18461 · 8865690481_<10> · C193
C193 = P35 · C158
P35 = 75489457323208605217787830670233307_<35>
C158 = [98055067697465091816689131698585149675657995487502821941906044701157348721437441754279639798790119281752053294533196233210198961184141683435508604336743525047_<158>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1144671962 Step 1 took 16225ms ********** Factor found in step 1: 75489457323208605217787830670233307 Found probable prime factor of 35 digits: 75489457323208605217787830670233307 Composite cofactor has 158 digits

6·10²³³+1 = 6(0)₂₃₂1_<234> = 294510113 · 1778348809_<10> · 778008505367081881201_<21> · C196
C196 = P31 · C165
P31 = 2561616974580876396755878639763_<31>
C165 = [574824873435899378320065034350864626543502944955975704501487535802286423132854167632694971627309959241359282121449541103533943009375174285144531117192634556032152531_<165>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=2878558676 Step 1 took 15537ms Step 2 took 15985ms ********** Factor found in step 2: 2561616974580876396755878639763 Found probable prime factor of 31 digits: 2561616974580876396755878639763 Composite cofactor has 165 digits

Apr 27, 2009 (2nd)

By Tyler Cadigan / ggnfs, msieve / Apr 27, 2009
6·10¹⁹⁴+1 = 6(0)₁₉₃1_<195> = 153817 · 33881245227068299278185531_<26> · 901361069267656452128353133474957_<33> · C132
C132 = P51 · P81
P51 = 266634767326292612283152421868647275640368024889323_<51>
P81 = 479040217579134298529209937599938953347103505261874490787658533513714122044192133_<81>

Number: 60001_194 N=127728776954149061732629779151943546510736581677373866290113899810994265965188567884730521444012921154476658141238516044262272295959 ( 132 digits) Divisors found: r1=266634767326292612283152421868647275640368024889323 (pp51) r2=479040217579134298529209937599938953347103505261874490787658533513714122044192133 (pp81) Version: Msieve-1.40 Total time: 172.66 hours. Scaled time: 437.34 units (timescale=2.533). Factorization parameters were as follows: name: 60001_194 n: 127728776954149061732629779151943546510736581677373866290113899810994265965188567884730521444012921154476658141238516044262272295959 skew: 135621.62 # norm 3.35e+18 c5: 118440 c4: -198636398962 c3: -14944684265948103 c2: -3350417460951912749221 c1: 53455124993580901826489895 c0: 1773295866630335112183564218255 # alpha -6.78 Y1: 439575619875863 Y0: -16090222539693828700212894 # Murphy_E 6.47e-11 # M 59533760174489839394087245664387266171938052700247014464675137044353023313433652697868784876534862498628846968815646467114351145795 type: gnfs rlim: 8000000 alim: 8000000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5 qintsize: 1000000 Factor base limits: 8000000/8000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved algebraic special-q in [4000000, 11000001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1368948 x 1369196 Total sieving time: 166.98 hours. Total relation processing time: 0.38 hours. Matrix solve time: 3.76 hours. Time per square root: 1.54 hours. Prototype def-par.txt line would be: gnfs,131,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,8000000,8000000,28,28,55,55,2.5,2.5,100000 total time: 172.66 hours. --------- CPU info (if available) ----------

Apr 27, 2009

Factorizations of 600...001 have been extended up to n=250. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Apr 26, 2009 (3rd)

By Ignacio Santos / GGNFS, Msieve / Apr 26, 2009
(53·10¹⁴⁹+1)/9 = 5(8)₁₄₈9_<150> = 7 · 89 · 181 · 13860095467_<11> · 127907351040860227747_<21> · C115
C115 = P36 · P79
P36 = 298749405551037697759977109415955797_<36>
P79 = 9860477861640212173667954263879056032708182342505378235882532507138565347054351_<79>

Number: 58889_149 N=2945811899614180730648502625419787915632663325606645886918019990610313348603055671902651871116824477221833172522747 ( 115 digits) SNFS difficulty: 151 digits. Divisors found: r1=298749405551037697759977109415955797 (pp36) r2=9860477861640212173667954263879056032708182342505378235882532507138565347054351 (pp79) Version: Msieve-1.39 Total time: 11.63 hours. Scaled time: 29.90 units (timescale=2.571). Factorization parameters were as follows: n: 2945811899614180730648502625419787915632663325606645886918019990610313348603055671902651871116824477221833172522747 m: 1000000000000000000000000000000 deg: 5 c5: 53 c0: 10 skew: 0.72 type: snfs lss: 1 rlim: 2400000 alim: 2400000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1200000, 1800001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 361280 x 361528 Total sieving time: 11.63 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,49,49,2.4,2.4,100000 total time: 11.63 hours. --------- CPU info (if available) ----------

(53·10¹⁵⁰-17)/9 = 5(8)₁₄₉7_<151> = 23 · 853 · 1003753 · 816312569 · 3680454677_<10> · C122
C122 = P42 · P81
P42 = 646588374346983737232638435333887307048501_<42>
P81 = 153937272537308898972231509958686605521190984086624596387981731443058693734868357_<81>

Number: 58887_150 N=99534050801307145446580083087138050744490378834399385389609897359260896132388374257778620864667781554294052423079449182857 ( 122 digits) SNFS difficulty: 151 digits. Divisors found: r1=646588374346983737232638435333887307048501 (pp42) r2=153937272537308898972231509958686605521190984086624596387981731443058693734868357 (pp81) Version: Msieve-1.39 Total time: 13.05 hours. Scaled time: 33.54 units (timescale=2.571). Factorization parameters were as follows: n: 99534050801307145446580083087138050744490378834399385389609897359260896132388374257778620864667781554294052423079449182857 m: 1000000000000000000000000000000 deg: 5 c5: 53 c0: -17 skew: 0.80 type: snfs lss: 1 rlim: 2400000 alim: 2400000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1200000, 1900001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 410988 x 411236 Total sieving time: 13.05 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,49,49,2.4,2.4,100000 total time: 13.05 hours. --------- CPU info (if available) ----------

(85·10¹⁸⁰+41)/9 = 9(4)₁₇₉9_<181> = 7 · 127 · 2011 · C175
C175 = P81 · P95
P81 = 414375958481886884185001240050648075749952502026192245534940573345783519916635579_<81>
P95 = 12748762611266692012282983698888185917241129880100555296765430261008552339575567088257949707889_<95>

Number: 94449_180 N=5282780726501678588038255536307588602642968982432640972091318023337585039562744860771070945818495711407531045193194709438048239991880676775174361285396262314550313234714382731 ( 175 digits) SNFS difficulty: 181 digits. Divisors found: r1=414375958481886884185001240050648075749952502026192245534940573345783519916635579 (pp81) r2=12748762611266692012282983698888185917241129880100555296765430261008552339575567088257949707889 (pp95) Version: Msieve-1.39 Total time: 128.77 hours. Scaled time: 223.92 units (timescale=1.739). Factorization parameters were as follows: n: 5282780726501678588038255536307588602642968982432640972091318023337585039562744860771070945818495711407531045193194709438048239991880676775174361285396262314550313234714382731 m: 1000000000000000000000000000000000000 deg: 5 c5: 85 c0: 41 skew: 0.86 type: snfs lss: 1 rlim: 7500000 alim: 7500000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 7500000/7500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3750000, 5850001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1247569 x 1247817 Total sieving time: 128.77 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,181,5,0,0,0,0,0,0,0,0,7500000,7500000,28,28,53,53,2.5,2.5,100000 total time: 128.77 hours. --------- CPU info (if available) ----------

(53·10¹⁶²+1)/9 = 5(8)₁₆₁9_<163> = 3 · 1723 · 2655315417745817_<16> · 171350162476640484283_<21> · C124
C124 = P47 · P77
P47 = 26342549352212524177658708353759886900127603649_<47>
P77 = 95053560209664005393787353568489591164108220293809699182000297998744547765379_<77>

Number: 58889_162 N=2503953100926578709140928919928972652459114083988579647062913004484757863174594928313473290166903382947849977348817156267971 ( 124 digits) SNFS difficulty: 165 digits. Divisors found: r1=26342549352212524177658708353759886900127603649 (pp47) r2=95053560209664005393787353568489591164108220293809699182000297998744547765379 (pp77) Version: Msieve-1.39 Total time: 35.93 hours. Scaled time: 91.98 units (timescale=2.560). Factorization parameters were as follows: n: 2503953100926578709140928919928972652459114083988579647062913004484757863174594928313473290166903382947849977348817156267971 m: 500000000000000000000000000000000 deg: 5 c5: 212 c0: 125 skew: 0.90 type: snfs lss: 1 rlim: 4100000 alim: 4100000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 4100000/4100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [2050000, 3850001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 724072 x 724320 Total sieving time: 35.93 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000 total time: 35.93 hours. --------- CPU info (if available) ----------

Apr 26, 2009 (2nd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve / Apr 26, 2009
(53·10¹⁴⁰+1)/9 = 5(8)₁₃₉9_<141> = 577153 · 11923297 · C128
C128 = P34 · P45 · P50
P34 = 3492350119576818700587648285417907_<34>
P45 = 626497419541031597886693211292085596727199999_<45>
P50 = 39111905731165024668312789845345170825587785659453_<50>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM] Input number is 85574829142419551318043870019681831105246990546938000717559749678652140035247595216207608491893437943546231263497379972501175129 (128 digits) Using B1=882000, B2=871165692, polynomial Dickson(3), sigma=3328769994 Step 1 took 10904ms Step 2 took 4243ms ********** Factor found in step 2: 3492350119576818700587648285417907 Found probable prime factor of 34 digits: 3492350119576818700587648285417907 Composite cofactor 24503508013906972671895221182159865490563135055105532257550937518736971877266849444954435940547 has 95 digits Number: n N=24503508013906972671895221182159865490563135055105532257550937518736971877266849444954435940547 ( 95 digits) Divisors found: r1=626497419541031597886693211292085596727199999 (pp45) r2=39111905731165024668312789845345170825587785659453 (pp50) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 3.36 hours. Scaled time: 8.94 units (timescale=2.660). Factorization parameters were as follows: name: KA_5_8_139_9 n: 24503508013906972671895221182159865490563135055105532257550937518736971877266849444954435940547 m: 4878869189112173983388 deg: 4 c4: 43246560 c3: 243773149584 c2: 347355289183340212 c1: -1107047333699642379 c0: -74718258204081308948937 skew: 1635.250 type: gnfs # adj. I(F,S) = 55.819 # E(F1,F2) = 4.143619e-05 # GGNFS version 0.77.1-20060513-pentium-m polyselect. # Options were: # lcd=1, enumLCD=24, maxS1=60.00000000, seed=1240667234. # maxskew=2000.0 # These parameters should be manually set: rlim: 1200000 alim: 1200000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.4 alambda: 2.4 qintsize: 60000 type: gnfs Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved algebraic special-q in [600000, 1440001) Primes: RFBsize:92938, AFBsize:92998, largePrimes:1843462 encountered Relations: rels:1887158, finalFF:211814 Max relations in full relation-set: 28 Initial matrix: 186017 x 211814 with sparse part having weight 16131864. Pruned matrix : 174225 x 175219 with weight 11184565. Total sieving time: 3.17 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.07 hours. Total square root time: 0.07 hours, sqrts: 2. Prototype def-par.txt line would be: gnfs,94,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000 total time: 3.36 hours. --------- CPU info (if available) ----------

(53·10¹⁴²+1)/9 = 5(8)₁₄₁9_<143> = 17² · 6379 · 2008796784103_<13> · 24838614894526801_<17> · C108
C108 = P43 · P66
P43 = 2068776505732953917580438564404929945073177_<43>
P66 = 309461026129065613336287718747252395686825797638200927646978423349_<66>

Number: n N=640205700295822709913287799054834670776087148367279389602473482798865277861406545945488212501320225890409773 ( 108 digits) Divisors found: Sun Apr 26 14:28:43 2009 prp43 factor: 2068776505732953917580438564404929945073177 Sun Apr 26 14:28:43 2009 prp66 factor: 309461026129065613336287718747252395686825797638200927646978423349 Sun Apr 26 14:28:43 2009 elapsed time 00:27:26 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 9.15 hours. Scaled time: 23.74 units (timescale=2.595). Factorization parameters were as follows: name: KA_5_8_141_9 n: 640205700295822709913287799054834670776087148367279389602473482798865277861406545945488212501320225890409773 Y0: -715245836271708223585 Y1: 146694848041 c0: 286853924357173847644917408 c1: 9917237000351373716964 c2: -1001623086484141097 c3: -14504523771059 c4: 642729609 c5: 3420 skew: 32438.62 type: gnfs rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [1250000, 2346959) Primes: RFBsize:183072, AFBsize:182762, largePrimes:15313352 encountered Relations: rels:13294024, finalFF:336894 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1147672 hash collisions in 14735925 relations Msieve: matrix is 368338 x 368586 (100.7 MB) Total sieving time: 8.61 hours. Total relation processing time: 0.54 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,28,28,56,56,2.6,2.6,150000 total time: 9.15 hours. --------- CPU info (if available) ----------

Apr 26, 2009

By matsui / GGNFS / Apr 26, 2009
4·10¹⁷⁷-9 = 3(9)₁₇₆1_<178> = 13 · 227 · 385001 · 5083123 · 1162925053_<10> · 332230023790700823439_<21> · C133
C133 = P41 · P92
P41 = 64657499314578118063033769725403663002679_<41>
P92 = 27726100791358863600050685537869345949466612785403199549604397338078169719410730274414575719_<92>

N=1792700342913209540033076226702597938072348072879606518518071854016188520494872504571755209446502225955209177348084664558615345351201 ( 133 digits) SNFS difficulty: 177 digits. Divisors found: r1=64657499314578118063033769725403663002679 (pp41) r2=27726100791358863600050685537869345949466612785403199549604397338078169719410730274414575719 (pp92) Version: GGNFS-0.77.1-20060722-nocona

Apr 25, 2009 (7th)

By Ignacio Santos / GGNFS, Msieve / Apr 25, 2009
(53·10¹¹³+1)/9 = 5(8)₁₁₂9_<114> = 7 · 47 · C112
C112 = P39 · P73
P39 = 289531175486154600675813449406456787961_<39>
P73 = 6182186873256482269014449455225313046649108060530092150465438847951149881_<73>

Number: 58889_113 N=1789935832489023978385680513340087808172914555893279297534616683552853765619723066531577169875042215467747382641 ( 112 digits) SNFS difficulty: 116 digits. Divisors found: r1=289531175486154600675813449406456787961 (pp39) r2=6182186873256482269014449455225313046649108060530092150465438847951149881 (pp73) Version: Msieve-1.39 Total time: 1.06 hours. Scaled time: 1.28 units (timescale=1.203). Factorization parameters were as follows: n: 1789935832489023978385680513340087808172914555893279297534616683552853765619723066531577169875042215467747382641 m: 100000000000000000000000 deg: 5 c5: 53 c0: 100 skew: 1.14 type: snfs lss: 1 rlim: 620000 alim: 620000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 Factor base limits: 620000/620000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [310000, 510001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 59612 x 59838 Total sieving time: 1.03 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.01 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,116,5,0,0,0,0,0,0,0,0,620000,620000,25,25,45,45,2.2,2.2,50000 total time: 1.06 hours. --------- CPU info (if available) ----------

(53·10¹²⁸+1)/9 = 5(8)₁₂₇9_<129> = 19 · 71 · 673 · 941 · 5903 · 921784063808351_<15> · C102
C102 = P29 · P74
P29 = 12421340045339931728781770009_<29>
P74 = 10198734659319124820400947026165352095142553000316341381362596248248760401_<74>

Number: 58889_128 N=126681951235596951070128622542082458491076664658048307858846714431283866232339985443226702580928613609 ( 102 digits) SNFS difficulty: 131 digits. Divisors found: r1=12421340045339931728781770009 (pp29) r2=10198734659319124820400947026165352095142553000316341381362596248248760401 (pp74) Version: Msieve-1.39 Total time: 2.59 hours. Scaled time: 3.08 units (timescale=1.186). Factorization parameters were as follows: n: 126681951235596951070128622542082458491076664658048307858846714431283866232339985443226702580928613609 m: 100000000000000000000000000 deg: 5 c5: 53 c0: 100 skew: 1.14 type: snfs lss: 1 rlim: 1100000 alim: 1100000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1100000/1100000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [550000, 950001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 148952 x 149186 Total sieving time: 2.48 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.06 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000 total time: 2.59 hours. --------- CPU info (if available) ----------

(53·10¹³³+1)/9 = 5(8)₁₃₂9_<134> = 262918391 · C126
C126 = P58 · P68
P58 = 6902507297954552900544343980154530186562139765296085565049_<58>
P68 = 32449313991032259990721014237413613972619180694610646930008757342471_<68>

Number: 58889_133 N=223981626636718953939166959563847661341001013842690406883286034140110377021472373489798546990533229335367752531578853640896079 ( 126 digits) SNFS difficulty: 136 digits. Divisors found: r1=6902507297954552900544343980154530186562139765296085565049 (pp58) r2=32449313991032259990721014237413613972619180694610646930008757342471 (pp68) Version: Msieve-1.39 Total time: 4.06 hours. Scaled time: 4.83 units (timescale=1.189). Factorization parameters were as follows: n: 223981626636718953939166959563847661341001013842690406883286034140110377021472373489798546990533229335367752531578853640896079 m: 1000000000000000000000000000 deg: 5 c5: 53 c0: 100 skew: 1.14 type: snfs lss: 1 rlim: 1330000 alim: 1330000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3Factor base limits: 1330000/1330000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [665000, 1265001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 197595 x 197831 Total sieving time: 3.86 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.10 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,136,5,0,0,0,0,0,0,0,0,1330000,1330000,26,26,48,48,2.3,2.3,75000 total time: 4.06 hours. --------- CPU info (if available) ----------

(53·10¹³⁸+1)/9 = 5(8)₁₃₇9_<139> = 3 · 568606156271_<12> · 421748910868721_<15> · C112
C112 = P42 · P71
P42 = 633237938276842858605725159374066027361003_<42>
P71 = 12926461350690842029880554414352022638905256637045133099332495876548231_<71>

Number: 58889_138 N=8185525734926762194466972507409641598365163339665518849949331023072147151841412623469926862436337252969778035693 ( 112 digits) SNFS difficulty: 141 digits. Divisors found: r1=633237938276842858605725159374066027361003 (pp42) r2=12926461350690842029880554414352022638905256637045133099332495876548231 (pp71) Version: Msieve-1.39 Total time: 5.99 hours. Scaled time: 7.06 units (timescale=1.178). Factorization parameters were as follows: n: 8185525734926762194466972507409641598365163339665518849949331023072147151841412623469926862436337252969778035693 m: 10000000000000000000000000000 deg: 5 c5: 53 c0: 100 skew: 1.14 type: snfs lss: 1 rlim: 1610000 alim: 1610000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1610000/1610000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [805000, 1705001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 238513 x 238750 Total sieving time: 5.82 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.09 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,141,5,0,0,0,0,0,0,0,0,1610000,1610000,26,26,48,48,2.3,2.3,100000 total time: 5.99 hours. --------- CPU info (if available) ----------

(53·10¹⁴⁶+1)/9 = 5(8)₁₄₅9_<147> = 19 · 541 · 1172317 · 235060575725579_<15> · C123
C123 = P34 · P89
P34 = 9237495928744902899345213964123421_<34>
P89 = 22506262284520226043638845786993481451478146780791861537970684431898609724245820689195797_<89>

Number: 58889_146 N=207901506224520545540916343484854785474436665052904598304605157182071243981211522776531317754495948145242139489790542461537 ( 123 digits) SNFS difficulty: 148 digits. Divisors found: r1=9237495928744902899345213964123421 (pp34) r2=22506262284520226043638845786993481451478146780791861537970684431898609724245820689195797 (pp89) Version: Msieve-1.39 Total time: 8.46 hours. Scaled time: 21.74 units (timescale=2.571). Factorization parameters were as follows: n: 207901506224520545540916343484854785474436665052904598304605157182071243981211522776531317754495948145242139489790542461537 m: 200000000000000000000000000000 deg: 5 c5: 265 c0: 16 skew: 0.57 type: snfs lss: 1 rlim: 2100000 alim: 2100000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 2100000/2100000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [1050000, 2350001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 347190 x 347428 Total sieving time: 8.46 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,148,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,49,49,2.3,2.3,100000 total time: 8.46 hours. --------- CPU info (if available) ----------

Apr 25, 2009 (6th)

By Sinkiti Sibata / Msieve / Apr 25, 2009
(53·10¹²⁵-17)/9 = 5(8)₁₂₄7_<126> = 13 · 339749 · 35535200978096463458378999_<26> · C94
C94 = P36 · P59
P36 = 333310210633105268385300246208958849_<36>
P59 = 11257045633707776513130579531935967239498275141186226824801_<59>

Sat Apr 25 07:11:07 2009 Msieve v. 1.41 Sat Apr 25 07:11:07 2009 random seeds: 54733750 bd397ade Sat Apr 25 07:11:07 2009 factoring 3752088251277616965378755358494011502094212586258828900203423274576430990063210653009341614049 (94 digits) Sat Apr 25 07:11:08 2009 searching for 15-digit factors Sat Apr 25 07:11:09 2009 commencing quadratic sieve (94-digit input) Sat Apr 25 07:11:10 2009 using multiplier of 1 Sat Apr 25 07:11:10 2009 using 32kb Intel Core sieve core Sat Apr 25 07:11:10 2009 sieve interval: 36 blocks of size 32768 Sat Apr 25 07:11:10 2009 processing polynomials in batches of 6 Sat Apr 25 07:11:10 2009 using a sieve bound of 2023667 (75294 primes) Sat Apr 25 07:11:10 2009 using large prime bound of 271171378 (28 bits) Sat Apr 25 07:11:10 2009 using double large prime bound of 1512999890036866 (42-51 bits) Sat Apr 25 07:11:10 2009 using trial factoring cutoff of 51 bits Sat Apr 25 07:11:10 2009 polynomial 'A' values have 12 factors Sat Apr 25 10:02:45 2009 75406 relations (18873 full + 56533 combined from 1065411 partial), need 75390 Sat Apr 25 10:02:47 2009 begin with 1084284 relations Sat Apr 25 10:02:48 2009 reduce to 194604 relations in 11 passes Sat Apr 25 10:02:48 2009 attempting to read 194604 relations Sat Apr 25 10:02:51 2009 recovered 194604 relations Sat Apr 25 10:02:51 2009 recovered 177197 polynomials Sat Apr 25 10:02:51 2009 attempting to build 75406 cycles Sat Apr 25 10:02:51 2009 found 75406 cycles in 6 passes Sat Apr 25 10:02:51 2009 distribution of cycle lengths: Sat Apr 25 10:02:51 2009 length 1 : 18873 Sat Apr 25 10:02:51 2009 length 2 : 13359 Sat Apr 25 10:02:51 2009 length 3 : 12926 Sat Apr 25 10:02:51 2009 length 4 : 10168 Sat Apr 25 10:02:51 2009 length 5 : 7471 Sat Apr 25 10:02:51 2009 length 6 : 5003 Sat Apr 25 10:02:51 2009 length 7 : 3191 Sat Apr 25 10:02:51 2009 length 9+: 4415 Sat Apr 25 10:02:51 2009 largest cycle: 21 relations Sat Apr 25 10:02:51 2009 matrix is 75294 x 75406 (19.0 MB) with weight 4689045 (62.18/col) Sat Apr 25 10:02:51 2009 sparse part has weight 4689045 (62.18/col) Sat Apr 25 10:02:53 2009 filtering completed in 3 passes Sat Apr 25 10:02:53 2009 matrix is 71416 x 71480 (18.2 MB) with weight 4481400 (62.69/col) Sat Apr 25 10:02:53 2009 sparse part has weight 4481400 (62.69/col) Sat Apr 25 10:02:53 2009 saving the first 48 matrix rows for later Sat Apr 25 10:02:53 2009 matrix is 71368 x 71480 (10.9 MB) with weight 3486418 (48.77/col) Sat Apr 25 10:02:53 2009 sparse part has weight 2428371 (33.97/col) Sat Apr 25 10:02:53 2009 matrix includes 64 packed rows Sat Apr 25 10:02:53 2009 using block size 28592 for processor cache size 1024 kB Sat Apr 25 10:02:53 2009 commencing Lanczos iteration Sat Apr 25 10:02:53 2009 memory use: 10.9 MB Sat Apr 25 10:03:25 2009 lanczos halted after 1130 iterations (dim = 71366) Sat Apr 25 10:03:25 2009 recovered 16 nontrivial dependencies Sat Apr 25 10:03:26 2009 prp36 factor: 333310210633105268385300246208958849 Sat Apr 25 10:03:26 2009 prp59 factor: 11257045633707776513130579531935967239498275141186226824801 Sat Apr 25 10:03:26 2009 elapsed time 02:52:19

(44·10²⁰⁰-53)/9 = 4(8)₁₉₉3_<201> = 3 · 7 · 23 · 490151 · 603522709 · 12983684697563_<14> · 485460576989519_<15> · 7046882295480502467634870497200027_<34> · C122
C122 = P41 · P82
P41 = 17093319897861558819189989484935430767783_<41>
P82 = 4506757199284748937489169617028628948676844119512148373046760090531769332278731307_<82>

Number: 48883_200 N=77035442509364829592824984655079160994427570285601319384761126720874299891224577489225266938170642713438522459468169082381 ( 122 digits) Divisors found: r1=17093319897861558819189989484935430767783 (pp41) r2=4506757199284748937489169617028628948676844119512148373046760090531769332278731307 (pp82) Version: Msieve-1.40 Total time: 79.27 hours. Scaled time: 154.97 units (timescale=1.955). Factorization parameters were as follows: name: 48883_200 # Murphy_E = 2.266954e-10, selected by Jeff Gilchrist n: 77035442509364829592824984655079160994427570285601319384761126720874299891224577489225266938170642713438522459468169082381 Y0: -368091799120498919063005 Y1: 12847974784117 c0: 109359585716408333906284552008 c1: 3405141569669740082931020 c2: -37901142473314887746 c3: -844999055076687 c4: 3776565670 c5: 11400 skew: 118654.68 type: gnfs # selected mechanically rlim: 5900000 alim: 5900000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 Factor base limits: 5900000/5900000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved algebraic special-q in [2950000, 5350001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 810955 x 811203 Total sieving time: 79.27 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,121,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5900000,5900000,27,27,52,52,2.5,2.5,100000 total time: 79.27 hours. --------- CPU info (if available) ----------

Apr 25, 2009 (5th)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve / Apr 25, 2009
(53·10¹³⁷+1)/9 = 5(8)₁₃₆9_<138> = 7 · 31 · 83 · 563 · C131
C131 = P35 · P97
P35 = 36467916497685454043561178729676819_<35>
P97 = 1592488069431850510302639201300386274192150371140061427937716746570830122530356070413043274127267_<97>

GMP-ECM 6.2.1 [powered by GMP 4.1.4] [ECM] Input number is 58074721939601040028418481668829073459340358599573882754390265440597520075691743627452543446548688855220890656508104815055185723673 (131 digits) Using B1=2328000, B2=3567716890, polynomial Dickson(6), sigma=2561432034 Step 1 took 30984ms Step 2 took 14000ms ********** Factor found in step 2: 36467916497685454043561178729676819 Found probable prime factor of 35 digits: 36467916497685454043561178729676819 Probable prime cofactor 1592488069431850510302639201300386274192150371140061427937716746570830122530356070413043274127267 has 97 digits

(53·10¹⁴⁹-17)/9 = 5(8)₁₄₈7_<150> = 13 · 71 · 103 · 349 · 45001306334623_<14> · C129
C129 = P60 · P70
P60 = 131330752110030357457784241422186029366093966226597288556911_<60>
P70 = 3003152975980207409359615676165557286711523353567898461432663515019759_<70>

Number: n N=394406339036956571634680918351574479618516919731322456206028760825031051850575746378939836515426834482961187849144726626761004449 ( 129 digits) SNFS difficulty: 151 digits. Divisors found: Sat Apr 25 14:53:44 2009 prp60 factor: 131330752110030357457784241422186029366093966226597288556911 Sat Apr 25 14:53:44 2009 prp70 factor: 3003152975980207409359615676165557286711523353567898461432663515019759 Sat Apr 25 14:53:44 2009 elapsed time 00:30:53 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 14.25 hours. Scaled time: 23.12 units (timescale=1.623). Factorization parameters were as follows: name: KA_5_8_148_7 n: 394406339036956571634680918351574479618516919731322456206028760825031051850575746378939836515426834482961187849144726626761004449 m: 1000000000000000000000000000000 deg: 5 c5: 53 c0: -170 skew: 1.26 type: snfs lss: 1 rlim: 2400000 alim: 2400000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [1200000, 2100000) Primes: RFBsize:176302, AFBsize:177593, largePrimes:12023284 encountered Relations: rels:11768502, finalFF:640523 Max relations in full relation-set: 28 Initial matrix: 353960 x 640523 with sparse part having weight 76137185. Pruned matrix : 278048 x 279881 with weight 34253707. Msieve: found 1026664 hash collisions in 12593327 relations Msieve: matrix is 353458 x 353706 (92.8 MB) Total sieving time: 13.96 hours. Total relation processing time: 0.27 hours. Matrix solve time: 0.02 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,28,28,56,56,2.4,2.4,100000 total time: 14.25 hours. --------- CPU info (if available) ----------

(17·10¹⁶⁸+7)/3 = 5(6)₁₆₇9_<169> = 739 · 857 · 4229411 · 851745859 · C148
C148 = P62 · P87
P62 = 17750314911886256685469328373006864448252907163669091067552591_<62>
P87 = 139928578638319314678328668947574395690000477539047365624769415108634425048302841672417_<87>

Number: n N=2483776336002808045620469682926685372479589939012661589982962543702359427428652288125288118566905146030280923577515033415821039268567270581541582447 ( 148 digits) SNFS difficulty: 170 digits. Divisors found: Sat Apr 25 15:59:55 2009 prp62 factor: 17750314911886256685469328373006864448252907163669091067552591 Sat Apr 25 15:59:55 2009 prp87 factor: 139928578638319314678328668947574395690000477539047365624769415108634425048302841672417 Sat Apr 25 15:59:55 2009 elapsed time 01:36:27 (Msieve 1.39 - dependency 3) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 60.77 hours. Scaled time: 160.36 units (timescale=2.639). Factorization parameters were as follows: name: KA_5_6_167_9 n: 2483776336002808045620469682926685372479589939012661589982962543702359427428652288125288118566905146030280923577515033415821039268567270581541582447 m: 5000000000000000000000000000000000 deg: 5 c5: 136 c0: 175 skew: 1.05 type: snfs lss: 1 rlim: 4900000 alim: 4900000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4900000/4900000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2450000, 5951689) Primes: RFBsize:341992, AFBsize:341883, largePrimes:17859820 encountered Relations: rels:18199396, finalFF:629046 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 2359672 hash collisions in 20150521 relations Msieve: matrix is 817865 x 818113 (216.9 MB) Total sieving time: 59.83 hours. Total relation processing time: 0.94 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,4900000,4900000,28,28,56,56,2.4,2.4,100000 total time: 60.77 hours. --------- CPU info (if available) ----------

Apr 25, 2009 (4th)

By Serge Batalov / GMP-ECM 6.2.2, Msieve-1.41 / Apr 25, 2009
(53·10¹⁸⁸+1)/9 = 5(8)₁₈₇9_<189> = 23 · 149 · 9133 · 1021637597731_<13> · C170
C170 = P35 · C135
P35 = 29078929780665430520713512844261283_<35>
C135 = [633330658677630357428348768527318821653634753038708389251181720953905597265954465448747588805040851833232202227201717842921321235662823_<135>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1241649351 Step 1 took 11620ms Step 2 took 13245ms ********** Factor found in step 2: 29078929780665430520713512844261283 Found probable prime factor of 35 digits: 29078929780665430520713512844261283 Composite cofactor has 135 digits

(53·10¹⁷⁸+1)/9 = 5(8)₁₇₇9_<179> = 29 · 83 · 56671 · 397302042061058419_<18> · C154
C154 = P30 · C124
P30 = 764648480363550491427385880911_<30>
C124 = [1421064422676721817294303535151760278742043022221943758499295816466638534361724872580455743508352819227160020715265251355093_<124>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3079772143 Step 1 took 9764ms Step 2 took 11665ms ********** Factor found in step 2: 764648480363550491427385880911 Found probable prime factor of 30 digits: 764648480363550491427385880911 Composite cofactor has 124 digits

(53·10¹⁴³+1)/9 = 5(8)₁₄₂9_<144> = 7³ · C142
C142 = P53 · P89
P53 = 79473050106862706275240784169605362262487122995225933_<53>
P89 = 21603263304638811935007782608993962985407454791157017884866832547047245476678698092370731_<89>

SNFS difficulty: 146 digits. Divisors found: r1=79473050106862706275240784169605362262487122995225933 (pp53) r2=21603263304638811935007782608993962985407454791157017884866832547047245476678698092370731 (pp89) Version: Msieve-1.41 Total time: 6.28 hours. Factorization parameters were as follows: n: 1716877227081308713961775186264982183349530288305798509880142533203757693553611920958859734369938451571104632329122125040492387431162941367023 m: 100000000000000000000000000000 deg: 5 c5: 53 c0: 100 skew: 1.14 type: snfs lss: 1 rlim: 1950000 alim: 1950000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1950000/1950000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [975000, 2175001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 319085 x 319317 Total sieving time: 6.00 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.15 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,146.000,5,0,0,0,0,0,0,0,0,1950000,1950000,26,26,49,49,2.3,2.3,100000 total time: 6.28 hours.

Apr 25, 2009 (3rd)

By Wataru Sakai / Msieve / Apr 25, 2009
(7·10²⁰⁰+11)/9 = (7)₁₉₉9_<200> = 31 · C199
C199 = P46 · P154
P46 = 1224138868623984405220163344723881547828209211_<46>
P154 = 2049571856416049713388251526936262340434423910767572808137910239843291577199511366868089995800953673223303727077940898700883017337359301880186873070702519_<154>

Number: 77779_200 N=2508960573476702508960573476702508960573476702508960573476702508960573476702508960573476702508960573476702508960573476702508960573476702508960573476702508960573476702508960573476702508960573476702509 ( 199 digits) SNFS difficulty: 200 digits. Divisors found: r1=1224138868623984405220163344723881547828209211 r2=2049571856416049713388251526936262340434423910767572808137910239843291577199511366868089995800953673223303727077940898700883017337359301880186873070702519 Version: Total time: 659.25 hours. Scaled time: 1318.50 units (timescale=2.000). Factorization parameters were as follows: n: 2508960573476702508960573476702508960573476702508960573476702508960573476702508960573476702508960573476702508960573476702508960573476702508960573476702508960573476702508960573476702508960573476702509 m: 10000000000000000000000000000000000000000 deg: 5 c5: 7 c0: 11 skew: 1.09 type: snfs lss: 1 rlim: 15600000 alim: 15600000 lpbr: 29 lpba: 29 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6Factor base limits: 15600000/15600000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 56/56 Sieved rational special-q in [7800000, 14200001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2392576 x 2392824 Total sieving time: 659.25 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,200,5,0,0,0,0,0,0,0,0,15600000,15600000,29,29,56,56,2.6,2.6,100000 total time: 659.25 hours. --------- CPU info (if available) ----------

Apr 25, 2009 (2nd)

By Max Dettweiler / GGNFS via factLat.pl / Apr 25, 2009
(53·10¹⁰³+1)/9 = 5(8)₁₀₂9_<104> = 17597 · 35327 · C95
C95 = P30 · P66
P30 = 660234879222823531615373589467_<30>
P66 = 143479384203030468046198093958135532280512482215395035709729983593_<66>

Number: c95 N=94730093900252915605913258436650410862800245694330855242156893772095109619833510783979427614931 ( 95 digits) SNFS difficulty: 105 digits. Divisors found: r1=660234879222823531615373589467 (pp30) r2=143479384203030468046198093958135532280512482215395035709729983593 (pp66) Version: GGNFS-0.77.1-VC8(Sat Total time: 0.35 hours. Scaled time: 0.38 units (timescale=1.083). Factorization parameters were as follows: n: 94730093900252915605913258436650410862800245694330855242156893772095109619833510783979427614931 m: 100000000000000000000000000 deg: 4 c4: 53 c0: 10 skew: 0.66 type: snfs lss: 1 rlim: 400000 alim: 400000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 Factor base limits: 400000/400000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [200000, 260001) Primes: RFBsize:33860, AFBsize:33767, largePrimes:1130050 encountered Relations: rels:1106897, finalFF:145363 Max relations in full relation-set: 32 Initial matrix: 67692 x 145363 with sparse part having weight 5316144. Pruned matrix : 41195 x 41597 with weight 1145405. Total sieving time: 0.32 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.00 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,105,4,0,0,0,0,0,0,0,0,400000,400000,25,25,44,44,2.2,2.2,20000 total time: 0.35 hours. --------- CPU info (if available) ----------

Apr 25, 2009

Factorizations of 588...889 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Apr 24, 2009 (5th)

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Apr 24, 2009
(53·10¹⁶⁵-71)/9 = 5(8)₁₆₄1_<166> = 367 · 1942027 · 1371144007102407524796878911_<28> · C130
C130 = P37 · P93
P37 = 7456075032830949289097809630839141133_<37>
P93 = 808199714463033799839895000646180717663570250954579698107795831316200571506223546388577376143_<93>

Number: 58881_165 N=6025997712548928580140437380295469588477406790695466700698973804134750409989600365698409400134707346602045944981706534764804190019 ( 130 digits) SNFS difficulty: 166 digits. Divisors found: r1=7456075032830949289097809630839141133 r2=808199714463033799839895000646180717663570250954579698107795831316200571506223546388577376143 Version: Total time: 24.84 hours. Scaled time: 59.16 units (timescale=2.382). Factorization parameters were as follows: n: 6025997712548928580140437380295469588477406790695466700698973804134750409989600365698409400134707346602045944981706534764804190019 m: 1000000000000000000000000000000000 deg: 5 c5: 53 c0: -71 skew: 1.06 type: snfs lss: 1 rlim: 4800000 alim: 4800000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 4800000/4800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [2400000, 4400001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9904777 Max relations in full relation-set: Initial matrix: Pruned matrix : 778856 x 779104 Total sieving time: 22.38 hours. Total relation processing time: 0.97 hours. Matrix solve time: 1.39 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,4800000,4800000,27,27,51,51,2.4,2.4,100000 total time: 24.84 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672387) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672339) Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379)

2·10¹⁹¹-1 = 1(9)_191<192> = 2749 · 218227091623637911_<18> · 1634251873308525786539681_<25> · C147
C147 = P39 · P108
P39 = 374917624436804778786980691929301633251_<39>
P108 = 544116308602057079193319001051462073305059198331631713353356980808064530293851666207891990993563912562753711_<108>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 203998793838406605456849058402298086054508973666863581672079665320253658796228665748890577906627191442159765577090127199451780519415081662361244461 (147 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2535079878 Step 1 took 13915ms Step 2 took 6304ms ********** Factor found in step 2: 374917624436804778786980691929301633251 Found probable prime factor of 39 digits: 374917624436804778786980691929301633251 Probable prime cofactor 544116308602057079193319001051462073305059198331631713353356980808064530293851666207891990993563912562753711 has 108 digits

2·10¹⁸⁰-1 = 1(9)_180<181> = 2089 · 25247 · 906097649 · 2812810690923703_<16> · C149
C149 = P37 · P112
P37 = 3646742702319169110919751900918642423_<37>
P112 = 4080009229030868132507753050857621102187848916600309751871730009887972204041194243916993303782420351451924397113_<112>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 14878743881363177813121181985179871892369482209890801997246302818188423938858501010328725657818896907386546241733098581247875698793343660876700524799 (149 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=386652535 Step 1 took 13915ms Step 2 took 6364ms ********** Factor found in step 2: 3646742702319169110919751900918642423 Found probable prime factor of 37 digits: 3646742702319169110919751900918642423 Probable prime cofactor 4080009229030868132507753050857621102187848916600309751871730009887972204041194243916993303782420351451924397113 has 112 digits

Apr 24, 2009 (4th)

By Sinkiti Sibata / Msieve / Apr 24, 2009
(53·10¹¹³-17)/9 = 5(8)₁₁₂7_<114> = 13 · 2963 · 255383398285427_<15> · C95
C95 = P34 · P62
P34 = 5067488575798423942258912441786211_<34>
P62 = 11813345789802296777872794313744435491728937700087705183033609_<62>

Fri Apr 24 06:48:16 2009 Msieve v. 1.41 Fri Apr 24 06:48:16 2009 random seeds: 4fb1af00 b2fd5f23 Fri Apr 24 06:48:16 2009 factoring 59863994831779548547391373386370555107607649273242788480501437709143034117417916270887605765499 (95 digits) Fri Apr 24 06:48:17 2009 searching for 15-digit factors Fri Apr 24 06:48:19 2009 commencing quadratic sieve (95-digit input) Fri Apr 24 06:48:19 2009 using multiplier of 3 Fri Apr 24 06:48:19 2009 using 32kb Intel Core sieve core Fri Apr 24 06:48:19 2009 sieve interval: 36 blocks of size 32768 Fri Apr 24 06:48:19 2009 processing polynomials in batches of 6 Fri Apr 24 06:48:19 2009 using a sieve bound of 2150039 (80000 primes) Fri Apr 24 06:48:19 2009 using large prime bound of 322505850 (28 bits) Fri Apr 24 06:48:19 2009 using double large prime bound of 2067129303583950 (43-51 bits) Fri Apr 24 06:48:19 2009 using trial factoring cutoff of 51 bits Fri Apr 24 06:48:19 2009 polynomial 'A' values have 12 factors Fri Apr 24 06:48:19 2009 restarting with 1761 full and 115577 partial relations Fri Apr 24 11:14:39 2009 80263 relations (18873 full + 61390 combined from 1218465 partial), need 80096 Fri Apr 24 11:14:40 2009 begin with 1237338 relations Fri Apr 24 11:14:42 2009 reduce to 213249 relations in 11 passes Fri Apr 24 11:14:42 2009 attempting to read 213249 relations Fri Apr 24 11:14:46 2009 recovered 213249 relations Fri Apr 24 11:14:46 2009 recovered 200611 polynomials Fri Apr 24 11:14:46 2009 attempting to build 80263 cycles Fri Apr 24 11:14:46 2009 found 80263 cycles in 6 passes Fri Apr 24 11:14:46 2009 distribution of cycle lengths: Fri Apr 24 11:14:46 2009 length 1 : 18873 Fri Apr 24 11:14:46 2009 length 2 : 13543 Fri Apr 24 11:14:46 2009 length 3 : 13334 Fri Apr 24 11:14:46 2009 length 4 : 11007 Fri Apr 24 11:14:46 2009 length 5 : 8458 Fri Apr 24 11:14:46 2009 length 6 : 5909 Fri Apr 24 11:14:46 2009 length 7 : 3736 Fri Apr 24 11:14:46 2009 length 9+: 5403 Fri Apr 24 11:14:46 2009 largest cycle: 21 relations Fri Apr 24 11:14:46 2009 matrix is 80000 x 80263 (22.1 MB) with weight 5481572 (68.30/col) Fri Apr 24 11:14:46 2009 sparse part has weight 5481572 (68.30/col) Fri Apr 24 11:14:48 2009 filtering completed in 3 passes Fri Apr 24 11:14:48 2009 matrix is 76727 x 76791 (21.3 MB) with weight 5264271 (68.55/col) Fri Apr 24 11:14:48 2009 sparse part has weight 5264271 (68.55/col) Fri Apr 24 11:14:48 2009 saving the first 48 matrix rows for later Fri Apr 24 11:14:48 2009 matrix is 76679 x 76791 (14.7 MB) with weight 4313718 (56.17/col) Fri Apr 24 11:14:48 2009 sparse part has weight 3380078 (44.02/col) Fri Apr 24 11:14:48 2009 matrix includes 64 packed rows Fri Apr 24 11:14:48 2009 using block size 30716 for processor cache size 1024 kB Fri Apr 24 11:14:49 2009 commencing Lanczos iteration Fri Apr 24 11:14:49 2009 memory use: 13.4 MB Fri Apr 24 11:15:34 2009 lanczos halted after 1214 iterations (dim = 76677) Fri Apr 24 11:15:35 2009 recovered 16 nontrivial dependencies Fri Apr 24 11:15:37 2009 prp34 factor: 5067488575798423942258912441786211 Fri Apr 24 11:15:37 2009 prp62 factor: 11813345789802296777872794313744435491728937700087705183033609 Fri Apr 24 11:15:37 2009 elapsed time 04:27:21

(53·10¹¹⁴-17)/9 = 5(8)₁₁₃7_<115> = 71 · 181 · 277 · 10789 · 18899 · 68813 · C96
C96 = P36 · P60
P36 = 167266927763015205609857861924093563_<36>
P60 = 704881442955466017239089882681824408103143399235767556204409_<60>

Fri Apr 24 12:54:32 2009 Msieve v. 1.41 Fri Apr 24 12:54:32 2009 random seeds: 59d15950 4f27dd33 Fri Apr 24 12:54:32 2009 factoring 117903353400321857683749787677987415989823219588292979192960515969393246858575069561884069119267 (96 digits) Fri Apr 24 12:54:33 2009 searching for 15-digit factors Fri Apr 24 12:54:34 2009 commencing quadratic sieve (96-digit input) Fri Apr 24 12:54:34 2009 using multiplier of 3 Fri Apr 24 12:54:34 2009 using 32kb Intel Core sieve core Fri Apr 24 12:54:34 2009 sieve interval: 36 blocks of size 32768 Fri Apr 24 12:54:34 2009 processing polynomials in batches of 6 Fri Apr 24 12:54:34 2009 using a sieve bound of 2191457 (81176 primes) Fri Apr 24 12:54:34 2009 using large prime bound of 328718550 (28 bits) Fri Apr 24 12:54:34 2009 using double large prime bound of 2139358506583350 (43-51 bits) Fri Apr 24 12:54:34 2009 using trial factoring cutoff of 51 bits Fri Apr 24 12:54:34 2009 polynomial 'A' values have 12 factors Fri Apr 24 17:40:31 2009 81350 relations (19358 full + 61992 combined from 1224123 partial), need 81272 Fri Apr 24 17:40:33 2009 begin with 1243481 relations Fri Apr 24 17:40:34 2009 reduce to 214446 relations in 11 passes Fri Apr 24 17:40:34 2009 attempting to read 214446 relations Fri Apr 24 17:40:37 2009 recovered 214446 relations Fri Apr 24 17:40:37 2009 recovered 201995 polynomials Fri Apr 24 17:40:38 2009 attempting to build 81350 cycles Fri Apr 24 17:40:38 2009 found 81350 cycles in 5 passes Fri Apr 24 17:40:38 2009 distribution of cycle lengths: Fri Apr 24 17:40:38 2009 length 1 : 19358 Fri Apr 24 17:40:38 2009 length 2 : 13809 Fri Apr 24 17:40:38 2009 length 3 : 13726 Fri Apr 24 17:40:38 2009 length 4 : 11158 Fri Apr 24 17:40:38 2009 length 5 : 8472 Fri Apr 24 17:40:38 2009 length 6 : 5816 Fri Apr 24 17:40:38 2009 length 7 : 3810 Fri Apr 24 17:40:38 2009 length 9+: 5201 Fri Apr 24 17:40:38 2009 largest cycle: 20 relations Fri Apr 24 17:40:38 2009 matrix is 81176 x 81350 (22.6 MB) with weight 5591847 (68.74/col) Fri Apr 24 17:40:38 2009 sparse part has weight 5591847 (68.74/col) Fri Apr 24 17:40:40 2009 filtering completed in 3 passes Fri Apr 24 17:40:40 2009 matrix is 77874 x 77938 (21.8 MB) with weight 5392030 (69.18/col) Fri Apr 24 17:40:40 2009 sparse part has weight 5392030 (69.18/col) Fri Apr 24 17:40:40 2009 saving the first 48 matrix rows for later Fri Apr 24 17:40:40 2009 matrix is 77826 x 77938 (15.6 MB) with weight 4492035 (57.64/col) Fri Apr 24 17:40:40 2009 sparse part has weight 3631965 (46.60/col) Fri Apr 24 17:40:40 2009 matrix includes 64 packed rows Fri Apr 24 17:40:40 2009 using block size 31175 for processor cache size 1024 kB Fri Apr 24 17:40:41 2009 commencing Lanczos iteration Fri Apr 24 17:40:41 2009 memory use: 14.0 MB Fri Apr 24 17:41:26 2009 lanczos halted after 1233 iterations (dim = 77826) Fri Apr 24 17:41:26 2009 recovered 18 nontrivial dependencies Fri Apr 24 17:41:27 2009 prp36 factor: 167266927763015205609857861924093563 Fri Apr 24 17:41:27 2009 prp60 factor: 704881442955466017239089882681824408103143399235767556204409 Fri Apr 24 17:41:27 2009 elapsed time 04:46:55

(53·10¹²¹-17)/9 = 5(8)₁₂₀7_<122> = 3² · 21211 · 620505581 · 136569534114199_<15> · C94
C94 = P37 · P58
P37 = 3631090387354731446722862437746442697_<37>
P58 = 1002520188473252584276320790788755291702994964270538468591_<58>

Fri Apr 24 18:28:38 2009 Msieve v. 1.41 Fri Apr 24 18:28:38 2009 random seeds: 752e6e18 d6e9ebde Fri Apr 24 18:28:38 2009 factoring 3640241419494281102214649384034662170741936618630879393491492058162045661401457588404315829927 (94 digits) Fri Apr 24 18:28:39 2009 searching for 15-digit factors Fri Apr 24 18:28:41 2009 commencing quadratic sieve (94-digit input) Fri Apr 24 18:28:41 2009 using multiplier of 3 Fri Apr 24 18:28:41 2009 using 32kb Intel Core sieve core Fri Apr 24 18:28:41 2009 sieve interval: 36 blocks of size 32768 Fri Apr 24 18:28:41 2009 processing polynomials in batches of 6 Fri Apr 24 18:28:41 2009 using a sieve bound of 2024387 (75294 primes) Fri Apr 24 18:28:41 2009 using large prime bound of 271267858 (28 bits) Fri Apr 24 18:28:41 2009 using double large prime bound of 1513968973265930 (42-51 bits) Fri Apr 24 18:28:41 2009 using trial factoring cutoff of 51 bits Fri Apr 24 18:28:41 2009 polynomial 'A' values have 12 factors Fri Apr 24 21:36:38 2009 75663 relations (18586 full + 57077 combined from 1073486 partial), need 75390 Fri Apr 24 21:36:39 2009 begin with 1092072 relations Fri Apr 24 21:36:40 2009 reduce to 196620 relations in 11 passes Fri Apr 24 21:36:40 2009 attempting to read 196620 relations Fri Apr 24 21:36:43 2009 recovered 196620 relations Fri Apr 24 21:36:43 2009 recovered 180006 polynomials Fri Apr 24 21:36:43 2009 attempting to build 75663 cycles Fri Apr 24 21:36:44 2009 found 75663 cycles in 5 passes Fri Apr 24 21:36:44 2009 distribution of cycle lengths: Fri Apr 24 21:36:44 2009 length 1 : 18586 Fri Apr 24 21:36:44 2009 length 2 : 13344 Fri Apr 24 21:36:44 2009 length 3 : 12710 Fri Apr 24 21:36:44 2009 length 4 : 10087 Fri Apr 24 21:36:44 2009 length 5 : 7735 Fri Apr 24 21:36:44 2009 length 6 : 5214 Fri Apr 24 21:36:44 2009 length 7 : 3265 Fri Apr 24 21:36:44 2009 length 9+: 4722 Fri Apr 24 21:36:44 2009 largest cycle: 20 relations Fri Apr 24 21:36:44 2009 matrix is 75294 x 75663 (19.9 MB) with weight 4913605 (64.94/col) Fri Apr 24 21:36:44 2009 sparse part has weight 4913605 (64.94/col) Fri Apr 24 21:36:45 2009 filtering completed in 4 passes Fri Apr 24 21:36:45 2009 matrix is 71656 x 71720 (18.9 MB) with weight 4671198 (65.13/col) Fri Apr 24 21:36:45 2009 sparse part has weight 4671198 (65.13/col) Fri Apr 24 21:36:45 2009 saving the first 48 matrix rows for later Fri Apr 24 21:36:46 2009 matrix is 71608 x 71720 (12.0 MB) with weight 3712909 (51.77/col) Fri Apr 24 21:36:46 2009 sparse part has weight 2707303 (37.75/col) Fri Apr 24 21:36:46 2009 matrix includes 64 packed rows Fri Apr 24 21:36:46 2009 using block size 28688 for processor cache size 1024 kB Fri Apr 24 21:36:46 2009 commencing Lanczos iteration Fri Apr 24 21:36:46 2009 memory use: 11.5 MB Fri Apr 24 21:37:20 2009 lanczos halted after 1134 iterations (dim = 71607) Fri Apr 24 21:37:20 2009 recovered 17 nontrivial dependencies Fri Apr 24 21:37:21 2009 prp37 factor: 3631090387354731446722862437746442697 Fri Apr 24 21:37:21 2009 prp58 factor: 1002520188473252584276320790788755291702994964270538468591 Fri Apr 24 21:37:21 2009 elapsed time 03:08:43

Apr 24, 2009 (3rd)

By Ignacio Santos / GGNFS, Msieve / Apr 24, 2009
(52·10¹⁸⁰+11)/9 = 5(7)₁₇₉9_<181> = 7 · C180
C180 = P83 · P97
P83 = 85953570641100435302364859126378100802894940416504268380526330442075309405460436217_<83>
P97 = 9602821840215038595051714729650614572066911996666266197149048428837644236481298696881375472096541_<97>

Number: 57779_180 N=825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825397 ( 180 digits) SNFS difficulty: 181 digits. Divisors found: r1=85953570641100435302364859126378100802894940416504268380526330442075309405460436217 (pp83) r2=9602821840215038595051714729650614572066911996666266197149048428837644236481298696881375472096541 (pp97) Version: Msieve-1.39 Total time: 110.43 hours. Scaled time: 192.03 units (timescale=1.739). Factorization parameters were as follows: n: 825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825396825397 m: 1000000000000000000000000000000000000 deg: 5 c5: 52 c0: 11 skew: 0.73 type: snfs lss: 1 rlim: 7500000 alim: 7500000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 7500000/7500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3750000, 5550001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1404538 x 1404784 Total sieving time: 110.43 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,181,5,0,0,0,0,0,0,0,0,7500000,7500000,28,28,53,53,2.5,2.5,100000 total time: 110.43 hours. --------- CPU info (if available) ----------

(53·10¹⁴⁷-17)/9 = 5(8)₁₄₆7_<148> = 7 · 157090823 · 108192642452257497081257210337049_<33> · C107
C107 = P52 · P56
P52 = 2579775523673369950784734958514551180203035362426083_<52>
P56 = 19186902085390185374523921439602412837798066940823099701_<56>

Number: 58887_147 N=49497900375007139446580117975996554390248271087641053217622845679414045570759456353804961562101355551901183 ( 107 digits) SNFS difficulty: 149 digits. Divisors found: r1=2579775523673369950784734958514551180203035362426083 (pp52) r2=19186902085390185374523921439602412837798066940823099701 (pp56) Version: Msieve-1.39 Total time: 12.45 hours. Scaled time: 32.15 units (timescale=2.583). Factorization parameters were as follows: n: 49497900375007139446580117975996554390248271087641053217622845679414045570759456353804961562101355551901183 m: 200000000000000000000000000000 deg: 5 c5: 1325 c0: -136 skew: 0.63 type: snfs lss: 1 rlim: 2200000 alim: 2200000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 2200000/2200000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [1100000, 3100001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 402501 x 402749 Total sieving time: 12.45 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,149,5,0,0,0,0,0,0,0,0,2200000,2200000,26,26,49,49,2.3,2.3,100000 total time: 12.45 hours. --------- CPU info (if available) ----------

(53·10¹⁴³-17)/9 = 5(8)₁₄₂7_<144> = 13² · 29 · 127 · 268114348509373801_<18> · C121
C121 = P52 · P70
P52 = 3197499649810280310555966924736478732434405762799143_<52>
P70 = 1103606817437336719982382319701730917790387846170402709338588861412267_<70>

Number: 58887_143 N=3528782412284122116403286244880646943846723460132929373308594335392789097445085449072815348528186472100920160758037287181 ( 121 digits) SNFS difficulty: 146 digits. Divisors found: r1=3197499649810280310555966924736478732434405762799143 (pp52) r2=1103606817437336719982382319701730917790387846170402709338588861412267 (pp70) Version: Msieve-1.39 Total time: 9.26 hours. Scaled time: 23.82 units (timescale=2.571). Factorization parameters were as follows: n: 3528782412284122116403286244880646943846723460132929373308594335392789097445085449072815348528186472100920160758037287181 m: 50000000000000000000000000000 deg: 5 c5: 424 c0: -425 skew: 1.00 type: snfs lss: 1 rlim: 1910000 alim: 1910000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1910000/1910000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [955000, 2455001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 319640 x 319868 Total sieving time: 9.26 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1910000,1910000,26,26,49,49,2.3,2.3,100000 total time: 9.26 hours. --------- CPU info (if available) ----------

(53·10¹⁶⁴-17)/9 = 5(8)₁₆₃7_<165> = 800977 · C159
C159 = P35 · P43 · P83
P35 = 26420433379971578160086373777968563_<35>
P43 = 1931614398915714664197849198169905631094719_<43>
P83 = 14406316220093108541547534674609427084176701563508733048745187396069463990428743523_<83>

Number: 58887_164 N=735213231951590231540841857992038334295352911368102815547623575819141983963196057925369753299893616032531382160647420448887906754986583745711660745425759901831 ( 159 digits) SNFS difficulty: 166 digits. Divisors found: r1=26420433379971578160086373777968563 (pp35) r2=1931614398915714664197849198169905631094719 (pp43) r3=14406316220093108541547534674609427084176701563508733048745187396069463990428743523 (pp83) Version: Msieve-1.39 Total time: 44.59 hours. Scaled time: 77.54 units (timescale=1.739). Factorization parameters were as follows: n: 735213231951590231540841857992038334295352911368102815547623575819141983963196057925369753299893616032531382160647420448887906754986583745711660745425759901831 m: 1000000000000000000000000000000000 deg: 5 c5: 53 c0: -170 skew: 1.26 type: snfs lss: 1 rlim: 4200000 alim: 4200000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 4200000/4200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [2100000, 4700001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 784296 x 784544 Total sieving time: 44.59 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000 total time: 44.59 hours. --------- CPU info (if available) ----------

Apr 24, 2009 (2nd)

By Robert Backstrom / GGNFS, GMP-ECM, Msieve / Apr 24, 2009
(53·10¹²⁸-17)/9 = 5(8)₁₂₇7_<129> = 23 · 63691 · 4788800872882184084781263_<25> · C98
C98 = P48 · P51
P48 = 112604159725354687671910018636786167653258924591_<48>
P51 = 745497589659523189147719856571126344213064487387523_<51>

Number: n N=83946129660887876362622100012087832005382299917977951928607011873563078474950417997646958051278093 ( 98 digits) SNFS difficulty: 131 digits. Divisors found: r1=112604159725354687671910018636786167653258924591 (pp48) r2=745497589659523189147719856571126344213064487387523 (pp51) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 2.60 hours. Scaled time: 6.88 units (timescale=2.649). Factorization parameters were as follows: name: KA_5_8_127_7 n: 83946129660887876362622100012087832005382299917977951928607011873563078474950417997646958051278093 m: 50000000000000000000000000 deg: 5 c5: 424 c0: -425 skew: 1.00 type: snfs lss: 1 rlim: 1070000 alim: 1070000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 qintsize: 20000 Factor base limits: 1070000/1070000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [535000, 1055001) Primes: RFBsize:83548, AFBsize:84061, largePrimes:2777007 encountered Relations: rels:2655347, finalFF:192381 Max relations in full relation-set: 28 Initial matrix: 167676 x 192381 with sparse part having weight 15348036. Pruned matrix : 160977 x 161879 with weight 10790182. Total sieving time: 2.33 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.06 hours. Total square root time: 0.14 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,1070000,1070000,26,26,47,47,2.3,2.3,50000 total time: 2.60 hours. --------- CPU info (if available) ----------

(53·10¹⁴⁴-17)/9 = 5(8)₁₄₃7_<145> = 17519 · 106957 · 6636577684770897967_<19> · C117
C117 = P36 · P81
P36 = 493043766422451686167629421455051011_<36>
P81 = 960473041699645228846742337228722619911387336255548265515490052356974875912822097_<81>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM] Input number is 473555246026821580479096651610338154141012072413920587982512535283509902483472861171889354142003106781845080102990067 (117 digits) Using B1=2400000, B2=3567796060, polynomial Dickson(6), sigma=4105013632 Step 1 took 26785ms Step 2 took 9594ms ********** Factor found in step 2: 493043766422451686167629421455051011 Found probable prime factor of 36 digits: 493043766422451686167629421455051011 Probable prime cofactor 960473041699645228846742337228722619911387336255548265515490052356974875912822097 has 81 digits

(17·10¹⁶⁷-53)/9 = 1(8)₁₆₆3_<168> = 3² · 2842894383216641696187208791071_<31> · C136
C136 = P48 · P88
P48 = 823828965221082614714987491762129205824830523981_<48>
P88 = 8961198957496977939253687411601927777122185598907503134441460972542651247105156582110937_<88>

Number: n N=7382495264294979622827850118446254916311984354166976601889891234115975629567482988730135681174541273056980748634482050644700216780880197 ( 136 digits) SNFS difficulty: 169 digits. Divisors found: Fri Apr 24 20:49:26 2009 prp48 factor: 823828965221082614714987491762129205824830523981 Fri Apr 24 20:49:26 2009 prp88 factor: 8961198957496977939253687411601927777122185598907503134441460972542651247105156582110937 Fri Apr 24 20:49:26 2009 elapsed time 01:44:44 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 56.29 hours. Scaled time: 149.11 units (timescale=2.649). Factorization parameters were as follows: name: KA_1_8_166_3 n: 7382495264294979622827850118446254916311984354166976601889891234115975629567482988730135681174541273056980748634482050644700216780880197 m: 2000000000000000000000000000000000 deg: 5 c5: 425 c0: -424 skew: 1.00 type: snfs lss: 1 rlim: 4600000 alim: 4600000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4600000/4600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2300000, 5636291) Primes: RFBsize:322441, AFBsize:322881, largePrimes:16952467 encountered Relations: rels:16721012, finalFF:607071 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 2174169 hash collisions in 18710656 relations Msieve: matrix is 829496 x 829744 (220.4 MB) Total sieving time: 55.50 hours. Total relation processing time: 0.79 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,169,5,0,0,0,0,0,0,0,0,4600000,4600000,28,28,56,56,2.4,2.4,100000 total time: 56.29 hours. --------- CPU info (if available) ----------

Apr 24, 2009

By Erik Branger / GGNFS, Msieve / Apr 24, 2009
(53·10¹³⁷-17)/9 = 5(8)₁₃₆7_<138> = 13 · 257 · 1187573234723866457_<19> · C117
C117 = P49 · P68
P49 = 5584838927938453061724271226184215519985376889149_<49>
P68 = 26575768460269751918333188566808886042747046132589556424376472164199_<68>

Number: 58887_137 N=148421386236793474713355586446923384287979293005900666819660923606388680051470227246194467606188867817466602149376651 ( 117 digits) SNFS difficulty: 139 digits. Divisors found: r1=5584838927938453061724271226184215519985376889149 r2=26575768460269751918333188566808886042747046132589556424376472164199 Version: Total time: 7.27 hours. Scaled time: 7.31 units (timescale=1.005). Factorization parameters were as follows: n: 148421386236793474713355586446923384287979293005900666819660923606388680051470227246194467606188867817466602149376651 m: 2000000000000000000000000000 deg: 5 c5: 1325 c0: -136 skew: 0.63 type: snfs lss: 1 rlim: 1490000 alim: 1490000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3Factor base limits: 1490000/1490000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [745000, 1645001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 265186 x 265427 Total sieving time: 7.27 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,139,5,0,0,0,0,0,0,0,0,1490000,1490000,26,26,48,48,2.3,2.3,75000 total time: 7.27 hours. --------- CPU info (if available) ----------

(53·10¹²⁶-17)/9 = 5(8)₁₂₅7_<127> = 139 · 2152525333033_<13> · C113
C113 = P49 · P64
P49 = 4186857306152507699817842593643290853547861453707_<49>
P64 = 4700912079944416830169055586945991616973525269591821004558075543_<64>

Number: 58887_126 N=19682048087495862967660904785941718578127783173067256935609610238613756161755275463953558441169432519094303387901 ( 113 digits) SNFS difficulty: 128 digits. Divisors found: r1=4186857306152507699817842593643290853547861453707 r2=4700912079944416830169055586945991616973525269591821004558075543 Version: Total time: 3.85 hours. Scaled time: 3.00 units (timescale=0.779). Factorization parameters were as follows: n: 19682048087495862967660904785941718578127783173067256935609610238613756161755275463953558441169432519094303387901 m: 20000000000000000000000000 deg: 5 c5: 265 c0: -272 skew: 1.01 type: snfs lss: 1 rlim: 990000 alim: 990000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 990000/990000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [495000, 895001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 157081 x 157329 Total sieving time: 3.85 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,128,5,0,0,0,0,0,0,0,0,990000,990000,26,26,47,47,2.3,2.3,50000 total time: 3.85 hours. --------- CPU info (if available) ----------

Apr 23, 2009 (5th)

By Ignacio Santos / GGNFS, Msieve / Apr 23, 2009
(35·10¹⁷⁶-71)/9 = 3(8)₁₇₅1_<177> = 3² · 367 · 232568767 · 60323230600525753781_<20> · 8193256915460198815721_<22> · C124
C124 = P61 · P63
P61 = 1320105305128237839759047437665736026132731396793537417927679_<61>
P63 = 775918004093695593851387986591834584873455900442876905422417139_<63>

Number: 38881_176 N=1024293473548601319173469912038505104746286056967893105461707929204618101281103354521416633306699402398601839123952472090381 ( 124 digits) Divisors found: r1=1320105305128237839759047437665736026132731396793537417927679 (pp61) r2=775918004093695593851387986591834584873455900442876905422417139 (pp63) Version: Msieve-1.39 Total time: 61.25 hours. Scaled time: 156.80 units (timescale=2.560). Factorization parameters were as follows: # Murphy_E = 1.931282e-10, selected by Jeff Gilchrist n: 1024293473548601319173469912038505104746286056967893105461707929204618101281103354521416633306699402398601839123952472090381 Y0: -520935780629937847389521 Y1: 22406701384781 c0: -94888778317472415354353368632 c1: 14232405039257419376998134 c2: -339826485793637340641 c3: -3544791087233806 c4: -11143299794 c5: 26700 skew: 129910.61 type: gnfs # selected mechanically rlim: 6300000 alim: 6300000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 Factor base limits: 6300000/6300000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved algebraic special-q in [3150000, 5970001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 917653 x 917901 Total sieving time: 61.25 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,123,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,6300000,6300000,27,27,52,52,2.5,2.5,60000 total time: 61.25 hours. --------- CPU info (if available) ----------

(53·10¹²⁹-17)/9 = 5(8)₁₂₈7_<130> = 7 · 4623547 · 5222837 · C116
C116 = P35 · P81
P35 = 57168349928028616133688579199585387_<35>
P81 = 609393635442267750361101031452473824611828346367866478338485749744303280641982437_<81>

Number: 58887_129 N=34838028594877064284253557354927967622169804547748141483986966848529666618721039767304379796183953057786696135848119 ( 116 digits) SNFS difficulty: 131 digits. Divisors found: r1=57168349928028616133688579199585387 (pp35) r2=609393635442267750361101031452473824611828346367866478338485749744303280641982437 (pp81) Version: Msieve-1.39 Total time: 2.82 hours. Scaled time: 7.26 units (timescale=2.571). Factorization parameters were as follows: n: 34838028594877064284253557354927967622169804547748141483986966848529666618721039767304379796183953057786696135848119 m: 100000000000000000000000000 deg: 5 c5: 53 c0: -170 skew: 1.26 type: snfs lss: 1 rlim: 1100000 alim: 1100000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1100000/1100000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [550000, 1050001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 160216 x 160464 Total sieving time: 2.82 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000 total time: 2.82 hours. --------- CPU info (if available) ----------

Apr 23, 2009 (4th)

By Robert Backstrom / GGNFS, Msieve / Apr 23, 2009
(53·10¹⁶⁷-71)/9 = 5(8)₁₆₆1_<168> = 73 · 769 · 66501587107_<11> · 353614322081_<12> · C141
C141 = P41 · P101
P41 = 15289508170453564157615559715265886034189_<41>
P101 = 29176204089714079058424787149185032695439825811546932354672800303249154820310505588922930701582824751_<101>

Number: n N=446089810812504105158182504969145136704663270654799288006352123575641893590592744605656997178397333941887287764109361491827634663159581411939 ( 141 digits) SNFS difficulty: 169 digits. Divisors found: Thu Apr 23 06:30:42 2009 prp41 factor: 15289508170453564157615559715265886034189 Thu Apr 23 06:30:42 2009 prp101 factor: 29176204089714079058424787149185032695439825811546932354672800303249154820310505588922930701582824751 Thu Apr 23 06:30:42 2009 elapsed time 01:28:32 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 61.86 hours. Scaled time: 164.56 units (timescale=2.660). Factorization parameters were as follows: name: KA_5_8_166_1 n: 446089810812504105158182504969145136704663270654799288006352123575641893590592744605656997178397333941887287764109361491827634663159581411939 m: 2000000000000000000000000000000000 deg: 5 c5: 1325 c0: -568 skew: 0.84 type: snfs lss: 1 rlim: 4700000 alim: 4700000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4700000/4700000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2350000, 6054613) Primes: RFBsize:328964, AFBsize:327815, largePrimes:17382610 encountered Relations: rels:17432208, finalFF:658654 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 2355284 hash collisions in 19429834 relations Msieve: matrix is 837045 x 837293 (221.6 MB) Total sieving time: 60.95 hours. Total relation processing time: 0.91 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,169,5,0,0,0,0,0,0,0,0,4700000,4700000,28,28,56,56,2.4,2.4,100000 total time: 61.86 hours. --------- CPU info (if available) ----------

(52·10¹⁶⁴-43)/9 = 5(7)₁₆₃3_<165> = 3 · 241 · 107897 · 36883061 · 6612904342793249107_<19> · C131
C131 = P57 · P74
P57 = 428137267533980125175224262378383639832168779350627365977_<57>
P74 = 70926893194183362183806185858869881540459489448292533660130576984615410977_<74>

Number: n N=30366446246832116288365725625880877232177375057371824681954491156869978949948474947696757112176249442217908790306207886226842129529 ( 131 digits) SNFS difficulty: 166 digits. Divisors found: Thu Apr 23 22:54:37 2009 prp57 factor: 428137267533980125175224262378383639832168779350627365977 Thu Apr 23 22:54:37 2009 prp74 factor: 70926893194183362183806185858869881540459489448292533660130576984615410977 Thu Apr 23 22:54:37 2009 elapsed time 01:04:41 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 36.73 hours. Scaled time: 97.29 units (timescale=2.649). Factorization parameters were as follows: name: KA_5_7_163_3 n: 30366446246832116288365725625880877232177375057371824681954491156869978949948474947696757112176249442217908790306207886226842129529 m: 1000000000000000000000000000000000 deg: 5 c5: 26 c0: -215 skew: 1.53 type: snfs lss: 1 rlim: 4200000 alim: 4200000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4200000/4200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2100000, 4258643) Primes: RFBsize:296314, AFBsize:296491, largePrimes:15450463 encountered Relations: rels:14663369, finalFF:610735 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1605925 hash collisions in 16362314 relations Msieve: matrix is 745844 x 746092 (199.0 MB) Total sieving time: 36.28 hours. Total relation processing time: 0.44 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,4200000,4200000,28,28,56,56,2.4,2.4,100000 total time: 36.73 hours. --------- CPU info (if available) ----------

(53·10¹⁰⁹-17)/9 = 5(8)₁₀₈7_<110> = 3 · 19 · 479 · 34483 · 62171 · C97
C97 = P43 · P54
P43 = 1184825813345484206359746383415693747268967_<43>
P54 = 849132744499225818718955971430604327755370155419332359_<54>

Number: n N=1006074394639578460861665960829727793726759540115934699440062720584295891926720766143730739603153 ( 97 digits) SNFS difficulty: 111 digits. Divisors found: r1=1184825813345484206359746383415693747268967 (pp43) r2=849132744499225818718955971430604327755370155419332359 (pp54) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 0.60 hours. Scaled time: 1.56 units (timescale=2.627). Factorization parameters were as follows: name: KA_5_8_108_7 n: 1006074394639578460861665960829727793726759540115934699440062720584295891926720766143730739603153 m: 10000000000000000000000 deg: 5 c5: 53 c0: -170 skew: 1.26 type: snfs lss: 1 rlim: 510000 alim: 510000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 qintsize: 20000 Factor base limits: 510000/510000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [255000, 395001) Primes: RFBsize:42291, AFBsize:42411, largePrimes:1076456 encountered Relations: rels:1001878, finalFF:95374 Max relations in full relation-set: 28 Initial matrix: 84767 x 95374 with sparse part having weight 4131287. Pruned matrix : 78247 x 78734 with weight 2783143. Total sieving time: 0.55 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.01 hours. Total square root time: 0.02 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,111,5,0,0,0,0,0,0,0,0,510000,510000,25,25,44,44,2.2,2.2,50000 total time: 0.60 hours. --------- CPU info (if available) ----------

Apr 23, 2009 (3rd)

By Serge Batalov / GMP-ECM 6.2.2, Msieve-1.41 / Apr 23, 2009
(53·10¹²⁴-17)/9 = 5(8)₁₂₃7_<125> = 3 · 89 · 1191809 · 4836787 · C110
C110 = P33 · P78
P33 = 162409129263521507054727247357759_<33>
P78 = 235585218437968568279588300257584868514845787402833345248144612223210092321113_<78>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1932810670 Step 1 took 7136ms Step 2 took 9389ms ********** Factor found in step 2: 162409129263521507054727247357759 Found probable prime factor of 33 digits: 162409129263521507054727247357759 Probable prime cofactor has 78 digits

(53·10¹⁰²-17)/9 = 5(8)₁₀₁7_<103> = 59 · 1399 · C98
C98 = P49 · P50
P49 = 3536462375192796870546965456753026665578804701991_<49>
P50 = 20174119642955981100844036468742758967519435241877_<50>

SNFS difficulty: 105 digits. Divisors found: r1=3536462375192796870546965456753026665578804701991 (pp49) r2=20174119642955981100844036468742758967519435241877 (pp50) Version: Msieve-1.40 Total time: 0.42 hours. Scaled time: 0.84 units (timescale=2.015). Factorization parameters were as follows: n: 71345015069951768077547992983958140668139335468299255992644732785995915834420335213880239988477107 m: 50000000000000000000000000 deg: 4 c4: 212 c0: -425 skew: 1.19 type: snfs lss: 1 rlim: 400000 alim: 400000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 Factor base limits: 400000/400000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [200000, 320001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 34633 x 34864 Total sieving time: 0.40 hours. Total relation processing time: 0.01 hours. Matrix solve time: 0.01 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,105.000,4,0,0,0,0,0,0,0,0,400000,400000,25,25,44,44,2.2,2.2,20000 total time: 0.42 hours.

(53·10¹⁰⁴-17)/9 = 5(8)₁₀₃7_<105> = 409 · 34159 · C98
C98 = P38 · P60
P38 = 66094496635789648498726769864747288141_<38>
P60 = 637734048402595454621522275124133541105908678950119792488997_<60>

SNFS difficulty: 105 digits. Divisors found: r1=66094496635789648498726769864747288141 (pp38) r2=637734048402595454621522275124133541105908678950119792488997 (pp60) Version: Msieve-1.41 Total time: 0.42 hours. Scaled time: 0.84 units (timescale=1.848). Factorization parameters were as follows: n: 42150710916673858134656553899915395570225911665995794361124020760449882967755843422642816331084577 m: 100000000000000000000000000 deg: 4 c4: 53 c0: -17 skew: 0.75 type: snfs lss: 1 rlim: 400000 alim: 400000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 Factor base limits: 400000/400000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [200000, 260001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 39510 x 39752 Total sieving time: 0.40 hours. Total relation processing time: 0.01 hours. Matrix solve time: 0.01 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,105,4,0,0,0,0,0,0,0,0,400000,400000,25,25,44,44,2.2,2.2,20000 total time: 0.42 hours.

(53·10¹⁹³-17)/9 = 5(8)₁₉₂7_<194> = 3³ · 7018213 · 17851313 · 679746483103291781_<18> · C161
C161 = P32 · C130
P32 = 20572446508725500234225553940201_<32>
C130 = [1244915789843555096011732458304270596627375015872090006518666492540398283834017403659916118975910672983647063299114503997601252229_<130>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=376038659 Step 1 took 11933ms Step 2 took 12688ms ********** Factor found in step 2: 20572446508725500234225553940201 Found probable prime factor of 32 digits: 20572446508725500234225553940201 Composite cofactor has 130 digits

(53·10²⁰¹-17)/9 = 5(8)₂₀₀7_<202> = 7 · 941 · 5749 · 33767 · 276508825669_<12> · 296805472688401_<15> · C164
C164 = P31 · P133
P31 = 7137096825470911352763152350693_<31>
P133 = 7862459463037571684520567683265681573742169480804138362430647497393328622184882892466314752452755748772299349279963553756975752154591_<133>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1668989920 Step 1 took 11501ms Step 2 took 12549ms ********** Factor found in step 2: 7137096825470911352763152350693 Found probable prime factor of 31 digits: 7137096825470911352763152350693 Probable prime cofactor has 133 digits

(53·10¹⁹⁷-17)/9 = 5(8)₁₉₆7_<198> = 13 · 97 · 1381 · 8093 · 199895588321879_<15> · C174
C174 = P33 · P142
P33 = 124131209152910945615138358610613_<33>
P142 = 1683956464285538192987701175282364657277752256350514234040551728309986650671586386857006585378655255901615254486990382871923560979892400767137_<142>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3750431010 Step 1 took 12365ms Step 2 took 12241ms ********** Factor found in step 2: 124131209152910945615138358610613 Found probable prime factor of 33 digits: 124131209152910945615138358610613 Probable prime cofactor has 142 digits

(53·10¹³⁰-17)/9 = 5(8)₁₂₉7_<131> = 3² · 31 · 1787 · 689561 · 1251681026599_<13> · C108
C108 = P34 · P74
P34 = 2684522574849883505513247949489097_<34>
P74 = 50976637352551995002585907351700594122427409787504925659946717615102657493_<74>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=2846608915 Step 1 took 7404ms Step 2 took 5757ms ********** Factor found in step 2: 2684522574849883505513247949489097 Found probable prime factor of 34 digits: 2684522574849883505513247949489097 Probable prime cofactor has 74 digits

(53·10¹⁴⁸-17)/9 = 5(8)₁₄₇7_<149> = 3² · 1669 · 27337 · 218487524683_<12> · 66654703895377530032933214908629_<32> · C97
C97 = P49 · P49
P49 = 1293513234549944335404040049217391458765838967629_<49>
P49 = 7612991358325177921065847363673485843300748322977_<49>

N=9847505076507975189294121039002185454967285936943322205169240479190597831569216491897858739911533 ( 97 digits) Divisors found: r1=1293513234549944335404040049217391458765838967629 (pp49) r2=7612991358325177921065847363673485843300748322977 (pp49) Version: Msieve-1.40 Total time: 2.08 hours. Factorization parameters were as follows: n: 9847505076507975189294121039002185454967285936943322205169240479190597831569216491897858739911533 skew: 3372.48 # norm 5.25e+13 c5: 140400 c4: -913012644 c3: -6915870530610 c2: 2736702776419444 c1: 6677853531088220367 c0: 9789361965300509717732 # alpha -6.05 Y1: 1013445211 Y0: -2339871812921506437 # Murphy_E 4.64e-09 # M 1911477931379528567900052509646008537492807656147084893400253968977167626506619701535654175781347 type: gnfs rlim: 1200000 alim: 1200000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved algebraic special-q in [600000, 1020001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 137001 x 137249 Polynomial selection time: 0.26 hours. Total sieving time: 1.60 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.07 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: gnfs,96,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000 total time: 2.08 hours.

(53·10¹³⁸-17)/9 = 5(8)₁₃₇7_<139> = C139
C139 = P50 · P90
P50 = 14212328108433255333011168440885868143857201519173_<50>
P90 = 414350755482105931010853345568490156490520800534066379136735288507168858874680066897030219_<90>

SNFS difficulty: 141 digits. Divisors found: r1=14212328108433255333011168440885868143857201519173 (pp50) r2=414350755482105931010853345568490156490520800534066379136735288507168858874680066897030219 (pp90) Version: Msieve-1.40 Total time: 6.39 hours. Factorization parameters were as follows: n: 5888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888887 m: 5000000000000000000000000000 deg: 5 c5: 424 c0: -425 skew: 1.00 type: snfs lss: 1 rlim: 1570000 alim: 1570000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1570000/1570000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [785000, 1885001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 260637 x 260870 Total sieving time: 6.00 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.10 hours. Time per square root: 0.23 hours. Prototype def-par.txt line would be: snfs,141.000,5,0,0,0,0,0,0,0,0,1570000,1570000,26,26,48,48,2.3,2.3,100000 total time: 6.39 hours.

Apr 23, 2009 (2nd)

By matsui / GGNFS / Apr 23, 2009
5·10¹⁶⁹+3 = 5(0)₁₆₈3_<170> = 31 · 16244243 · 29298332253113065055747_<23> · C139
C139 = P63 · P77
P63 = 219470599991522042446043080605252718567618567796903842516245509_<63>
P77 = 15441503431769976028446348762595181204879730780351588237227771804855548607617_<77>

N=3388956022941703290284911268189108916185410146351262338185883006343651520714919578492806480155277094510806544535131569600239126927479442053 ( 139 digits) SNFS difficulty: 170 digits. Divisors found: r1=219470599991522042446043080605252718567618567796903842516245509 (pp63) r2=15441503431769976028446348762595181204879730780351588237227771804855548607617 (pp77) Version: GGNFS-0.77.1-20060722-nocona

Apr 23, 2009

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Apr 23, 2009
(52·10¹⁶⁵-43)/9 = 5(7)₁₆₄3_<166> = 2132023 · 139451311 · 41362644195312023971_<20> · C132
C132 = P43 · P90
P43 = 2212108396188581657218483107142706525530369_<43>
P90 = 212388818457277709952441788024194276072656999962330691651813192423763170730676394041761159_<90>

Number: 57773_165 N=469827088565916424848798223220483523992904480604340677368464169830717413232119283714579864983812929914816116960729561312397299137671 ( 132 digits) SNFS difficulty: 166 digits. Divisors found: r1=2212108396188581657218483107142706525530369 r2=212388818457277709952441788024194276072656999962330691651813192423763170730676394041761159 Version: Total time: 24.79 hours. Scaled time: 58.87 units (timescale=2.375). Factorization parameters were as follows: n: 469827088565916424848798223220483523992904480604340677368464169830717413232119283714579864983812929914816116960729561312397299137671 m: 1000000000000000000000000000000000 deg: 5 c5: 52 c0: -43 skew: 0.96 type: snfs lss: 1 rlim: 4800000 alim: 4800000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 4800000/4800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [2400000, 4400001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9737720 Max relations in full relation-set: Initial matrix: Pruned matrix : 825721 x 825969 Total sieving time: 22.27 hours. Total relation processing time: 0.94 hours. Matrix solve time: 1.48 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,4800000,4800000,27,27,51,51,2.4,2.4,100000 total time: 24.79 hours. --------- CPU info (if available) ----------

Apr 22, 2009 (6th)

By Ignacio Santos / GGNFS, Msieve / Apr 22, 2009
(4·10¹⁸¹+17)/3 = 1(3)₁₈₀9_<182> = 19 · 199 · 1453 · C175
C175 = P56 · P57 · P63
P56 = 22309717107372494315385593361862526662022588401333102253_<56>
P57 = 156122557936970418953523058188454015963068329714979720107_<57>
P63 = 696797723896822116787571000843431402872490055258855522222137813_<63>

Number: 13339_181 N=2426981383050532361400098863086638563435741633027187834221881554935421362496427028345140294389201291954999639289891944114627786910306473748343509362899791334208138772853897723 ( 175 digits) SNFS difficulty: 181 digits. Divisors found: r1=22309717107372494315385593361862526662022588401333102253 (pp56) r2=156122557936970418953523058188454015963068329714979720107 (pp57) r3=696797723896822116787571000843431402872490055258855522222137813 (pp63) Version: Msieve-1.39 Total time: 131.58 hours. Scaled time: 228.81 units (timescale=1.739). Factorization parameters were as follows: n: 2426981383050532361400098863086638563435741633027187834221881554935421362496427028345140294389201291954999639289891944114627786910306473748343509362899791334208138772853897723 m: 1000000000000000000000000000000000000 deg: 5 c5: 40 c0: 17 skew: 0.84 type: snfs lss: 1 rlim: 7400000 alim: 7400000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3700000, 5900001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1446798 x 1447043 Total sieving time: 131.58 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,181,5,0,0,0,0,0,0,0,0,7400000,7400000,28,28,53,53,2.5,2.5,100000 total time: 131.58 hours. --------- CPU info (if available) ----------

(8·10¹⁷³-11)/3 = 2(6)₁₇₂3_<174> = 26026517172463_<14> · 835337687643105193_<18> · 133430923595218323637_<21> · C122
C122 = P40 · P83
P40 = 2420995607054671044108003821518248239767_<40>
P83 = 37969957194046514176647750464622844630717776681886775745942777306692010895939678283_<83>

Number: 26663_173 N=91925099566840514579862159855723574163615261031069756391977117342379508653758020321481439131791263848497042220577026880061 ( 122 digits) Divisors found: r1=2420995607054671044108003821518248239767 (pp40) r2=37969957194046514176647750464622844630717776681886775745942777306692010895939678283 (pp83) Version: Msieve-1.39 Total time: 54.53 hours. Scaled time: 140.20 units (timescale=2.571). Factorization parameters were as follows: # Murphy_E = 2.150701e-10, selected by Jeff Gilchrist n: 91925099566840514579862159855723574163615261031069756391977117342379508653758020321481439131791263848497042220577026880061 Y0: -349452957735598923964078 Y1: 10362996766331 c0: -1062632721513365353062035043615 c1: 316697255897387397597827777 c2: 1563572907539943899645 c3: -3712873729966849 c4: -11060071302 c5: 17640 skew: 347138.3 type: gnfs # selected mechanically rlim: 5900000 alim: 5900000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 Factor base limits: 5900000/5900000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved algebraic special-q in [2950000, 5470001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 809289 x 809537 Total sieving time: 54.53 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,121,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5900000,5900000,27,27,52,52,2.5,2.5,60000 total time: 54.53 hours. --------- CPU info (if available) ----------

Apr 22, 2009 (5th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Apr 21, 2009
(17·10¹⁶⁴+7)/3 = 5(6)₁₆₃9_<165> = 631 · 20411 · 546745561 · 36771006513555924569_<20> · C130
C130 = P53 · P77
P53 = 24684467871388862668725282027781049084155761016849459_<53>
P77 = 88658314742674979794126359600408571068896112076998888313552681943961026591339_<77>

Number: 56669_164 N=2188483321797042080199208926466285626226356003556927267628384147997644819195672652362693649569098240692076340501181169127676235601 ( 130 digits) SNFS difficulty: 166 digits. Divisors found: r1=24684467871388862668725282027781049084155761016849459 r2=88658314742674979794126359600408571068896112076998888313552681943961026591339 Version: Total time: 21.83 hours. Scaled time: 52.00 units (timescale=2.382). Factorization parameters were as follows: n: 2188483321797042080199208926466285626226356003556927267628384147997644819195672652362693649569098240692076340501181169127676235601 m: 1000000000000000000000000000000000 deg: 5 c5: 17 c0: 70 skew: 1.33 type: snfs lss: 1 rlim: 4400000 alim: 4400000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 4400000/4400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [2200000, 4000001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9658440 Max relations in full relation-set: Initial matrix: Pruned matrix : 757735 x 757983 Total sieving time: 19.70 hours. Total relation processing time: 0.84 hours. Matrix solve time: 1.21 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,4400000,4400000,27,27,51,51,2.4,2.4,100000 total time: 21.83 hours. --------- CPU info (if available) ----------

By Jo Yeong Uk / GMP-ECM / Apr 22, 2009
2·10¹⁸³-1 = 1(9)_183<184> = 298385575419109_<15> · C169
C169 = P39 · P131
P39 = 138315648629492573181397043870991531509_<39>
P131 = 48459714744214666303053112592352799187563839995254738535415184574936072669072865614713121962535167281027204906904020713946527407079_<131>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 6702736877246236350782731803505581851819006651598315170749396069506347157382739930428866242940491670173578185223001548816068081968260436967719825339733369220980898152211 (169 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3048775659 Step 1 took 16609ms Step 2 took 7140ms ********** Factor found in step 2: 138315648629492573181397043870991531509 Found probable prime factor of 39 digits: 138315648629492573181397043870991531509 Probable prime cofactor 48459714744214666303053112592352799187563839995254738535415184574936072669072865614713121962535167281027204906904020713946527407079 has 131 digits

Apr 22, 2009 (4th)

By matsui / GGNFS / Apr 22, 2009
7·10¹⁷⁵+1 = 7(0)₁₇₄1_<176> = 17 · 43 · 16106554067_<11> · C163
C163 = P42 · P50 · P72
P42 = 546424038802294846052914856058998495168369_<42>
P50 = 50847756028512910420533268455094582971422236487293_<50>
P72 = 213981604431953258247908719407251822585834319843385691315588724389559589_<72>

N=5945358239123625634011428660866607620137468294219930437924782752600840851464522625179701735071778160104909516766334428716890094478708550908337237518092811760086913 ( 163 digits) SNFS difficulty: 175 digits. Divisors found: r1=546424038802294846052914856058998495168369 (pp42) r2=50847756028512910420533268455094582971422236487293 (pp50) r3=213981604431953258247908719407251822585834319843385691315588724389559589 (pp72) Version: GGNFS-0.77.1-20060722-nocona

Apr 22, 2009 (3rd)

By Sinkiti Sibata / GGNFS / Apr 22, 2009
5·10¹⁸⁸+9 = 5(0)₁₈₇9_<189> = 89 · 20644698707_<11> · 2095779451075181845289_<22> · 17069365974029360492115172688628301_<35> · C121
C121 = P54 · P68
P54 = 112851366896191612350337923343819108022586261622918801_<54>
P68 = 67406481306382958257320834957187828313474877802170323638967682116047_<68>

Number: 50009_188 N=7606913553087904523289891655928436341384431709516903459521491661869372564112334503851881776661479063881775251744140099647 ( 121 digits) Divisors found: r1=112851366896191612350337923343819108022586261622918801 (pp54) r2=67406481306382958257320834957187828313474877802170323638967682116047 (pp68) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 140.12 hours. Scaled time: 62.64 units (timescale=0.447). Factorization parameters were as follows: name: 50009_188 n: 7606913553087904523289891655928436341384431709516903459521491661869372564112334503851881776661479063881775251744140099647 skew: 109016.74 # norm 2.11e+16 c5: 5700 c4: 4393438342 c3: -159644453182350 c2: -66523826013641583182 c1: -1678125279183183409996345 c0: 13790779317453160370267289525 # alpha -5.21 Y1: 9695498203633 Y0: -266111893921478002019566 # Murphy_E 2.41e-10 # M 5755240981910880162683132603904024483240966666901395640250549525151778137375628477746712617517491336934374610157755148949 type: gnfs rlim: 5000000 alim: 5000000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2500000, 5380001) Primes: RFBsize:348513, AFBsize:347346, largePrimes:7784026 encountered Relations: rels:7980316, finalFF:810325 Max relations in full relation-set: 28 Initial matrix: 695939 x 810325 with sparse part having weight 73710325. Pruned matrix : 602700 x 606243 with weight 51408708. Total sieving time: 117.79 hours. Total relation processing time: 1.23 hours. Matrix solve time: 20.51 hours. Time per square root: 0.59 hours. Prototype def-par.txt line would be: gnfs,120,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.4,2.4,60000 total time: 140.12 hours. --------- CPU info (if available) ----------

Apr 22, 2009 (2nd)

By Robert Backstrom / GGNFS / Apr 22, 2009
(53·10¹⁶²-71)/9 = 5(8)₁₆₁1_<163> = 70679701 · 44026722517_<11> · 1236279080219216121922252206884753_<34> · C112
C112 = P42 · P70
P42 = 443544821402465146063268358238856200246841_<42>
P70 = 3451185210796963823875477889316547070862232437023870711320410226459441_<70>

Number: KA_5_8_161_1 N=1530755327949768346559116010704472935748277600679650175511082917507123042329452736442582425054160912093674875881 ( 112 digits) Divisors found: r1=443544821402465146063268358238856200246841 (pp42) r2=3451185210796963823875477889316547070862232437023870711320410226459441 (pp70) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 15.86 hours. Scaled time: 42.37 units (timescale=2.671). Factorization parameters were as follows: n: 1530755327949768346559116010704472935748277600679650175511082917507123042329452736442582425054160912093674875881 Y0: -2793386256401126466886 Y1: 580659604429 c0: 1249418291818091229406104855 c1: 87816497597904215717963 c2: -2303223579921404027 c3: -109127595890605 c4: 828480114 c5: 9000 skew: 36890.51 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved algebraic special-q in [1750000, 2400001) Primes: RFBsize:250150, AFBsize:250833, largePrimes:16869364 encountered Relations: rels:15156758, finalFF:588554 Max relations in full relation-set: 28 Initial matrix: 501060 x 588554 with sparse part having weight 51733363. Pruned matrix : 430049 x 432618 with weight 33187546. Total sieving time: 14.33 hours. Total relation processing time: 0.49 hours. Matrix solve time: 0.80 hours. Total square root time: 0.25 hours, sqrts: 1. Prototype def-par.txt line would be: gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,28,28,56,56,2.6,2.6,100000 total time: 15.86 hours. --------- CPU info (if available) ----------

Apr 22, 2009

Factorizations of 588...887 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Apr 21, 2009 (5th)

By Wataru Sakai / GMP-ECM / Apr 21, 2009
8·10¹⁹⁰-9 = 7(9)₁₈₉1_<191> = 31 · 257 · 30319 · 2445649 · 568034078420777_<15> · 1118584622077795641597568510231_<31> · C132
C132 = P46 · P86
P46 = 5956694674603727915072852316779388032674317487_<46>
P86 = 35779774073720156830334101164802233650029559245191540826257705794588243741259881976407_<86>

Apr 21, 2009 (4th)

By Sinkiti Sibata / Msieve / Apr 21, 2009
(13·10¹⁹⁵-1)/3 = 4(3)_195<196> = 7 · C195
C195 = P55 · P141
P55 = 4108959678924632386368511921044689765845824495413027737_<55>
P141 = 150657993122393397191374958950288699170836432534995369715829292300612307048500313165210751477061418430213152010301608423612711599020092518587_<141>

Number: 43333_195 N=619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619 ( 195 digits) SNFS difficulty: 196 digits. Divisors found: r1=4108959678924632386368511921044689765845824495413027737 r2=150657993122393397191374958950288699170836432534995369715829292300612307048500313165210751477061418430213152010301608423612711599020092518587 Version: Total time: 441.44 hours. Scaled time: 1473.97 units (timescale=3.339). Factorization parameters were as follows: name: 43333_195 n: 619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619047619 m: 1000000000000000000000000000000000000000 deg: 5 c5: 13 c0: -1 skew: 0.60 type: snfs rlim: 9500000 alim: 9500000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5 Factor base limits: 9500000/9500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved algebraic special-q in [4750000, 12750001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1926738 x 1926986 Total sieving time: 441.44 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,196,5,0,0,0,0,0,0,0,0,9500000,9500000,28,28,55,55,2.5,2.5,100000 total time: 441.44 hours. --------- CPU info (if available) ----------

Apr 21, 2009 (3rd)

By Andreas Tete / Msieve v1.41, GGNFS / Apr 21, 2009
(52·10¹⁸⁸+11)/9 = 5(7)₁₈₇9_<189> = 3² · 1093 · 5081 · 64231 · 11552017 · 14214270311_<11> · 96882854526001774645678465981_<29> · C131
C131 = P44 · P87
P44 = 81794757600323035554827444059633541274214747_<44>
P87 = 138308699903585154803319669716002943598265094204006724265991671763585624304306433563833_<87>

Mon Apr 20 19:08:11 2009 Mon Apr 20 19:08:11 2009 Mon Apr 20 19:08:11 2009 Msieve v. 1.41 Mon Apr 20 19:08:11 2009 random seeds: 87569ffc 473e86b3 Mon Apr 20 19:08:11 2009 factoring 11312926582629569735706825148931447422166875763212917695378460963807918703953528423373129743219702130852404196787051012831774445251 (131 digits) Mon Apr 20 19:08:12 2009 searching for 15-digit factors Mon Apr 20 19:08:14 2009 commencing number field sieve (131-digit input) Mon Apr 20 19:08:14 2009 R0: -12083212830902574969747860 Mon Apr 20 19:08:14 2009 R1: 213108260669881 Mon Apr 20 19:08:14 2009 A0: 56090967640472498013392023696851 Mon Apr 20 19:08:14 2009 A1: 332754979081695566842805070 Mon Apr 20 19:08:14 2009 A2: -1465196442719012042647 Mon Apr 20 19:08:14 2009 A3: -25753535061241090 Mon Apr 20 19:08:14 2009 A4: 2934479696 Mon Apr 20 19:08:14 2009 A5: 43920 Mon Apr 20 19:08:14 2009 skew 392473.78, size 1.303298e-012, alpha -6.358696, combined = 6.937147e-011 Mon Apr 20 19:08:14 2009 Mon Apr 20 19:08:14 2009 commencing relation filtering Mon Apr 20 19:08:14 2009 commencing duplicate removal, pass 1 Mon Apr 20 19:10:10 2009 error -15 reading relation 9581126 Mon Apr 20 19:10:11 2009 error -15 reading relation 9725613 Mon Apr 20 19:11:18 2009 found 3444048 hash collisions in 15840366 relations Mon Apr 20 19:11:59 2009 added 104414 free relations Mon Apr 20 19:11:59 2009 commencing duplicate removal, pass 2 Mon Apr 20 19:13:09 2009 found 3625670 duplicates and 12319109 unique relations Mon Apr 20 19:13:09 2009 memory use: 106.6 MB Mon Apr 20 19:13:09 2009 reading rational ideals above 10420224 Mon Apr 20 19:13:09 2009 reading algebraic ideals above 10420224 Mon Apr 20 19:13:09 2009 commencing singleton removal, pass 1 Mon Apr 20 19:16:02 2009 relations with 0 large ideals: 374026 Mon Apr 20 19:16:02 2009 relations with 1 large ideals: 2578236 Mon Apr 20 19:16:02 2009 relations with 2 large ideals: 5243824 Mon Apr 20 19:16:02 2009 relations with 3 large ideals: 3361638 Mon Apr 20 19:16:02 2009 relations with 4 large ideals: 647320 Mon Apr 20 19:16:02 2009 relations with 5 large ideals: 15067 Mon Apr 20 19:16:02 2009 relations with 6 large ideals: 98994 Mon Apr 20 19:16:02 2009 relations with 7+ large ideals: 4 Mon Apr 20 19:16:02 2009 12319109 relations and about 11869560 large ideals Mon Apr 20 19:16:02 2009 commencing singleton removal, pass 2 Mon Apr 20 19:18:33 2009 found 5868335 singletons Mon Apr 20 19:18:33 2009 current dataset: 6450774 relations and about 4791520 large ideals Mon Apr 20 19:18:33 2009 commencing singleton removal, pass 3 Mon Apr 20 19:20:20 2009 found 1098994 singletons Mon Apr 20 19:20:20 2009 current dataset: 5351780 relations and about 3626493 large ideals Mon Apr 20 19:20:20 2009 commencing singleton removal, pass 4 Mon Apr 20 19:21:59 2009 found 274520 singletons Mon Apr 20 19:21:59 2009 current dataset: 5077260 relations and about 3346643 large ideals Mon Apr 20 19:21:59 2009 commencing singleton removal, final pass Mon Apr 20 19:23:46 2009 memory use: 74.7 MB Mon Apr 20 19:23:46 2009 commencing in-memory singleton removal Mon Apr 20 19:23:46 2009 begin with 5077260 relations and 3647012 unique ideals Mon Apr 20 19:23:52 2009 reduce to 4263128 relations and 2811805 ideals in 14 passes Mon Apr 20 19:23:52 2009 max relations containing the same ideal: 23 Mon Apr 20 19:23:53 2009 reading rational ideals above 720000 Mon Apr 20 19:23:53 2009 reading algebraic ideals above 720000 Mon Apr 20 19:23:53 2009 commencing singleton removal, final pass Mon Apr 20 19:25:41 2009 keeping 4000705 ideals with weight <= 20, new excess is 343752 Mon Apr 20 19:25:46 2009 memory use: 128.7 MB Mon Apr 20 19:25:46 2009 commencing in-memory singleton removal Mon Apr 20 19:25:47 2009 begin with 4290130 relations and 4000705 unique ideals Mon Apr 20 19:25:54 2009 reduce to 4190944 relations and 3768298 ideals in 12 passes Mon Apr 20 19:25:54 2009 max relations containing the same ideal: 20 Mon Apr 20 19:25:57 2009 removing 149756 relations and 137809 ideals in 11947 cliques Mon Apr 20 19:25:57 2009 commencing in-memory singleton removal Mon Apr 20 19:25:58 2009 begin with 4041188 relations and 3768298 unique ideals Mon Apr 20 19:26:02 2009 reduce to 4037824 relations and 3627111 ideals in 8 passes Mon Apr 20 19:26:02 2009 max relations containing the same ideal: 20 Mon Apr 20 19:26:05 2009 removing 110736 relations and 98789 ideals in 11947 cliques Mon Apr 20 19:26:05 2009 commencing in-memory singleton removal Mon Apr 20 19:26:06 2009 begin with 3927088 relations and 3627111 unique ideals Mon Apr 20 19:26:10 2009 reduce to 3925129 relations and 3526358 ideals in 7 passes Mon Apr 20 19:26:10 2009 max relations containing the same ideal: 20 Mon Apr 20 19:26:11 2009 relations with 0 large ideals: 8781 Mon Apr 20 19:26:11 2009 relations with 1 large ideals: 84877 Mon Apr 20 19:26:11 2009 relations with 2 large ideals: 374180 Mon Apr 20 19:26:11 2009 relations with 3 large ideals: 893493 Mon Apr 20 19:26:11 2009 relations with 4 large ideals: 1203750 Mon Apr 20 19:26:11 2009 relations with 5 large ideals: 907674 Mon Apr 20 19:26:11 2009 relations with 6 large ideals: 366841 Mon Apr 20 19:26:11 2009 relations with 7+ large ideals: 85533 Mon Apr 20 19:26:11 2009 commencing 2-way merge Mon Apr 20 19:26:15 2009 reduce to 2337038 relation sets and 1938267 unique ideals Mon Apr 20 19:26:15 2009 commencing full merge Mon Apr 20 19:26:54 2009 memory use: 175.7 MB Mon Apr 20 19:26:55 2009 found 1180571 cycles, need 1128467 Mon Apr 20 19:26:55 2009 weight of 1128467 cycles is about 79026752 (70.03/cycle) Mon Apr 20 19:26:55 2009 distribution of cycle lengths: Mon Apr 20 19:26:55 2009 1 relations: 128978 Mon Apr 20 19:26:55 2009 2 relations: 137710 Mon Apr 20 19:26:55 2009 3 relations: 137141 Mon Apr 20 19:26:55 2009 4 relations: 123799 Mon Apr 20 19:26:55 2009 5 relations: 109162 Mon Apr 20 19:26:55 2009 6 relations: 93570 Mon Apr 20 19:26:55 2009 7 relations: 78142 Mon Apr 20 19:26:55 2009 8 relations: 66063 Mon Apr 20 19:26:55 2009 9 relations: 55092 Mon Apr 20 19:26:55 2009 10+ relations: 198810 Mon Apr 20 19:26:55 2009 heaviest cycle: 19 relations Mon Apr 20 19:26:55 2009 commencing cycle optimization Mon Apr 20 19:26:58 2009 start with 6454929 relations Mon Apr 20 19:27:15 2009 pruned 170048 relations Mon Apr 20 19:27:15 2009 memory use: 171.3 MB Mon Apr 20 19:27:15 2009 distribution of cycle lengths: Mon Apr 20 19:27:15 2009 1 relations: 128978 Mon Apr 20 19:27:15 2009 2 relations: 141126 Mon Apr 20 19:27:15 2009 3 relations: 142718 Mon Apr 20 19:27:15 2009 4 relations: 126930 Mon Apr 20 19:27:15 2009 5 relations: 112065 Mon Apr 20 19:27:15 2009 6 relations: 94751 Mon Apr 20 19:27:15 2009 7 relations: 78734 Mon Apr 20 19:27:15 2009 8 relations: 65542 Mon Apr 20 19:27:15 2009 9 relations: 54402 Mon Apr 20 19:27:15 2009 10+ relations: 183221 Mon Apr 20 19:27:15 2009 heaviest cycle: 19 relations Mon Apr 20 19:27:17 2009 RelProcTime: 895 Mon Apr 20 19:27:17 2009 Mon Apr 20 19:27:17 2009 commencing linear algebra Mon Apr 20 19:27:17 2009 read 1128467 cycles Mon Apr 20 19:27:20 2009 cycles contain 3583964 unique relations Mon Apr 20 19:28:27 2009 read 3583964 relations Mon Apr 20 19:28:33 2009 using 20 quadratic characters above 268430840 Mon Apr 20 19:28:56 2009 building initial matrix Mon Apr 20 19:29:53 2009 memory use: 407.2 MB Mon Apr 20 19:30:05 2009 read 1128467 cycles Mon Apr 20 19:30:25 2009 matrix is 1128216 x 1128467 (323.7 MB) with weight 105969391 (93.91/col) Mon Apr 20 19:30:25 2009 sparse part has weight 75825912 (67.19/col) Mon Apr 20 19:30:49 2009 filtering completed in 3 passes Mon Apr 20 19:30:49 2009 matrix is 1122687 x 1122887 (322.9 MB) with weight 105636528 (94.08/col) Mon Apr 20 19:30:49 2009 sparse part has weight 75655471 (67.38/col) Mon Apr 20 19:30:55 2009 read 1122887 cycles Mon Apr 20 19:30:56 2009 matrix is 1122687 x 1122887 (322.9 MB) with weight 105636528 (94.08/col) Mon Apr 20 19:30:56 2009 sparse part has weight 75655471 (67.38/col) Mon Apr 20 19:30:56 2009 saving the first 48 matrix rows for later Mon Apr 20 19:30:57 2009 matrix is 1122639 x 1122887 (309.2 MB) with weight 84191763 (74.98/col) Mon Apr 20 19:30:57 2009 sparse part has weight 74309659 (66.18/col) Mon Apr 20 19:30:57 2009 matrix includes 64 packed rows Mon Apr 20 19:30:57 2009 using block size 65536 for processor cache size 3072 kB Mon Apr 20 19:31:07 2009 commencing Lanczos iteration Mon Apr 20 19:31:07 2009 memory use: 307.1 MB Mon Apr 20 22:47:31 2009 lanczos halted after 17753 iterations (dim = 1122639) Mon Apr 20 22:47:34 2009 recovered 30 nontrivial dependencies Mon Apr 20 22:47:34 2009 BLanczosTime: 12017 Mon Apr 20 22:47:34 2009 Mon Apr 20 22:47:34 2009 commencing square root phase Mon Apr 20 22:47:34 2009 reading relations for dependency 1 Mon Apr 20 22:47:35 2009 read 560536 cycles Mon Apr 20 22:47:36 2009 cycles contain 2179676 unique relations Mon Apr 20 22:48:35 2009 read 2179676 relations Mon Apr 20 22:48:49 2009 multiplying 1789248 relations Mon Apr 20 22:55:12 2009 multiply complete, coefficients have about 83.73 million bits Mon Apr 20 22:55:16 2009 initial square root is modulo 1023313 Mon Apr 20 23:03:42 2009 reading relations for dependency 2 Mon Apr 20 23:03:43 2009 read 562605 cycles Mon Apr 20 23:03:44 2009 cycles contain 2184477 unique relations Mon Apr 20 23:04:41 2009 read 2184477 relations Mon Apr 20 23:04:55 2009 multiplying 1793096 relations Mon Apr 20 23:11:28 2009 multiply complete, coefficients have about 83.91 million bits Mon Apr 20 23:11:31 2009 initial square root is modulo 1054013 Mon Apr 20 23:20:00 2009 reading relations for dependency 3 Mon Apr 20 23:20:01 2009 read 561085 cycles Mon Apr 20 23:20:02 2009 cycles contain 2178671 unique relations Mon Apr 20 23:20:59 2009 read 2178671 relations Mon Apr 20 23:21:13 2009 multiplying 1788758 relations Mon Apr 20 23:27:36 2009 multiply complete, coefficients have about 83.70 million bits Mon Apr 20 23:27:40 2009 initial square root is modulo 1017953 Mon Apr 20 23:36:06 2009 sqrtTime: 2912 Mon Apr 20 23:36:06 2009 prp44 factor: 81794757600323035554827444059633541274214747 Mon Apr 20 23:36:06 2009 prp87 factor: 138308699903585154803319669716002943598265094204006724265991671763585624304306433563833 Mon Apr 20 23:36:06 2009 elapsed time 04:27:55 total time 191,26 hours

Apr 21, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve / Apr 21, 2009
(53·10¹⁵⁴-71)/9 = 5(8)₁₅₃1_<155> = 3 · 229 · 784913 · C147
C147 = P44 · P49 · P54
P44 = 58432003235623530165281017016867956379005573_<44>
P49 = 1909904305005828208979377889723705736501215261699_<49>
P54 = 978571848436525753147014195992938337808040799827522913_<54>

Number: n N=109208162789513448702851703858513074211371194492462397897159818344452513876803589060910022195654513695691535571956886639124083657821847491431599151 ( 147 digits) SNFS difficulty: 156 digits. Divisors found: r1=58432003235623530165281017016867956379005573 (pp44) r2=1909904305005828208979377889723705736501215261699 (pp49) r3=978571848436525753147014195992938337808040799827522913 (pp54) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 24.35 hours. Scaled time: 35.09 units (timescale=1.441). Factorization parameters were as follows: name: KA_5_8_153_1 n: 109208162789513448702851703858513074211371194492462397897159818344452513876803589060910022195654513695691535571956886639124083657821847491431599151 m: 10000000000000000000000000000000 deg: 5 c5: 53 c0: -710 skew: 1.68 type: snfs lss: 1 rlim: 2900000 alim: 2900000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 20000 Factor base limits: 2900000/2900000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved rational special-q in [1450000, 2950001) Primes: RFBsize:210109, AFBsize:209895, largePrimes:13516363 encountered Relations: rels:13120834, finalFF:478919 Max relations in full relation-set: 28 Initial matrix: 420069 x 478918 with sparse part having weight 55190721. Pruned matrix : 400471 x 402635 with weight 43607320. Total sieving time: 22.43 hours. Total relation processing time: 0.54 hours. Matrix solve time: 0.94 hours. Total square root time: 0.45 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,2900000,2900000,28,28,56,56,2.4,2.4,100000 total time: 24.35 hours. --------- CPU info (if available) ----------

2·10¹⁸⁹-1 = 1(9)_189<190> = 31 · 5439829 · 2720009561_<10> · 13767101225803399878919_<23> · 317174697888724493139312350540581_<33> · C117
C117 = P54 · P64
P54 = 513218192797005307893534212745911015541469979463052889_<54>
P64 = 1945671599615643697213895686057854815110769046170890008443525071_<64>

Number: n N=998554062131199145511682309200429404184445404728977563784886142161737708964524438853301713011987413991352186470480119 ( 117 digits) Divisors found: Tue Apr 21 14:48:53 2009 prp54 factor: 513218192797005307893534212745911015541469979463052889 Tue Apr 21 14:48:53 2009 prp64 factor: 1945671599615643697213895686057854815110769046170890008443525071 Tue Apr 21 14:48:53 2009 elapsed time 00:56:00 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 21.19 hours. Scaled time: 56.37 units (timescale=2.660). Factorization parameters were as follows: name: KA_1_9_189 n: 998554062131199145511682309200429404184445404728977563784886142161737708964524438853301713011987413991352186470480119 Y0: -39549417387425509027250 Y1: 1988506022909 c0: 2486995315355389860517375156431 c1: 58401840270545545618714084 c2: 125760847171208808779 c3: -1783059507957566 c4: -4048042212 c5: 10320 skew: 217819.22 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 50000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2250000, 3451699) Primes: RFBsize:315948, AFBsize:315612, largePrimes:13634890 encountered Relations: rels:12392196, finalFF:666830 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 934308 hash collisions in 13111368 relations Msieve: matrix is 654514 x 654762 (184.4 MB) Total sieving time: 20.61 hours. Total relation processing time: 0.59 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,28,28,56,56,2.4,2.4,60000 total time: 21.19 hours. --------- CPU info (if available) ----------

Apr 21, 2009

By Ignacio Santos / GGNFS, Msieve / Apr 21, 2009
(25·10¹⁷³+11)/9 = 2(7)₁₇₂9_<174> = 3² · 19 · 67 · 941 · 15161 · 10094239 · 34387963 · 92007751184296289889437071_<26> · C122
C122 = P39 · P84
P39 = 309663452002993767114281190640908937591_<39>
P84 = 171836221375684041886673540732326857211429098070211664166511506444287611655348677411_<84>

Number: 27779_173 N=53211397490344946900536786881309863034780265482886037675997088339278604798975900411608112094043137173327508782150990456901 ( 122 digits) Divisors found: r1=309663452002993767114281190640908937591 (pp39) r2=171836221375684041886673540732326857211429098070211664166511506444287611655348677411 (pp84) Version: Msieve-1.39 Total time: 45.64 hours. Scaled time: 117.34 units (timescale=2.571). Factorization parameters were as follows: # Murphy_E = 2.358547e-10, selected by Jeff Gilchrist n: 53211397490344946900536786881309863034780265482886037675997088339278604798975900411608112094043137173327508782150990456901 Y0: -348709088850161602305536 Y1: 11955423470957 c0: 21632123064086795098280205422505 c1: 296416490313361015058593979 c2: -1664067767180628526287 c3: -3283788797457339 c4: 5983105142 c5: 10320 skew: 411539.22 type: gnfs # selected mechanically rlim: 5800000 alim: 5800000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 Factor base limits: 5800000/5800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved algebraic special-q in [2900000, 5000001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 792665 x 792913 Total sieving time: 45.64 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,121,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5800000,5800000,27,27,52,52,2.5,2.5,60000 total time: 45.64 hours. --------- CPU info (if available) ----------

(49·10¹⁷³-31)/9 = 5(4)₁₇₂1_<174> = 2741 · 807085684543_<12> · 15477414385463353_<17> · 294569208541863507869_<21> · C122
C122 = P40 · P82
P40 = 5931851484368810751905079921740369165257_<40>
P82 = 9100156549889364411984182615500796454801011418152264037858984439499480211034026343_<82>

Number: 54441_173 N=53980777138449781902663795465980934453425776747350796708496115707652003245333207846637476138009335666563011187390658365151 ( 122 digits) Divisors found: r1=5931851484368810751905079921740369165257 (pp40) r2=9100156549889364411984182615500796454801011418152264037858984439499480211034026343 (pp82) Version: Msieve-1.39 Total time: 49.31 hours. Scaled time: 130.12 units (timescale=2.639). Factorization parameters were as follows: # Murphy_E = 2.256858e-10, selected by Jeff Gilchrist n: 53980777138449781902663795465980934453425776747350796708496115707652003245333207846637476138009335666563011187390658365151 Y0: -323737180325506520777503 Y1: 16149092889517 c0: 427754643269965365750037883136 c1: 71856727713288899503966296 c2: -221173711071066753176 c3: -1988180336202337 c4: 3126697882 c5: 15180 skew: 249593.92 type: gnfs # selected mechanically rlim: 5900000 alim: 5900000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 Factor base limits: 5900000/5900000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved algebraic special-q in [2950000, 5230001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 804752 x 805000 Total sieving time: 49.31 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,121,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5900000,5900000,27,27,52,52,2.5,2.5,60000 total time: 49.31 hours. --------- CPU info (if available) ----------

Apr 20, 2009 (5th)

By Wataru Sakai / Msieve / Apr 20, 2009
2·10¹⁸³-9 = 1(9)₁₈₂1_<184> = 11 · 29 · 89 · 181 · C177
C177 = P60 · P118
P60 = 199744837434442791340990120371036864210437097079699444679911_<60>
P118 = 1948476479308863608330608439312461206938858412379710908007928999570893351886680145473233888864975347874868634937712811_<118>

Number: 19991_183 N=389198117604384394634436911082435858690725856435322764917915198011353298288637497175881159133185736433867163958074800375420504241189187064377844430117629293074161117512339039821 ( 177 digits) SNFS difficulty: 183 digits. Divisors found: r1=199744837434442791340990120371036864210437097079699444679911 r2=1948476479308863608330608439312461206938858412379710908007928999570893351886680145473233888864975347874868634937712811 Version: Total time: 168.64 hours. Scaled time: 317.05 units (timescale=1.880). Factorization parameters were as follows: n: 389198117604384394634436911082435858690725856435322764917915198011353298288637497175881159133185736433867163958074800375420504241189187064377844430117629293074161117512339039821 m: 2000000000000000000000000000000000000 deg: 5 c5: 125 c0: -18 skew: 0.68 type: snfs lss: 1 rlim: 8000000 alim: 8000000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 8000000/8000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [4000000, 5500001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1426873 x 1427120 Total sieving time: 168.64 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,183,5,0,0,0,0,0,0,0,0,8000000,8000000,28,28,53,53,2.5,2.5,100000 total time: 168.64 hours. --------- CPU info (if available) ----------

2·10¹⁹¹-7 = 1(9)₁₉₀3_<192> = 17 · 31 · 389 · C186
C186 = P75 · P112
P75 = 128310718329815993931447087546082492234669614032972499261568404331467602141_<75>
P112 = 7603382568421390295289669853703818922067601220779471394301400646577106498502213407372609170471837455808074363591_<112>

Number: 19993_191 N=975595479090549894391789388447973932088798700506821851387540670136534587298722457720130924913293951795827378135929718101686316785608015492456207957932322941615488553826041570123364048331 ( 186 digits) SNFS difficulty: 191 digits. Divisors found: r1=128310718329815993931447087546082492234669614032972499261568404331467602141 r2=7603382568421390295289669853703818922067601220779471394301400646577106498502213407372609170471837455808074363591 Version: Total time: 339.94 hours. Scaled time: 675.12 units (timescale=1.986). Factorization parameters were as follows: n: 975595479090549894391789388447973932088798700506821851387540670136534587298722457720130924913293951795827378135929718101686316785608015492456207957932322941615488553826041570123364048331 m: 100000000000000000000000000000000000000 deg: 5 c5: 20 c0: -7 skew: 0.81 type: snfs lss: 1 rlim: 10800000 alim: 10800000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5Factor base limits: 10800000/10800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [5400000, 9000001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1393898 x 1394146 Total sieving time: 339.94 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,191,5,0,0,0,0,0,0,0,0,10800000,10800000,28,28,54,54,2.5,2.5,100000 total time: 339.94 hours. --------- CPU info (if available) ----------

Apr 20, 2009 (4th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Apr 20, 2009
(53·10¹⁶³-71)/9 = 5(8)₁₆₂1_<164> = 3 · 23 · 2389 · 96513550638754153673_<20> · C139
C139 = P57 · P82
P57 = 377498624063625239463952264309281335010127635110927025061_<57>
P82 = 9805380550742964674231939389316251929069674579746840643746394494793350010716857197_<82>

Number: 58881_163 N=3701517666325701027779366640216236218837963742983531931726635303099814464739514466644120549856564034083324033280638783693272531866777214017 ( 139 digits) SNFS difficulty: 166 digits. Divisors found: r1=377498624063625239463952264309281335010127635110927025061 r2=9805380550742964674231939389316251929069674579746840643746394494793350010716857197 Version: Total time: 34.87 hours. Scaled time: 83.23 units (timescale=2.387). Factorization parameters were as follows: n: 3701517666325701027779366640216236218837963742983531931726635303099814464739514466644120549856564034083324033280638783693272531866777214017 m: 1000000000000000000000000000000000 deg: 5 c5: 53 c0: -7100 skew: 2.66 type: snfs lss: 1 rlim: 4800000 alim: 4800000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 4800000/4800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [2400000, 5300001) Primes: rational ideals reading, algebraic ideals reading, Relations: 10183017 Max relations in full relation-set: Initial matrix: Pruned matrix : 870654 x 870902 Total sieving time: 31.70 hours. Total relation processing time: 1.43 hours. Matrix solve time: 1.63 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,4800000,4800000,27,27,51,51,2.4,2.4,100000 total time: 34.87 hours. --------- CPU info (if available) ----------

Apr 20, 2009 (3rd)

By Ignacio Santos / GGNFS, Msieve / Apr 20, 2009
(52·10¹⁸³+11)/9 = 5(7)₁₈₂9_<184> = 199 · 229 · 1381 · 27093641 · 3271989401_<10> · 75894316021_<11> · 13201833342001_<14> · 25458040823627_<14> · C122
C122 = P51 · P71
P51 = 760709516823435322284803971154506765518059289320909_<51>
P71 = 53371819833679274984631391612038926591773108484753524753906129523475223_<71>

Number: 57779_183 N=40600451277665603438462039829671810932492997712468478849840455596499272861676146916196939261839959572308339955745357337707 ( 122 digits) Divisors found: r1=760709516823435322284803971154506765518059289320909 (pp51) r2=53371819833679274984631391612038926591773108484753524753906129523475223 (pp71) Version: Msieve-1.39 Total time: 51.53 hours. Scaled time: 132.99 units (timescale=2.581). Factorization parameters were as follows: # Murphy_E = 2.262445e-10, selected by Jeff Gilchrist n: 40600451277665603438462039829671810932492997712468478849840455596499272861676146916196939261839959572308339955745357337707 Y0: -293254863654452879987050 Y1: 12192311360713 c0: -63029949335627363746734079251 c1: -30365307533505781597878895 c2: -1310763885392580973715 c3: -1061241013495825 c4: -1142314074 c5: 18720 skew: 203548.67 type: gnfs rlim: 5800000 alim: 5800000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 Factor base limits: 5800000/5800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved algebraic special-q in [2900000, 5300001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 818639 x 818887 Total sieving time: 51.53 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,121,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5800000,5800000,27,27,52,52,2.5,2.5,60000 total time: 51.53 hours. --------- CPU info (if available) ----------

(17·10¹⁸⁰-11)/3 = 5(6)₁₇₉3_<181> = 4423 · C178
C178 = P42 · P136
P42 = 175738775151637385522300574841309392108541_<42>
P136 = 7290261927712186063891569599218901948236195147537934711419522834797162143981560091333540946292921842334124888216342937023769847028282741_<136>

Number: 56663_180 N=1281181701710754389931419097143718441480141683623483306956063003994272364157057803903836008742181023438088778355565604039490541864496194136709623935488733137387896601100308990881 ( 178 digits) SNFS difficulty: 181 digits. Divisors found: r1=175738775151637385522300574841309392108541 (pp42) r2=7290261927712186063891569599218901948236195147537934711419522834797162143981560091333540946292921842334124888216342937023769847028282741 (pp136) Version: Msieve-1.39 Total time: 131.06 hours. Scaled time: 227.92 units (timescale=1.739). Factorization parameters were as follows: n: 1281181701710754389931419097143718441480141683623483306956063003994272364157057803903836008742181023438088778355565604039490541864496194136709623935488733137387896601100308990881 m: 1000000000000000000000000000000000000 deg: 5 c5: 17 c0: -11 skew: 0.92 type: snfs lss: 1 rlim: 7300000 alim: 7300000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 7300000/7300000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3650000, 5850001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1378758 x 1379006 Total sieving time: 131.06 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,181,5,0,0,0,0,0,0,0,0,7300000,7300000,28,28,53,53,2.5,2.5,100000 total time: 131.06 hours. --------- CPU info (if available) ----------

Apr 20, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve / Apr 20, 2009
(13·10¹⁶⁷+17)/3 = 4(3)₁₆₆9_<168> = 263 · 341569 · 7993784054790885255053_<22> · C138
C138 = P49 · P90
P49 = 1846311335649698654729517594024921557409680683367_<49>
P90 = 326836501228653793160065539312213663723576161842178591891017245168156703068080309956568087_<90>

Number: n N=603441937122550160266933168238968012391700013260122407056599572853112687366988676069682707100660537151260148591255804012395446972223908929 ( 138 digits) SNFS difficulty: 169 digits. Divisors found: Mon Apr 20 10:46:06 2009 prp49 factor: 1846311335649698654729517594024921557409680683367 Mon Apr 20 10:46:06 2009 prp90 factor: 326836501228653793160065539312213663723576161842178591891017245168156703068080309956568087 Mon Apr 20 10:46:06 2009 elapsed time 00:58:38 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 61.67 hours. Scaled time: 164.72 units (timescale=2.671). Factorization parameters were as follows: name: KA_4_3_166_9 n: 603441937122550160266933168238968012391700013260122407056599572853112687366988676069682707100660537151260148591255804012395446972223908929 m: 2000000000000000000000000000000000 deg: 5 c5: 325 c0: 136 skew: 0.84 type: snfs lss: 1 rlim: 4600000 alim: 4600000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4600000/4600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved special-q in [2300000, 6034741) Primes: RFBsize:322441, AFBsize:321816, largePrimes:10466991 encountered Relations: rels:11329164, finalFF:647785 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1597998 hash collisions in 12898935 relations Msieve: matrix is 739632 x 739880 (193.8 MB) Total sieving time: 61.26 hours. Total relation processing time: 0.41 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,169,5,0,0,0,0,0,0,0,0,4600000,4600000,27,27,52,52,2.4,2.4,100000 total time: 61.67 hours. --------- CPU info (if available) ----------

Apr 20, 2009

By Markus Tervooren / Msieve, ggnfs, factMsieve.pl / Apr 20, 2009
(53·10¹⁸³-71)/9 = 5(8)₁₈₂1_<184> = 73 · 113 · 5779 · 80273 · 543483353732909_<15> · 1633503274622224469_<19> · 9329922208436263697241721_<25> · C114
C114 = P43 · P72
P43 = 1099460710064905094872964317328985126416851_<43>
P72 = 168984112509748557056357145099368984533273143568828753891708684224898777_<72>

Sun Apr 19 18:52:26 2009 random seeds: 83640b58 38b2f3fd factoring 185791392329655960317126843193149532656075039568978618086291692551310739540908266190324079981475502216424182091227 (114 digits) searching for 15-digit factors commencing number field sieve (114-digit input) R0: -5971029592928472269554 R1: 2129960935729 A0: 862370790294329460331503539 A1: -10194782863141842356898 A2: 1238072463545608887 A3: -92182453340548 A4: -5047177812 A5: 24480 skew 39869.06, size 7.804671e-11, alpha -6.508276, combined = 6.655291e-10 commencing relation filtering commencing duplicate removal, pass 1 error -5 reading relation 5820643 error -5 reading relation 7796563 found 689413 hash collisions in 7929051 relations added 509 free relations commencing duplicate removal, pass 2 found 775167 duplicates and 7154393 unique relations memory use: 48.6 MB reading rational ideals above 2686976 reading algebraic ideals above 2686976 commencing singleton removal, pass 1 relations with 0 large ideals: 73324 relations with 1 large ideals: 655600 relations with 2 large ideals: 2115377 relations with 3 large ideals: 2828898 relations with 4 large ideals: 1334809 relations with 5 large ideals: 88476 relations with 6 large ideals: 57908 relations with 7+ large ideals: 1 7154393 relations and about 7393740 large ideals commencing singleton removal, pass 2 found 3488166 singletons current dataset: 3666227 relations and about 3152132 large ideals commencing singleton removal, pass 3 found 720586 singletons current dataset: 2945641 relations and about 2375343 large ideals commencing singleton removal, pass 4 found 217203 singletons current dataset: 2728438 relations and about 2151780 large ideals commencing singleton removal, final pass memory use: 46.1 MB commencing in-memory singleton removal begin with 2728438 relations and 2260018 unique ideals reduce to 2313233 relations and 1835471 ideals in 16 passes max relations containing the same ideal: 65 reading rational ideals above 720000 reading algebraic ideals above 720000 commencing singleton removal, final pass keeping 2011906 ideals with weight <= 20, new excess is 218763 memory use: 65.5 MB commencing in-memory singleton removal begin with 2313746 relations and 2011906 unique ideals reduce to 2311378 relations and 2007004 ideals in 9 passes max relations containing the same ideal: 20 removing 254221 relations and 228917 ideals in 25304 cliques commencing in-memory singleton removal begin with 2057157 relations and 2007004 unique ideals reduce to 2037641 relations and 1758296 ideals in 8 passes max relations containing the same ideal: 20 removing 188091 relations and 162787 ideals in 25304 cliques commencing in-memory singleton removal begin with 1849550 relations and 1758296 unique ideals reduce to 1836735 relations and 1582524 ideals in 8 passes max relations containing the same ideal: 20 relations with 0 large ideals: 18963 relations with 1 large ideals: 140280 relations with 2 large ideals: 422112 relations with 3 large ideals: 621928 relations with 4 large ideals: 452573 relations with 5 large ideals: 152546 relations with 6 large ideals: 26344 relations with 7+ large ideals: 1989 commencing 2-way merge reduce to 1057712 relation sets and 803500 unique ideals commencing full merge memory use: 71.5 MB found 498479 cycles, need 465700 weight of 465700 cycles is about 32909516 (70.67/cycle) distribution of cycle lengths: 1 relations: 51136 2 relations: 49656 3 relations: 50299 4 relations: 45791 5 relations: 42157 6 relations: 37795 7 relations: 33099 8 relations: 28795 9 relations: 25932 10+ relations: 101040 heaviest cycle: 18 relations commencing cycle optimization start with 2870886 relations pruned 70362 relations memory use: 96.4 MB distribution of cycle lengths: 1 relations: 51136 2 relations: 50814 3 relations: 52098 4 relations: 47102 5 relations: 43351 6 relations: 38370 7 relations: 33575 8 relations: 29072 9 relations: 25739 10+ relations: 94443 heaviest cycle: 18 relations RelProcTime: 275 commencing linear algebra read 465700 cycles cycles contain 1621811 unique relations read 1621811 relations using 20 quadratic characters above 134217404 building initial matrix memory use: 198.4 MB read 465700 cycles matrix is 465414 x 465700 (140.0 MB) with weight 43993893 (94.47/col) sparse part has weight 31572525 (67.80/col) filtering completed in 3 passes matrix is 460957 x 461157 (139.2 MB) with weight 43699323 (94.76/col) sparse part has weight 31410540 (68.11/col) read 461157 cycles matrix is 460957 x 461157 (139.2 MB) with weight 43699323 (94.76/col) sparse part has weight 31410540 (68.11/col) saving the first 48 matrix rows for later matrix is 460909 x 461157 (133.7 MB) with weight 34683440 (75.21/col) sparse part has weight 30448887 (66.03/col) matrix includes 64 packed rows using block size 65536 for processor cache size 4096 kB commencing Lanczos iteration (4 threads) memory use: 134.9 MB linear algebra completed 459370 of 461157 dimensions (99.6%, ETA 0h 0m) lanczos halted after 7290 iterations (dim = 460906) recovered 27 nontrivial dependencies BLanczosTime: 1632 commencing square root phase reading relations for dependency 1 read 230605 cycles cycles contain 985785 unique relations read 985785 relations multiplying 807772 relations multiply complete, coefficients have about 36.24 million bits initial square root is modulo 159773 sqrtTime: 209 prp43 factor: 1099460710064905094872964317328985126416851 prp72 factor: 168984112509748557056357145099368984533273143568828753891708684224898777 elapsed time 00:32:31 Total Sieving time: 08:11:12

Apr 19, 2009 (5th)

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Apr 19, 2009
(53·10¹⁴⁸-71)/9 = 5(8)₁₄₇1_<149> = 3 · 19 · 2381 · 5711 · 13834209197_<11> · C130
C130 = P41 · P89
P41 = 82385359894943408004943162699533169281913_<41>
P89 = 66662648941747010745791795419173523195324651729972252459647715337503778584049915638822583_<89>

Number: 58881_148 N=5492026324616095798033102395215615366695629783537974299978961263104321958528283500871403176146355042788370590000930782242917841279 ( 130 digits) SNFS difficulty: 151 digits. Divisors found: r1=82385359894943408004943162699533169281913 r2=66662648941747010745791795419173523195324651729972252459647715337503778584049915638822583 Version: Total time: 9.99 hours. Scaled time: 23.83 units (timescale=2.386). Factorization parameters were as follows: n: 5492026324616095798033102395215615366695629783537974299978961263104321958528283500871403176146355042788370590000930782242917841279 m: 1000000000000000000000000000000 deg: 5 c5: 53 c0: -7100 skew: 2.66 type: snfs lss: 1 rlim: 2000000 alim: 2000000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1000000, 2000001) Primes: rational ideals reading, algebraic ideals reading, Relations: 6910517 Max relations in full relation-set: Initial matrix: Pruned matrix : 436261 x 436509 Total sieving time: 9.21 hours. Total relation processing time: 0.33 hours. Matrix solve time: 0.39 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2000000,2000000,27,27,49,49,2.4,2.4,100000 total time: 9.99 hours. --------- CPU info (if available) ----------

2·10¹⁹⁹-1 = 1(9)_199<200> = 19 · 17339562682791539_<17> · 7572092218037286911_<19> · C163
C163 = P35 · P129
P35 = 15088679290694653491630959079652649_<35>
P129 = 531338312951247025629014580036481987176765320031147478358915519016343794161299690194525950929141452320767635858987664888979395601_<129>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 8017193398980115789611498508984984667086036428422295572972632192194297168351927795512719154924815800899613373920817281990053320592884375557748210291511125038597049 (163 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1624952013 Step 1 took 5507ms ********** Factor found in step 1: 15088679290694653491630959079652649 Found probable prime factor of 35 digits: 15088679290694653491630959079652649 Probable prime cofactor 531338312951247025629014580036481987176765320031147478358915519016343794161299690194525950929141452320767635858987664888979395601 has 129 digits

Apr 19, 2009 (4th)

By Ignacio Santos / GGNFS, Msieve / Apr 19, 2009
(53·10¹⁵⁰-71)/9 = 5(8)₁₄₉1_<151> = 248747801 · 11462866529_<11> · C133
C133 = P61 · P73
P61 = 1006667291845049530667097296308918344203566521580425950778739_<61>
P73 = 2051610515873675499019042734361944316125748570732769002787444070163735651_<73>

Number: 58881_150 N=2065289201935377916361303754850202748421005648580776733236968519814503971051359873268351261206738974803314183796084499535780787124089 ( 133 digits) SNFS difficulty: 151 digits. Divisors found: r1=1006667291845049530667097296308918344203566521580425950778739 (pp61) r2=2051610515873675499019042734361944316125748570732769002787444070163735651 (pp73) Version: Msieve-1.39 Total time: 13.07 hours. Scaled time: 33.81 units (timescale=2.587). Factorization parameters were as follows: n: 2065289201935377916361303754850202748421005648580776733236968519814503971051359873268351261206738974803314183796084499535780787124089 m: 1000000000000000000000000000000 deg: 5 c5: 53 c0: -71 skew: 1.06 type: snfs lss: 1 rlim: 2400000 alim: 2400000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1200000, 1900001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 388006 x 388254 Total sieving time: 13.07 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,49,49,2.4,2.4,100000 total time: 13.07 hours. --------- CPU info (if available) ----------

(37·10¹⁸⁶+17)/9 = 4(1)₁₈₅3_<187> = 3 · 5431 · 48847 · 118529 · 20791445904137_<14> · 6636802404266483_<16> · 8319806456856435884237_<22> · C122
C122 = P54 · P68
P54 = 936611623971359060206147696654335999846721752617956297_<54>
P68 = 40530251017074094158289636271902336998641296433950350474105003157453_<68>

Number: 41113_186 N=37961104225068594578714829076645712945921588378067673385352537851945754998378505684467544660269645616821258158008963831541 ( 122 digits) Divisors found: r1=936611623971359060206147696654335999846721752617956297 (pp54) r2=40530251017074094158289636271902336998641296433950350474105003157453 (pp68) Version: Msieve-1.39 Total time: 49.82 hours. Scaled time: 128.79 units (timescale=2.585). Factorization parameters were as follows: n: 37961104225068594578714829076645712945921588378067673385352537851945754998378505684467544660269645616821258158008963831541 Y0: -318842747860980647659276 Y1: 12477258589133 c0: 182009490340765499157220857085 c1: 2767449488789833424934041 c2: -35423532070220414210 c3: -462278175788232 c4: 2468121056 c5: 11520 skew: 131899.69 type: gnfs Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2500000, 5020001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 678008 x 678256 Total sieving time: 49.82 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,121,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.4,2.4,60000 total time: 49.82 hours. --------- CPU info (if available) ----------

Apr 19, 2009 (3rd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / Apr 19, 2009
(53·10¹⁵⁹-71)/9 = 5(8)₁₅₈1_<160> = 73 · 5966567237_<10> · 4981932222649_<13> · 26273193042133_<14> · 2062452635612297_<16> · C107
C107 = P52 · P55
P52 = 6078143242188653953677512610851837554339876404942979_<52>
P55 = 8239870283677649983233243756347853355656983261837612011_<55>

Number: n N=50083111881246415258836189923446650619873710853182232529963769466745141613279822608636885515510257980520769 ( 107 digits) Divisors found: r1=6078143242188653953677512610851837554339876404942979 (pp52) r2=8239870283677649983233243756347853355656983261837612011 (pp55) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 8.87 hours. Scaled time: 23.49 units (timescale=2.649). Factorization parameters were as follows: name: KA_5_8_158_1 n: 50083111881246415258836189923446650619873710853182232529963769466745141613279822608636885515510257980520769 Y0: -476444653022084686012 Y1: 101590671413 c0: -176302300640800173013419063 c1: 18648490637306616368999 c2: 138703903042426525 c3: -19244747603213 c4: -25299728 c5: 2040 skew: 40590.29 type: gnfs rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved algebraic special-q in [1250000, 2200001) Primes: RFBsize:183072, AFBsize:182873, largePrimes:15737194 encountered Relations: rels:14081049, finalFF:507587 Max relations in full relation-set: 28 Initial matrix: 366022 x 507587 with sparse part having weight 47260200. Pruned matrix : 271239 x 273133 with weight 27017065. Total sieving time: 7.88 hours. Total relation processing time: 0.50 hours. Matrix solve time: 0.30 hours. Total square root time: 0.18 hours, sqrts: 1. Prototype def-par.txt line would be: gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,28,28,56,56,2.6,2.6,150000 total time: 8.87 hours. --------- CPU info (if available) ----------

2·10¹⁹³-1 = 1(9)_193<194> = 61 · 3011 · 3019 · 2630399 · 1921011481_<10> · 5467489597378404813936108409_<28> · 394666621455911984281003929471901_<33> · C109
C109 = P50 · P60
P50 = 27527725817981321521808835728186950658541825851539_<50>
P60 = 120167217091555354429467632255431770850693114035283138229779_<60>

Number: n N=3307930204406174659160459281208577919156483154925588805331903346568937950394323661593005058106900251722779881 ( 109 digits) Divisors found: r1=27527725817981321521808835728186950658541825851539 (pp50) r2=120167217091555354429467632255431770850693114035283138229779 (pp60) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 11.32 hours. Scaled time: 30.11 units (timescale=2.660). Factorization parameters were as follows: name: KA_1_9_193 n: 3307930204406174659160459281208577919156483154925588805331903346568937950394323661593005058106900251722779881 Y0: -839776940653718696932 Y1: 114057450119 c0: -1649652311583314793830770533 c1: 216144923746544112026007 c2: -3923772748444895801 c3: -94689262172047 c4: 1534734054 c5: 7920 skew: 54002.35 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved algebraic special-q in [1600000, 2700001) Primes: RFBsize:230209, AFBsize:230226, largePrimes:16506913 encountered Relations: rels:14758898, finalFF:602642 Max relations in full relation-set: 28 Initial matrix: 460518 x 602642 with sparse part having weight 53211012. Pruned matrix : 348381 x 350747 with weight 29897839. Total sieving time: 9.85 hours. Total relation processing time: 0.72 hours. Matrix solve time: 0.54 hours. Total square root time: 0.21 hours, sqrts: 1. Prototype def-par.txt line would be: gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,28,28,56,56,2.6,2.6,100000 total time: 11.32 hours. --------- CPU info (if available) ----------

(53·10¹⁴⁹-71)/9 = 5(8)₁₄₈1_<150> = 65563 · 1815347719_<10> · 321073852383149036798633_<24> · C113
C113 = P57 · P57
P57 = 106800209355250487145003373704765155010615558207705547567_<57>
P57 = 144290479211011391034524051927928805222760474712705729043_<57>

Number: n N=15410253387705434693965673668065684984653498882240991066120364949759038956067606885783711480075651457014249888381 ( 113 digits) SNFS difficulty: 151 digits. Divisors found: Sun Apr 19 10:39:07 2009 prp57 factor: 106800209355250487145003373704765155010615558207705547567 Sun Apr 19 10:39:07 2009 prp57 factor: 144290479211011391034524051927928805222760474712705729043 Sun Apr 19 10:39:07 2009 elapsed time 00:25:17 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 15.47 hours. Scaled time: 40.98 units (timescale=2.649). Factorization parameters were as follows: name: KA_5_8_148_1 n: 15410253387705434693965673668065684984653498882240991066120364949759038956067606885783711480075651457014249888381 m: 1000000000000000000000000000000 deg: 5 c5: 53 c0: -710 skew: 1.68 type: snfs lss: 1 rlim: 2400000 alim: 2400000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [1200000, 2207143) Primes: RFBsize:176302, AFBsize:176159, largePrimes:11666723 encountered Relations: rels:11027980, finalFF:373357 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1019499 hash collisions in 11953025 relations Msieve: matrix is 406774 x 407022 (108.2 MB) Total sieving time: 15.20 hours. Total relation processing time: 0.26 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,28,28,56,56,2.4,2.4,100000 total time: 15.47 hours. --------- CPU info (if available) ----------

(53·10¹⁵⁶-71)/9 = 5(8)₁₅₅1_<157> = 21893 · 414036871 · 5097582013_<10> · C135
C135 = P33 · P102
P33 = 458737405579699161469808051148151_<33>
P102 = 277818197649398752305269669956120329087419350051266481378494174971171347683342879820983467197939102529_<102>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM] Input number is 127445599212513259661167031097844600127945207600601649714644003218328810348288025994342263956141841235757118525999000793680536957773879 (135 digits) Using B1=2072000, B2=2854078510, polynomial Dickson(6), sigma=272239408 Step 1 took 25849ms Step 2 took 9266ms ********** Factor found in step 2: 458737405579699161469808051148151 Found probable prime factor of 33 digits: 458737405579699161469808051148151 Probable prime cofactor 277818197649398752305269669956120329087419350051266481378494174971171347683342879820983467197939102529 has 102 digits

Apr 19, 2009 (2nd)

By Markus Tervooren / Lattice siever (64bit/asm), msieve 1.40, factMsieve.pl / Apr 19, 2009
(53·10¹⁵²-71)/9 = 5(8)₁₅₁1_<153> = 7 · 47 · 132859 · C146
C146 = P39 · P107
P39 = 358120980514725128858958545331653679533_<39>
P107 = 37619820414914044458839692273435650922151956137997093517622555060481625863874724410536072161511382815906487_<107>

N=13472446973776891128080751122167770404510906719855480603757492405880322489403977649474835501358900905981133251349172146984833702939748174393830571 ( 146 digits) SNFS difficulty: 154 digits. Divisors found: r1=358120980514725128858958545331653679533 (pp39) r2=37619820414914044458839692273435650922151956137997093517622555060481625863874724410536072161511382815906487 (pp107) Version: Msieve-1.39 Total time: 11.66 hours. Scaled time: 26.15 units (timescale=2.243). Factorization parameters were as follows: n: 13472446973776891128080751122167770404510906719855480603757492405880322489403977649474835501358900905981133251349172146984833702939748174393830571 m: 2000000000000000000000000000000 deg: 5 c5: 1325 c0: -568 skew: 0.84 type: snfs lss: 1 rlim: 2600000 alim: 2600000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2600000/2600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1300000, 2500001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 479562 x 479810 Total sieving time: 10.80 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.73 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,154,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000 total time: 11.66 hours. --------- CPU info (if available) ---------- [ 0.144009] CPU0: Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b [ 0.238418] CPU1: Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b [ 0.335353] CPU2: Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b [ 0.432195] CPU3: Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b [ 0.004000] Memory: 8198000k/10485760k available (2226k kernel code, 189836k reserved, 1082k data, 392k init) [ 0.083969] Calibrating delay using timer specific routine.. 5804.04 BogoMIPS (lpj=11608082) [ 0.160010] Calibrating delay using timer specific routine.. 8120.06 BogoMIPS (lpj=16240129) [ 0.252015] Calibrating delay using timer specific routine.. 5800.09 BogoMIPS (lpj=11600186) [ 0.351781] Calibrating delay using timer specific routine.. 5800.09 BogoMIPS (lpj=11600195) [ 0.439785] Total of 4 processors activated (25524.29 BogoMIPS).

Apr 19, 2009

By Serge Batalov / GMP-ECM 6.2.2 / Apr 19, 2009
(53·10¹⁹⁵-71)/9 = 5(8)₁₉₄1_<196> = 1319 · 33857 · C189
C189 = P34 · P155
P34 = 6522546262176896794087564739115713_<34>
P155 = 20217289175101472176634624589120256959714664779605055451404756357758626997987860981678743694952263411707665143615277807384449498161455207993683372278411239_<155>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3935644505 Step 1 took 11044ms Step 2 took 11361ms ********** Factor found in step 2: 6522546262176896794087564739115713 Found probable prime factor of 34 digits: 6522546262176896794087564739115713 Probable prime cofactor has 155 digits

(53·10²⁰¹-71)/9 = 5(8)₂₀₀1_<202> = 845726166293_<12> · C190
C190 = P32 · C159
P32 = 26614080411265630091650323405683_<32>
C159 = [261632763104934685678706508770395191162055898507905747696347081652713863042849725984808309953127668896691497252042853273203709573229850203050723384365743227999_<159>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1279820415 Step 1 took 11153ms Step 2 took 11248ms ********** Factor found in step 2: 26614080411265630091650323405683 Found probable prime factor of 32 digits: 26614080411265630091650323405683 Composite cofactor has 159 digits

(53·10¹⁶²-71)/9 = 5(8)₁₆₁1_<163> = 70679701 · 44026722517_<11> · C145
C145 = P34 · C112
P34 = 1236279080219216121922252206884753_<34>
C112 = [1530755327949768346559116010704472935748277600679650175511082917507123042329452736442582425054160912093674875881_<112>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3167953602 Step 1 took 8465ms Step 2 took 8816ms ********** Factor found in step 2: 1236279080219216121922252206884753 Found probable prime factor of 34 digits: 1236279080219216121922252206884753 Composite cofactor has 112 digits

(53·10¹⁶⁹-71)/9 = 5(8)₁₆₈1_<170> = 3² · 55619 · C165
C165 = P33 · C132
P33 = 268408781245025917238865818507107_<33>
C132 = [438299479011775469486372343095698175154784520161586980563186912608598242291187115880197057529976739290204068936254644363207769097473_<132>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=504785334 Step 1 took 9505ms Step 2 took 9856ms ********** Factor found in step 2: 268408781245025917238865818507107 Found probable prime factor of 33 digits: 268408781245025917238865818507107 Composite cofactor has 132 digits

(53·10¹⁷⁵-71)/9 = 5(8)₁₇₄1_<176> = 3 · 73 · 1024183 · C168
C168 = P40 · P129
P40 = 2158548290899707807210634246105330347041_<40>
P129 = 121632578456805687673146582029186126326283394657268436697370779282164748561294068326344587870149269097387136954490861643986922133_<129>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=2926320089 Step 1 took 9548ms Step 2 took 4621ms ********** Factor found in step 2: 2158548290899707807210634246105330347041 Found probable prime factor of 40 digits: 2158548290899707807210634246105330347041 Probable prime cofactor has 129 digits

Apr 18, 2009 (8th)

By Ignacio Santos / GGNFS, Msieve / Apr 17, 2009
(53·10¹⁰⁷-71)/9 = 5(8)₁₀₆1_<108> = 97 · 269 · 461 · C101
C101 = P40 · P62
P40 = 1384979565662153197387040503504412975669_<40>
P62 = 35348016964029802824250185131245245092377627875980924329954213_<62>

Number: 58881_107 N=48956281181860419416589475081239022881768631931593997948842662890271506639806479700042463569853043497 ( 101 digits) SNFS difficulty: 109 digits. Divisors found: r1=1384979565662153197387040503504412975669 (pp40) r2=35348016964029802824250185131245245092377627875980924329954213 (pp62) Version: Msieve-1.39 Total time: 0.76 hours. Scaled time: 0.84 units (timescale=1.095). Factorization parameters were as follows: n: 48956281181860419416589475081239022881768631931593997948842662890271506639806479700042463569853043497 m: 2000000000000000000000 deg: 5 c5: 1325 c0: -568 skew: 0.84 type: snfs lss: 1 rlim: 470000 alim: 470000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2Factor base limits: 470000/470000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [235000, 385001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 52946 x 53184 Total sieving time: 0.72 hours. Total relation processing time: 0.01 hours. Matrix solve time: 0.01 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,109,5,0,0,0,0,0,0,0,0,470000,470000,25,25,44,44,2.2,2.2,50000 total time: 0.76 hours. --------- CPU info (if available) ----------

(53·10¹¹¹-71)/9 = 5(8)₁₁₀1_<112> = 73 · 73751 · 106363 · C101
C101 = P50 · P51
P50 = 14493900658606329765271121197487209608426062754421_<50>
P51 = 709523408350170592136127179652066112526467686866489_<51>

Number: 58881_111 N=10283761795583145401413388163687678748300979703369701831666106090610374480536842407958300829821497869 ( 101 digits) SNFS difficulty: 112 digits. Divisors found: r1=14493900658606329765271121197487209608426062754421 (pp50) r2=709523408350170592136127179652066112526467686866489 (pp51) Version: Msieve-1.39 Total time: 0.96 hours. Scaled time: 1.15 units (timescale=1.194). Factorization parameters were as follows: n: 10283761795583145401413388163687678748300979703369701831666106090610374480536842407958300829821497869 m: 10000000000000000000000 deg: 5 c5: 530 c0: -71 skew: 0.67 type: snfs lss: 1 rlim: 530000 alim: 530000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2Factor base limits: 530000/530000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [265000, 465001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 67516 x 67760 Total sieving time: 0.93 hours. Total relation processing time: 0.01 hours. Matrix solve time: 0.01 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,112,5,0,0,0,0,0,0,0,0,530000,530000,25,25,45,45,2.2,2.2,50000 total time: 0.96 hours. --------- CPU info (if available) ----------

(53·10¹¹⁵-71)/9 = 5(8)₁₁₄1_<116> = 3² · 223 · 5273 · C109
C109 = P51 · P59
P51 = 258714152872988458408233821774037897987784234433911_<51>
P59 = 21508396256747219765998592929869798919896339768469661174761_<59>

Number: 58881_115 N=5564526517220912931129146686473021353849511621980841461190488031968603807486322892528236218644273668075720271 ( 109 digits) SNFS difficulty: 116 digits. Divisors found: r1=258714152872988458408233821774037897987784234433911 (pp51) r2=21508396256747219765998592929869798919896339768469661174761 (pp59) Version: Msieve-1.39 Total time: 1.34 hours. Scaled time: 1.60 units (timescale=1.188). Factorization parameters were as follows: n: 5564526517220912931129146686473021353849511621980841461190488031968603807486322892528236218644273668075720271 m: 100000000000000000000000 deg: 5 c5: 53 c0: -71 skew: 1.06 type: snfs lss: 1 rlim: 620000 alim: 620000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2Factor base limits: 620000/620000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [310000, 510001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 59467 x 59698 Total sieving time: 1.30 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.01 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,116,5,0,0,0,0,0,0,0,0,620000,620000,25,25,45,45,2.2,2.2,50000 total time: 1.34 hours. --------- CPU info (if available) ----------

(53·10¹²⁰-71)/9 = 5(8)₁₁₉1_<121> = 331 · 43613 · 3706627 · C108
C108 = P50 · P58
P50 = 26786575570913598534091002158361449653541557924127_<50>
P58 = 4108594908349800945919523446359933990845020074836239443163_<58>

Number: 58881_120 N=110055188002782773317772931442183797479669644135257477753433827406525740778348919818614135594749472682893701 ( 108 digits) SNFS difficulty: 121 digits. Divisors found: r1=26786575570913598534091002158361449653541557924127 (pp50) r2=4108594908349800945919523446359933990845020074836239443163 (pp58) Version: Msieve-1.39 Total time: 1.36 hours. Scaled time: 1.63 units (timescale=1.196). Factorization parameters were as follows: n: 110055188002782773317772931442183797479669644135257477753433827406525740778348919818614135594749472682893701 m: 1000000000000000000000000 deg: 5 c5: 53 c0: -71 skew: 1.06 type: snfs lss: 1 rlim: 750000 alim: 750000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 750000/750000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [375000, 625001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 80948 x 81174 Total sieving time: 1.32 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.02 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,121,5,0,0,0,0,0,0,0,0,750000,750000,25,25,46,46,2.2,2.2,50000 total time: 1.36 hours. --------- CPU info (if available) ----------

(53·10¹¹⁹-71)/9 = 5(8)₁₁₈1_<120> = 23 · 73 · 3137 · C114
C114 = P36 · P78
P36 = 247302525192062034320407341931514849_<36>
P78 = 452105295957014023819909058843366067525219824276276508453661905503232282583903_<78>

Number: 58881_119 N=111806781342874122419607601654461901702135891354354991213991070266617193220703400932346201808666658354992732875647 ( 114 digits) SNFS difficulty: 121 digits. Divisors found: r1=247302525192062034320407341931514849 (pp36) r2=452105295957014023819909058843366067525219824276276508453661905503232282583903 (pp78) Version: Msieve-1.39 Total time: 1.79 hours. Scaled time: 2.10 units (timescale=1.175). Factorization parameters were as follows: n: 111806781342874122419607601654461901702135891354354991213991070266617193220703400932346201808666658354992732875647 m: 1000000000000000000000000 deg: 5 c5: 53 c0: -710 skew: 1.68 type: snfs lss: 1 rlim: 750000 alim: 750000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 750000/750000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [375000, 725001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 91225 x 91452 Total sieving time: 1.74 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.02 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,121,5,0,0,0,0,0,0,0,0,750000,750000,25,25,46,46,2.2,2.2,50000 total time: 1.79 hours. --------- CPU info (if available) ----------

(53·10¹²⁴-71)/9 = 5(8)₁₂₃1_<125> = 3² · 103 · 10391 · 313517 · 1925993 · C107
C107 = P42 · P65
P42 = 645449533165367934958837365343863903897071_<42>
P65 = 15686216002025477513604797878670354464346679288472277430682098283_<65>

Number: 58881_124 N=10124660795638468662831440992732320261481090609423641679678285332988429044938130752945016949841399137829093 ( 107 digits) SNFS difficulty: 126 digits. Divisors found: r1=645449533165367934958837365343863903897071 (pp42) r2=15686216002025477513604797878670354464346679288472277430682098283 (pp65) Version: Msieve-1.39 Total time: 2.33 hours. Scaled time: 2.75 units (timescale=1.178). Factorization parameters were as follows: n: 10124660795638468662831440992732320261481090609423641679678285332988429044938130752945016949841399137829093 m: 10000000000000000000000000 deg: 5 c5: 53 c0: -710 skew: 1.68 type: snfs lss: 1 rlim: 910000 alim: 910000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3Factor base limits: 910000/910000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [455000, 855001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 135894 x 136122 Total sieving time: 2.21 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.05 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,126,5,0,0,0,0,0,0,0,0,910000,910000,26,26,46,46,2.3,2.3,50000 total time: 2.33 hours. --------- CPU info (if available) ----------

(53·10¹²⁸-71)/9 = 5(8)₁₂₇1_<129> = 7 · 167 · C126
C126 = P53 · P74
P53 = 24969206764244227895770332415233048905828749459976209_<53>
P74 = 20175026012093362314000182915103646299439827080940433333601709650431305361_<74>

Number: 58881_128 N=503754395969964832240281342077749263378005892975952856192377150460982796312137629502898963976808288185533694515730443874156449 ( 126 digits) SNFS difficulty: 131 digits. Divisors found: r1=24969206764244227895770332415233048905828749459976209 (pp53) r2=20175026012093362314000182915103646299439827080940433333601709650431305361 (pp74) Version: Msieve-1.39 Total time: 3.22 hours. Scaled time: 3.79 units (timescale=1.176). Factorization parameters were as follows: n: 503754395969964832240281342077749263378005892975952856192377150460982796312137629502898963976808288185533694515730443874156449 m: 50000000000000000000000000 deg: 5 c5: 424 c0: -1775 skew: 1.33 type: snfs lss: 1 rlim: 1070000 alim: 1070000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3Factor base limits: 1070000/1070000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [535000, 1085001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 182936 x 183184 Total sieving time: 3.05 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.09 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,1070000,1070000,26,26,47,47,2.3,2.3,50000 total time: 3.22 hours. --------- CPU info (if available) ----------

(53·10¹²⁹-71)/9 = 5(8)₁₂₈1_<130> = 17 · 21589 · C125
C125 = P56 · P69
P56 = 25322624759976549455734598285790216107772481213399224703_<56>
P69 = 633640886576731402778133093433220256786188375338961718270777059934179_<69>

Number: 58881_129 N=16045450403361431036200049831719554590406576576003817000729916621179328494873175851778789549386231247636701939410562810823837 ( 125 digits) SNFS difficulty: 131 digits. Divisors found: r1=25322624759976549455734598285790216107772481213399224703 (pp56) r2=633640886576731402778133093433220256786188375338961718270777059934179 (pp69) Version: Msieve-1.39 Total time: 3.29 hours. Scaled time: 3.90 units (timescale=1.183). Factorization parameters were as follows: n: 16045450403361431036200049831719554590406576576003817000729916621179328494873175851778789549386231247636701939410562810823837 m: 100000000000000000000000000 deg: 5 c5: 53 c0: -710 skew: 1.68 type: snfs lss: 1 rlim: 1100000 alim: 1100000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1100000/1100000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [550000, 1100001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 178470 x 178705 Total sieving time: 3.15 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.08 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000 total time: 3.29 hours. --------- CPU info (if available) ----------

(28·10¹⁷⁶+71)/9 = 3(1)₁₇₅9_<177> = 11 · 4177 · 334891 · 78854016401726471_<17> · 20922377657995813028793412603_<29> · C122
C122 = P44 · P78
P44 = 17523944894902605507691685863551313076801221_<44>
P78 = 699339647751129622336695924473895312705541651662527802496178396153595100045639_<78>

Number: 31119_176 N=12255189450011394345886624005277270545972982902709668725171403353927774914407355488728521798333587784910725597129230925219 ( 122 digits) Divisors found: r1=17523944894902605507691685863551313076801221 (pp44) r2=699339647751129622336695924473895312705541651662527802496178396153595100045639 (pp78) Version: Msieve-1.39 Total time: 42.01 hours. Scaled time: 73.06 units (timescale=1.739). Factorization parameters were as follows: n: 12255189450011394345886624005277270545972982902709668725171403353927774914407355488728521798333587784910725597129230925219 Y0: -244870820893368151508838 Y1: 12427739286793 c0: -163742196505265923710132207365 c1: 65321964375096181901087226 c2: 197404084512766770793 c3: -2347860226599054 c4: -2773401392 c5: 13920 skew: 246057.74 type: gnfs Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [3000000, 5220001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 704331 x 704579 Total sieving time: 42.01 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,121,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,6000000,6000000,27,27,50,50,2.4,2.4,60000 total time: 42.01 hours. --------- CPU info (if available) ----------

(52·10¹⁶⁷-43)/9 = 5(7)₁₆₆3_<168> = 3⁴ · 7 · 61 · 129913170341_<12> · 867242538361868937630981343_<27> · C126
C126 = P44 · P82
P44 = 49637779755040036765627367016478664200260103_<44>
P82 = 2987045509611890878333062958493333869323375170995634475635740926374588918561839811_<82>

Number: 57773_167 N=148270307124396366588776691013993480723011390291670678142012858099810032240249803524315671307492094495902151881145156420360533 ( 126 digits) SNFS difficulty: 169 digits. Divisors found: r1=49637779755040036765627367016478664200260103 (pp44) r2=2987045509611890878333062958493333869323375170995634475635740926374588918561839811 (pp82) Version: Msieve-1.39 Total time: 52.12 hours. Scaled time: 134.21 units (timescale=2.575). Factorization parameters were as follows: n: 148270307124396366588776691013993480723011390291670678142012858099810032240249803524315671307492094495902151881145156420360533 m: 2000000000000000000000000000000000 deg: 5 c5: 325 c0: -86 skew: 0.77 type: snfs lss: 1 rlim: 4600000 alim: 4600000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 4600000/4600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2300000, 4900001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 877895 x 878143 Total sieving time: 52.12 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,169,5,0,0,0,0,0,0,0,0,4600000,4600000,27,27,52,52,2.4,2.4,100000 total time: 52.12 hours. --------- CPU info (if available) ----------

(53·10¹³⁵-71)/9 = 5(8)₁₃₄1_<136> = 73 · 17971 · C130
C130 = P39 · P42 · P50
P39 = 208950478073359106691735508553258069951_<39>
P42 = 238220374772566897555570835368515940408729_<42>
P50 = 90181194435531348598364513854322550480408866621333_<50>

Number: 58881_135 N=4488882689149023875520064585705347876974462576989631612642963502758164324782689377702804967279009552596450208508600910972159017907 ( 130 digits) SNFS difficulty: 136 digits. Divisors found: r1=208950478073359106691735508553258069951 (pp39) r2=238220374772566897555570835368515940408729 (pp42) r3=90181194435531348598364513854322550480408866621333 (pp50) Version: Msieve-1.39 Total time: 3.61 hours. Scaled time: 9.32 units (timescale=2.585). Factorization parameters were as follows: n: 4488882689149023875520064585705347876974462576989631612642963502758164324782689377702804967279009552596450208508600910972159017907 m: 1000000000000000000000000000 deg: 5 c5: 53 c0: -71 skew: 1.06 type: snfs lss: 1 rlim: 1330000 alim: 1330000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1330000/1330000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [665000, 1265001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 180652 x 180900 Total sieving time: 3.61 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,136,5,0,0,0,0,0,0,0,0,1330000,1330000,26,26,48,48,2.3,2.3,75000 total time: 3.61 hours. --------- CPU info (if available) ----------

(53·10¹⁴²-71)/9 = 5(8)₁₄₁1_<143> = 3² · 1709 · 278909 · 76152539500821414403933627_<26> · C108
C108 = P53 · P55
P53 = 71133922634174006030717975784795514715709640159273987_<53>
P55 = 2534107945612965006523312677086987427729240908255143361_<55>

Number: 58881_142 N=180261038549878282546405625387619251986666046371548632232487890600553463920445113493554792990997936363050307 ( 108 digits) SNFS difficulty: 144 digits. Divisors found: r1=71133922634174006030717975784795514715709640159273987 (pp53) r2=2534107945612965006523312677086987427729240908255143361 (pp55) Version: Msieve-1.39 Total time: 9.02 hours. Scaled time: 23.19 units (timescale=2.570). Factorization parameters were as follows: n: 180261038549878282546405625387619251986666046371548632232487890600553463920445113493554792990997936363050307 m: 20000000000000000000000000000 deg: 5 c5: 1325 c0: -568 skew: 0.84 type: snfs lss: 1 rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [900000, 2400001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 323665 x 323913 Total sieving time: 9.02 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,144,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,49,49,2.3,2.3,100000 total time: 9.02 hours. --------- CPU info (if available) ----------

(53·10¹⁵⁸-71)/9 = 5(8)₁₅₇1_<159> = 7 · 103² · 36843969518977_<14> · C141
C141 = P54 · P87
P54 = 590800533267749425396799989726967304158855580389298407_<54>
P87 = 364295308035138105843948238320786618697318570121178416315717666433432812884446432322033_<87>

Number: 58881_158 N=215225862254098635062373516145563229858180884948610690716839884723050559871095844778820344045193448097260622781286766391923370173940757901431 ( 141 digits) SNFS difficulty: 161 digits. Divisors found: r1=590800533267749425396799989726967304158855580389298407 (pp54) r2=364295308035138105843948238320786618697318570121178416315717666433432812884446432322033 (pp87) Version: Msieve-1.39 Total time: 36.12 hours. Scaled time: 62.82 units (timescale=1.739). Factorization parameters were as follows: n: 215225862254098635062373516145563229858180884948610690716839884723050559871095844778820344045193448097260622781286766391923370173940757901431 m: 50000000000000000000000000000000 deg: 5 c5: 424 c0: -1775 skew: 1.33 type: snfs lss: 1 rlim: 3400000 alim: 3400000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 3400000/3400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1700000, 3600001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 710549 x 710797 Total sieving time: 36.12 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000 total time: 36.12 hours. --------- CPU info (if available) ----------

By Ignacio Santos / GGNFS, Msieve / Apr 18, 2009
(53·10¹⁴⁷-71)/9 = 5(8)₁₄₆1_<148> = 173 · 911 · 1864678338609841_<16> · C128
C128 = P40 · P88
P40 = 8841650303160994912744847210119857502267_<40>
P88 = 2266374213407869403317452567641879525824318358979772631723729317593675170965387268563441_<88>

Number: 58881_147 N=20038488251053949891160955364517975958712532523335809074228319663764962729976432022531272278261934548560037253969985567490820747 ( 128 digits) SNFS difficulty: 149 digits. Divisors found: r1=8841650303160994912744847210119857502267 (pp40) r2=2266374213407869403317452567641879525824318358979772631723729317593675170965387268563441 (pp88) Version: Msieve-1.39 Total time: 13.69 hours. Scaled time: 35.28 units (timescale=2.577). Factorization parameters were as follows: n: 20038488251053949891160955364517975958712532523335809074228319663764962729976432022531272278261934548560037253969985567490820747 m: 200000000000000000000000000000 deg: 5 c5: 1325 c0: -568 skew: 0.84 type: snfs lss: 1 rlim: 2200000 alim: 2200000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 2200000/2200000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [1100000, 3300001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 406122 x 406370 Total sieving time: 13.69 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,149,5,0,0,0,0,0,0,0,0,2200000,2200000,26,26,49,49,2.3,2.3,100000 total time: 13.69 hours. --------- CPU info (if available) ----------

(32·10¹⁹⁴+13)/9 = 3(5)₁₉₃7_<195> = 3 · 7 · 17 · 167 · 166186338707_<12> · 494623864127202459693037_<24> · 3118053696717644861370191005951739_<34> · C122
C122 = P44 · P79
P44 = 19474818079230790147783809942972607846336609_<44>
P79 = 1194800501768501725770690816539500998982141406904802206750689178224457211794067_<79>

Number: 35557_194 N=23268522412915237066157072508677930272386856866646539514759309590878493431200958246887248353476180538089263618054471098803 ( 122 digits) Divisors found: r1=19474818079230790147783809942972607846336609 (pp44) r2=1194800501768501725770690816539500998982141406904802206750689178224457211794067 (pp79) Version: Msieve-1.39 Total time: 50.89 hours. Scaled time: 131.26 units (timescale=2.579). Factorization parameters were as follows: n: 23268522412915237066157072508677930272386856866646539514759309590878493431200958246887248353476180538089263618054471098803 Y0: -279098707443920442464360 Y1: 10054681781741 c0: 794709234251163174045516183 c1: -1662989921838592892427253 c2: 9037051214934208389 c3: -32437449469927 c4: -6193801292 c5: 13740 skew: 95344.69 type: gnfs Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2500000, 5080001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 686177 x 686425 Total sieving time: 50.89 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,121,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.4,2.4,60000 total time: 50.89 hours. --------- CPU info (if available) ----------

(52·10¹⁷⁵+11)/9 = 5(7)₁₇₄9_<176> = 59 · C174
C174 = P84 · P91
P84 = 221396733866059271753457736994463053326306135043477879714218658472367433821816422859_<84>
P91 = 4423210550645817710188763098309667499105730033402825302895493919405103994634059074107437659_<91>

Number: 57779_175 N=979284369114877589453860640301318267419962335216572504708097928436911487758945386064030131826741996233521657250470809792843691148775894538606403013182674199623352165725047081 ( 174 digits) SNFS difficulty: 176 digits. Divisors found: r1=221396733866059271753457736994463053326306135043477879714218658472367433821816422859 (pp84) r2=4423210550645817710188763098309667499105730033402825302895493919405103994634059074107437659 (pp91) Version: Msieve-1.39 Total time: 59.74 hours. Scaled time: 103.90 units (timescale=1.739). Factorization parameters were as follows: n: 979284369114877589453860640301318267419962335216572504708097928436911487758945386064030131826741996233521657250470809792843691148775894538606403013182674199623352165725047081 m: 100000000000000000000000000000000000 deg: 5 c5: 52 c0: 11 skew: 0.73 type: snfs lss: 1 rlim: 6200000 alim: 6200000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 6200000/6200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3100000, 6000001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1140797 x 1141045 Total sieving time: 59.74 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,176,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,53,53,2.5,2.5,100000 total time: 59.74 hours. --------- CPU info (if available) ----------

Apr 18, 2009 (7th)

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Apr 17, 2009
(47·10¹⁹⁶+61)/9 = 5(2)₁₉₅9_<197> = C197
C197 = P76 · P122
P76 = 1579229435921678256326591199705715594120801084508283699645866680988859851099_<76>
P122 = 33068166685826757029330791732171671095878658225580448280795059966475529175322301526715686040210443228306558116508701585871_<122>

Number: 52229_196 N=52222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222229 ( 197 digits) SNFS difficulty: 197 digits. Divisors found: r1=1579229435921678256326591199705715594120801084508283699645866680988859851099 r2=33068166685826757029330791732171671095878658225580448280795059966475529175322301526715686040210443228306558116508701585871 Version: Total time: 419.87 hours. Scaled time: 1003.49 units (timescale=2.390). Factorization parameters were as follows: n: 52222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222229 m: 1000000000000000000000000000000000000000 deg: 5 c5: 470 c0: 61 skew: 0.66 type: snfs lss: 1 rlim: 18000000 alim: 18000000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5 Factor base limits: 18000000/18000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [9000000, 18400001) Primes: rational ideals reading, algebraic ideals reading, Relations: 24409029 Max relations in full relation-set: Initial matrix: Pruned matrix : 2823593 x 2823841 Total sieving time: 384.51 hours. Total relation processing time: 12.75 hours. Matrix solve time: 21.79 hours. Time per square root: 0.82 hours. Prototype def-par.txt line would be: snfs,197,5,0,0,0,0,0,0,0,0,18000000,18000000,28,28,55,55,2.5,2.5,100000 total time: 419.87 hours. --------- CPU info (if available) ----------

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Apr 18, 2009
2·10¹⁸⁹-1 = 1(9)_189<190> = 31 · 5439829 · 2720009561_<10> · 13767101225803399878919_<23> · C150
C150 = P33 · C117
P33 = 317174697888724493139312350540581_<33>
C117 = [998554062131199145511682309200429404184445404728977563784886142161737708964524438853301713011987413991352186470480119_<117>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 316716082982021715964078119995152309103483041202058322413122073625672839431656295396252831115566430331967060364389847629059167242554614320568263209139 (150 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3783356541 Step 1 took 4615ms Step 2 took 2683ms ********** Factor found in step 2: 317174697888724493139312350540581 Found probable prime factor of 33 digits: 317174697888724493139312350540581 Composite cofactor 998554062131199145511682309200429404184445404728977563784886142161737708964524438853301713011987413991352186470480119 has 117 digits

Apr 18, 2009 (6th)

By Serge Batalov / GMP-ECM 6.2.2, Msieve-1.41 / Apr 17, 2009
(53·10¹³⁹-71)/9 = 5(8)₁₃₈1_<140> = 3 · 751 · 2415546311873706757_<19> · C119
C119 = P35 · P37 · P48
P35 = 19628836388346054508128484997147281_<35>
P37 = 1950538446329560608415371227959497329_<37>
P48 = 282623148366498362008930795950925297690193155889_<48>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2883563787 Step 1 took 6925ms ********** Factor found in step 1: 1950538446329560608415371227959497329 Found probable prime factor of 37 digits: 1950538446329560608415371227959497329 Composite cofactor has 82 digits Thu Apr 16 11:00:26 2009 Msieve v. 1.41 Thu Apr 16 11:00:26 2009 random seeds: 06ab07b0 44c37f3d Thu Apr 16 11:00:26 2009 factoring 5547563538845248822936990017294757100627630247645492603497532000944928035525487809 (82 digits) Thu Apr 16 11:00:26 2009 searching for 15-digit factors Thu Apr 16 11:00:27 2009 commencing quadratic sieve (82-digit input) Thu Apr 16 11:00:27 2009 using multiplier of 1 Thu Apr 16 11:00:27 2009 using 64kb Opteron sieve core Thu Apr 16 11:00:27 2009 sieve interval: 6 blocks of size 65536 Thu Apr 16 11:00:27 2009 processing polynomials in batches of 17 Thu Apr 16 11:00:27 2009 using a sieve bound of 1348597 (51765 primes) Thu Apr 16 11:00:27 2009 using large prime bound of 125419521 (26 bits) Thu Apr 16 11:00:27 2009 using trial factoring cutoff of 27 bits Thu Apr 16 11:00:27 2009 polynomial 'A' values have 10 factors Thu Apr 16 11:13:18 2009 51987 relations (27028 full + 24959 combined from 270581 partial), need 51861 Thu Apr 16 11:13:18 2009 begin with 297609 relations Thu Apr 16 11:13:18 2009 reduce to 73841 relations in 2 passes Thu Apr 16 11:13:18 2009 attempting to read 73841 relations Thu Apr 16 11:13:18 2009 recovered 73841 relations Thu Apr 16 11:13:18 2009 recovered 64025 polynomials Thu Apr 16 11:13:18 2009 attempting to build 51987 cycles Thu Apr 16 11:13:18 2009 found 51987 cycles in 1 passes Thu Apr 16 11:13:18 2009 distribution of cycle lengths: Thu Apr 16 11:13:18 2009 length 1 : 27028 Thu Apr 16 11:13:18 2009 length 2 : 24959 Thu Apr 16 11:13:18 2009 largest cycle: 2 relations Thu Apr 16 11:13:18 2009 matrix is 51765 x 51987 (7.6 MB) with weight 1583604 (30.46/col) Thu Apr 16 11:13:18 2009 sparse part has weight 1583604 (30.46/col) Thu Apr 16 11:13:19 2009 filtering completed in 3 passes Thu Apr 16 11:13:19 2009 matrix is 36391 x 36453 (5.9 MB) with weight 1254865 (34.42/col) Thu Apr 16 11:13:19 2009 sparse part has weight 1254865 (34.42/col) Thu Apr 16 11:13:19 2009 saving the first 48 matrix rows for later Thu Apr 16 11:13:19 2009 matrix is 36343 x 36453 (4.6 MB) with weight 1009631 (27.70/col) Thu Apr 16 11:13:19 2009 sparse part has weight 832049 (22.83/col) Thu Apr 16 11:13:19 2009 matrix includes 64 packed rows Thu Apr 16 11:13:19 2009 using block size 14581 for processor cache size 6144 kB Thu Apr 16 11:13:19 2009 commencing Lanczos iteration Thu Apr 16 11:13:19 2009 memory use: 4.3 MB Thu Apr 16 11:13:25 2009 lanczos halted after 576 iterations (dim = 36339) Thu Apr 16 11:13:25 2009 recovered 15 nontrivial dependencies Thu Apr 16 11:13:25 2009 prp35 factor: 19628836388346054508128484997147281 Thu Apr 16 11:13:25 2009 prp48 factor: 282623148366498362008930795950925297690193155889 Thu Apr 16 11:13:25 2009 elapsed time 00:12:59

By Serge Batalov / GMP-ECM 6.2.2, Msieve-1.41 / Apr 18, 2009
(53·10¹³⁸-71)/9 = 5(8)₁₃₇1_<139> = 29 · 647951 · 358891536869_<12> · 207918343886153_<15> · 6192700806701161_<16> · C90
C90 = P42 · P49
P42 = 343285591799040843138102857725593336454477_<42>
P49 = 1975611290293895905492495874305707347552169153691_<49>

Fri Apr 17 16:08:56 2009 Msieve v. 1.41 Fri Apr 17 16:08:56 2009 random seeds: c0d9302b 3e47c1e3 Fri Apr 17 16:08:56 2009 factoring 678198890953406730719061459299602476927341145140434803371927643801924003643416583638024607 (90 digits) Fri Apr 17 16:08:56 2009 searching for 15-digit factors Fri Apr 17 16:08:57 2009 commencing quadratic sieve (90-digit input) Fri Apr 17 16:08:57 2009 using multiplier of 15 Fri Apr 17 16:08:57 2009 using 64kb Opteron sieve core Fri Apr 17 16:08:57 2009 sieve interval: 18 blocks of size 65536 Fri Apr 17 16:08:57 2009 processing polynomials in batches of 6 Fri Apr 17 16:08:57 2009 using a sieve bound of 1618739 (61134 primes) Fri Apr 17 16:08:57 2009 using large prime bound of 135974076 (27 bits) Fri Apr 17 16:08:57 2009 using double large prime bound of 436737990159996 (42-49 bits) Fri Apr 17 16:08:57 2009 using trial factoring cutoff of 49 bits Fri Apr 17 16:08:57 2009 polynomial 'A' values have 12 factors Fri Apr 17 17:01:51 2009 61570 relations (16202 full + 45368 combined from 667867 partial), need 61230 Fri Apr 17 17:01:51 2009 begin with 684069 relations Fri Apr 17 17:01:51 2009 reduce to 150644 relations in 10 passes Fri Apr 17 17:01:51 2009 attempting to read 150644 relations Fri Apr 17 17:01:52 2009 recovered 150644 relations Fri Apr 17 17:01:52 2009 recovered 130162 polynomials Fri Apr 17 17:01:52 2009 attempting to build 61570 cycles Fri Apr 17 17:01:52 2009 found 61570 cycles in 5 passes Fri Apr 17 17:01:52 2009 distribution of cycle lengths: Fri Apr 17 17:01:52 2009 length 1 : 16202 Fri Apr 17 17:01:52 2009 length 2 : 11713 Fri Apr 17 17:01:52 2009 length 3 : 10999 Fri Apr 17 17:01:52 2009 length 4 : 8245 Fri Apr 17 17:01:52 2009 length 5 : 5920 Fri Apr 17 17:01:52 2009 length 6 : 3701 Fri Apr 17 17:01:52 2009 length 7 : 2252 Fri Apr 17 17:01:52 2009 length 9+: 2538 Fri Apr 17 17:01:52 2009 largest cycle: 16 relations Fri Apr 17 17:01:53 2009 matrix is 61134 x 61570 (16.2 MB) with weight 3746682 (60.85/col) Fri Apr 17 17:01:53 2009 sparse part has weight 3746682 (60.85/col) Fri Apr 17 17:01:53 2009 filtering completed in 3 passes Fri Apr 17 17:01:53 2009 matrix is 57223 x 57287 (15.1 MB) with weight 3493687 (60.99/col) Fri Apr 17 17:01:53 2009 sparse part has weight 3493687 (60.99/col) Fri Apr 17 17:01:53 2009 saving the first 48 matrix rows for later Fri Apr 17 17:01:53 2009 matrix is 57175 x 57287 (9.8 MB) with weight 2739358 (47.82/col) Fri Apr 17 17:01:53 2009 sparse part has weight 2003525 (34.97/col) Fri Apr 17 17:01:53 2009 matrix includes 64 packed rows Fri Apr 17 17:01:53 2009 using block size 22914 for processor cache size 6144 kB Fri Apr 17 17:01:53 2009 commencing Lanczos iteration Fri Apr 17 17:01:53 2009 memory use: 8.7 MB Fri Apr 17 17:02:08 2009 lanczos halted after 905 iterations (dim = 57171) Fri Apr 17 17:02:08 2009 recovered 15 nontrivial dependencies Fri Apr 17 17:02:09 2009 prp42 factor: 343285591799040843138102857725593336454477 Fri Apr 17 17:02:09 2009 prp49 factor: 1975611290293895905492495874305707347552169153691 Fri Apr 17 17:02:09 2009 elapsed time 00:53:13

(53·10¹³³-71)/9 = 5(8)₁₃₂1_<134> = 3³ · C133
C133 = P49 · P85
P49 = 1736132214682934259760138027279169156218659023617_<49>
P85 = 1256281025374591242622665628469340154953343169071606736108858272346763080946503313059_<85>

SNFS difficulty: 136 digits. Divisors found: r1=1736132214682934259760138027279169156218659023617 (pp49) r2=1256281025374591242622665628469340154953343169071606736108858272346763080946503313059 (pp85) Version: Msieve-1.41 Total time: 2.32 hours. Scaled time: 6.60 units (timescale=2.846). Factorization parameters were as follows: n: 2181069958847736625514403292181069958847736625514403292181069958847736625514403292181069958847736625514403292181069958847736625514403 m: 500000000000000000000000000 deg: 5 c5: 424 c0: -1775 skew: 1.33 type: snfs lss: 1 rlim: 1300000 alim: 1300000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [650000, 1475001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 230935 x 231183 Total sieving time: 2.06 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.18 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,136.000,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,48,48,2.3,2.3,75000 total time: 2.32 hours.

Apr 18, 2009 (5th)

By Robert Backstrom / GGNFS, Msieve / Apr 17, 2009
(89·10¹⁶⁷+1)/9 = 9(8)₁₆₆9_<168> = 11 · 47 · 247241048054093075068483_<24> · C142
C142 = P53 · P90
P53 = 11735515965675694227339384230495652756357364865648203_<53>
P90 = 659225790392093267074705101810375554863868616091506172922557608512373829311495920690579333_<90>

Number: n N=7736354788131589206605390894565669193375418184832672785771192551985407171377229803380722616315685306413508395609143695564930928388730640388599 ( 142 digits) SNFS difficulty: 171 digits. Divisors found: Fri Apr 17 03:58:58 2009 prp53 factor: 11735515965675694227339384230495652756357364865648203 Fri Apr 17 03:58:58 2009 prp90 factor: 659225790392093267074705101810375554863868616091506172922557608512373829311495920690579333 Fri Apr 17 03:58:58 2009 elapsed time 01:46:12 (Msieve 1.39 - dependency 4) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 38.58 hours. Scaled time: 102.19 units (timescale=2.649). Factorization parameters were as follows: name: KA_9_8_166_9 n: 7736354788131589206605390894565669193375418184832672785771192551985407171377229803380722616315685306413508395609143695564930928388730640388599 m: 5000000000000000000000000000000000 deg: 5 c5: 356 c0: 125 skew: 0.81 type: snfs lss: 1 rlim: 5000000 alim: 5000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2500000, 4700557) Primes: RFBsize:348513, AFBsize:349036, largePrimes:16214116 encountered Relations: rels:15325613, finalFF:700471 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1460658 hash collisions in 16448507 relations Msieve: matrix is 883293 x 883541 (238.8 MB) Total sieving time: 38.03 hours. Total relation processing time: 0.54 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.4,2.4,100000 total time: 38.58 hours. --------- CPU info (if available) ----------

(82·10¹⁶⁷-1)/9 = 9(1)_167<168> = 6136826462026924582665204373_<28> · C141
C141 = P52 · P89
P52 = 9296318818779243323402076699581821393618881424501441_<52>
P89 = 15970425640509844064334216093304767762181621347681644889750865211008039470305029735475627_<89>

Number: n N=148466168425786214041772406044824270769076040264514519242184892190960766848593410970947645326074786069119538379819788655771134770639481878507 ( 141 digits) SNFS difficulty: 171 digits. Divisors found: Fri Apr 17 19:21:19 2009 prp52 factor: 9296318818779243323402076699581821393618881424501441 Fri Apr 17 19:21:19 2009 prp89 factor: 15970425640509844064334216093304767762181621347681644889750865211008039470305029735475627 Fri Apr 17 19:21:19 2009 elapsed time 01:21:04 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 52.39 hours. Scaled time: 139.35 units (timescale=2.660). Factorization parameters were as follows: name: KA_9_1_167 n: 148466168425786214041772406044824270769076040264514519242184892190960766848593410970947645326074786069119538379819788655771134770639481878507 m: 5000000000000000000000000000000000 deg: 5 c5: 328 c0: -125 skew: 0.82 type: snfs lss: 1 rlim: 5000000 alim: 5000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2500000, 5581229) Primes: RFBsize:348513, AFBsize:348767, largePrimes:17098512 encountered Relations: rels:16600199, finalFF:677269 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 2019117 hash collisions in 18657465 relations Msieve: matrix is 870062 x 870310 (231.6 MB) Total sieving time: 51.69 hours. Total relation processing time: 0.70 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.4,2.4,100000 total time: 52.39 hours. --------- CPU info (if available) ----------

4·10²¹⁷+1 = 4(0)₂₁₆1_<218> = 18686807 · C211
C211 = P57 · P154
P57 = 578022421484392833484314349887736849483921909178334750733_<57>
P154 = 3703225908027418809075172754492065279505406206615636647652312656725745127646139680370212557167658670799266733808441570447351849092965953387204337084674371_<154>

Number: n N=2140547606661748045024492413283874553849675870254345753129467222516934005900526505143441573512264561837664401414324020149616785789032872229054433965096337753153869465232877933613805718654877743426150866758563943 ( 211 digits) SNFS difficulty: 218 digits. Divisors found: Sat Apr 18 00:43:41 2009 prp57 factor: 578022421484392833484314349887736849483921909178334750733 Sat Apr 18 00:43:41 2009 prp154 factor: 3703225908027418809075172754492065279505406206615636647652312656725745127646139680370212557167658670799266733808441570447351849092965953387204337084674371 Sat Apr 18 00:43:41 2009 elapsed time 56:50:02 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20050930-k8 Total time: 174.05 hours. Scaled time: 350.71 units (timescale=2.015). Factorization parameters were as follows: name: KA_4_0_216_1 n: 2140547606661748045024492413283874553849675870254345753129467222516934005900526505143441573512264561837664401414324020149616785789032872229054433965096337753153869465232877933613805718654877743426150866758563943 m: 2000000000000000000000000000000000000 deg: 6 c6: 5 c0: 8 skew: 1.08 type: snfs lss: 1 rlim: 31000000 alim: 31000000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 31000000/31000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [15500000, 45599990) Primes: RFBsize:1915979, AFBsize:1916784, largePrimes:34927111 encountered Relations: rels:29018997, finalFF:841025 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 8207149 hash collisions in 48938562 relations Msieve: matrix is 5272052 x 5272300 (1428.4 MB) Total sieving time: 173.00 hours. Total relation processing time: 1.05 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,218,6,0,0,0,0,0,0,0,0,31000000,31000000,29,29,58,58,2.6,2.6,100000 total time: 174.05 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU1: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU2: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU3: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 Memory: 3368968k/3407296k available (2747k kernel code, 36968k reserved, 1425k data, 416k init, 2489792k highmem) Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.97 BogoMIPS (lpj=2830489) Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830447) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830455) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830456) Total of 4 processors activated (22643.69 BogoMIPS).

By Robert Backstrom / GGNFS, Msieve / Apr 18, 2009
(53·10¹⁴⁵-71)/9 = 5(8)₁₄₄1_<146> = 3 · 17 · 929 · 485499853 · 850230413 · 1274328443_<10> · 4221790879_<10> · C105
C105 = P43 · P63
P43 = 3316688302115642889056012400773516430032419_<43>
P63 = 168748133784761883638959898979058638917739521572854314854336157_<63>

Number: n N=559684961327765247034503844891371736894556026815844268035413780122864846810001043646439238215822233873783 ( 105 digits) Divisors found: Sat Apr 18 02:54:26 2009 prp43 factor: 3316688302115642889056012400773516430032419 Sat Apr 18 02:54:26 2009 prp63 factor: 168748133784761883638959898979058638917739521572854314854336157 Sat Apr 18 02:54:26 2009 elapsed time 00:38:14 (Msieve 1.39 - dependency 4) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 5.68 hours. Scaled time: 15.10 units (timescale=2.660). Factorization parameters were as follows: name: KA_5_8_144_1 n: 559684961327765247034503844891371736894556026815844268035413780122864846810001043646439238215822233873783 Y0: -176799813543897703182 Y1: 72476416319 c0: -10442345234358626558524313 c1: 19040482229417220485271 c2: 581533457134543607 c3: -10679814889731 c4: -189005634 c5: 3240 skew: 43207.82 type: gnfs rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [1250000, 1851097) Primes: RFBsize:183072, AFBsize:183757, largePrimes:14104467 encountered Relations: rels:11862900, finalFF:384598 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 684206 hash collisions in 12317492 relations Msieve: matrix is 376672 x 376920 (104.9 MB) Total sieving time: 5.43 hours. Total relation processing time: 0.25 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,104,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,28,28,56,56,2.6,2.6,150000 total time: 5.68 hours. --------- CPU info (if available) ----------

(46·10¹⁶⁵+71)/9 = 5(1)₁₆₄9_<166> = 181 · 191 · 1361 · 23993 · 25637611 · 1804773857_<10> · C137
C137 = P57 · P81
P57 = 694575844284880677867191247137091366345427839339582636913_<57>
P81 = 140877189974738893565168112114361733965740981505111702335142003362792062349532543_<81>

Number: n N=97849893167185795053681505438158227359229056175828170023743411900227181839092558179099204573640195680027563053318468911424344244846559759 ( 137 digits) SNFS difficulty: 166 digits. Divisors found: Sat Apr 18 05:42:10 2009 prp57 factor: 694575844284880677867191247137091366345427839339582636913 Sat Apr 18 05:42:10 2009 prp81 factor: 140877189974738893565168112114361733965740981505111702335142003362792062349532543 Sat Apr 18 05:42:10 2009 elapsed time 00:59:04 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 34.25 hours. Scaled time: 91.11 units (timescale=2.660). Factorization parameters were as follows: name: KA_5_1_164_9 n: 97849893167185795053681505438158227359229056175828170023743411900227181839092558179099204573640195680027563053318468911424344244846559759 m: 1000000000000000000000000000000000 deg: 5 c5: 46 c0: 71 skew: 1.09 type: snfs lss: 1 rlim: 4200000 alim: 4200000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4200000/4200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved special-q in [2100000, 4073129) Primes: RFBsize:296314, AFBsize:296472, largePrimes:8717814 encountered Relations: rels:8479753, finalFF:538519 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 872510 hash collisions in 9552985 relations Msieve: matrix is 720695 x 720943 (193.3 MB) Total sieving time: 33.98 hours. Total relation processing time: 0.27 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000 total time: 34.25 hours. --------- CPU info (if available) ----------

Apr 18, 2009 (4th)

By Sinkiti Sibata / Msieve, GGNFS / Apr 17, 2009
(53·10¹³⁰-71)/9 = 5(8)₁₂₉1_<131> = 3 · 19 · 61 · 577 · 2927 · 7382416109_<10> · 1369886219328469_<16> · C96
C96 = P38 · P59
P38 = 37956724012464402598129885947865441919_<38>
P59 = 26125126047863880080771368057462882723263924827439187557293_<59>

Fri Apr 17 08:04:56 2009 Msieve v. 1.41 Fri Apr 17 08:04:56 2009 random seeds: 8d9111a4 23cf54e5 Fri Apr 17 08:04:56 2009 factoring 991624199189614174782401830448492816243117370394794813266981352510574370554134332396855576365267 (96 digits) Fri Apr 17 08:04:57 2009 searching for 15-digit factors Fri Apr 17 08:04:59 2009 commencing quadratic sieve (96-digit input) Fri Apr 17 08:04:59 2009 using multiplier of 67 Fri Apr 17 08:04:59 2009 using 32kb Intel Core sieve core Fri Apr 17 08:04:59 2009 sieve interval: 36 blocks of size 32768 Fri Apr 17 08:04:59 2009 processing polynomials in batches of 6 Fri Apr 17 08:04:59 2009 using a sieve bound of 2299963 (84681 primes) Fri Apr 17 08:04:59 2009 using large prime bound of 344994450 (28 bits) Fri Apr 17 08:04:59 2009 using double large prime bound of 2333789820820650 (43-52 bits) Fri Apr 17 08:04:59 2009 using trial factoring cutoff of 52 bits Fri Apr 17 08:04:59 2009 polynomial 'A' values have 13 factors Fri Apr 17 12:43:45 2009 85035 relations (21540 full + 63495 combined from 1262176 partial), need 84777 Fri Apr 17 12:43:47 2009 begin with 1283716 relations Fri Apr 17 12:43:48 2009 reduce to 219055 relations in 12 passes Fri Apr 17 12:43:48 2009 attempting to read 219055 relations Fri Apr 17 12:43:52 2009 recovered 219055 relations Fri Apr 17 12:43:52 2009 recovered 204927 polynomials Fri Apr 17 12:43:52 2009 attempting to build 85035 cycles Fri Apr 17 12:43:52 2009 found 85035 cycles in 6 passes Fri Apr 17 12:43:52 2009 distribution of cycle lengths: Fri Apr 17 12:43:52 2009 length 1 : 21540 Fri Apr 17 12:43:52 2009 length 2 : 15038 Fri Apr 17 12:43:52 2009 length 3 : 14584 Fri Apr 17 12:43:52 2009 length 4 : 11363 Fri Apr 17 12:43:52 2009 length 5 : 8571 Fri Apr 17 12:43:52 2009 length 6 : 5599 Fri Apr 17 12:43:52 2009 length 7 : 3502 Fri Apr 17 12:43:52 2009 length 9+: 4838 Fri Apr 17 12:43:52 2009 largest cycle: 21 relations Fri Apr 17 12:43:53 2009 matrix is 84681 x 85035 (22.9 MB) with weight 5657471 (66.53/col) Fri Apr 17 12:43:53 2009 sparse part has weight 5657471 (66.53/col) Fri Apr 17 12:43:54 2009 filtering completed in 3 passes Fri Apr 17 12:43:54 2009 matrix is 80389 x 80453 (21.7 MB) with weight 5370825 (66.76/col) Fri Apr 17 12:43:54 2009 sparse part has weight 5370825 (66.76/col) Fri Apr 17 12:43:54 2009 saving the first 48 matrix rows for later Fri Apr 17 12:43:54 2009 matrix is 80341 x 80453 (13.9 MB) with weight 4286515 (53.28/col) Fri Apr 17 12:43:54 2009 sparse part has weight 3167151 (39.37/col) Fri Apr 17 12:43:54 2009 matrix includes 64 packed rows Fri Apr 17 12:43:54 2009 using block size 32181 for processor cache size 1024 kB Fri Apr 17 12:43:55 2009 commencing Lanczos iteration Fri Apr 17 12:43:55 2009 memory use: 13.2 MB Fri Apr 17 12:44:38 2009 lanczos halted after 1272 iterations (dim = 80340) Fri Apr 17 12:44:38 2009 recovered 17 nontrivial dependencies Fri Apr 17 12:44:40 2009 prp38 factor: 37956724012464402598129885947865441919 Fri Apr 17 12:44:40 2009 prp59 factor: 26125126047863880080771368057462882723263924827439187557293 Fri Apr 17 12:44:40 2009 elapsed time 04:39:44

(44·10¹⁸⁵+1)/9 = 4(8)₁₈₄9_<186> = 3² · 19 · C184
C184 = P33 · P46 · P106
P33 = 301279492672528356310887081620281_<33>
P46 = 2007681696397209428158663231335805768631686309_<46>
P106 = 4726608434867671415692354975353016939132883160285222480786726238803221676691996179230672373731698457768071_<106>

Number: 48889_185 N=2858999350227420402858999350227420402858999350227420402858999350227420402858999350227420402858999350227420402858999350227420402858999350227420402858999350227420402858999350227420402859 ( 184 digits) SNFS difficulty: 187 digits. Divisors found: r1=301279492672528356310887081620281 (pp33) r2=2007681696397209428158663231335805768631686309 (pp46) r3=4726608434867671415692354975353016939132883160285222480786726238803221676691996179230672373731698457768071 (pp106) Version: GGNFS-0.77.1-20060513-nocona Total time: 342.67 hours. Scaled time: 871.76 units (timescale=2.544). Factorization parameters were as follows: name: 48889_185 n: 2858999350227420402858999350227420402858999350227420402858999350227420402858999350227420402858999350227420402858999350227420402858999350227420402858999350227420402858999350227420402859 m: 20000000000000000000000000000000000000 deg: 5 c5: 11 c0: 8 skew: 0.94 type: snfs rlim: 8000000 alim: 8000000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 Factor base limits: 8000000/8000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved algebraic special-q in [4000000, 8100001) Primes: RFBsize:539777, AFBsize:539726, largePrimes:19572351 encountered Relations: rels:20827886, finalFF:1635103 Max relations in full relation-set: 28 Initial matrix: 1079569 x 1635103 with sparse part having weight 203875562. Pruned matrix : 801126 x 806587 with weight 198989218. Total sieving time: 323.10 hours. Total relation processing time: 0.57 hours. Matrix solve time: 18.63 hours. Time per square root: 0.37 hours. Prototype def-par.txt line would be: snfs,187,5,0,0,0,0,0,0,0,0,8000000,8000000,28,28,54,54,2.5,2.5,100000 total time: 342.67 hours. --------- CPU info (if available) ----------

By Sinkiti Sibata / Msieve, GGNFS / Apr 18, 2009
(53·10¹⁵¹-71)/9 = 5(8)₁₅₀1_<152> = 3² · 73 · 601 · 3067 · 8360509 · 50792883547972719649_<20> · 542501417551026748883_<21> · C96
C96 = P47 · P49
P47 = 42936148687473484273728024786408390015437208617_<47>
P49 = 4916094149477628730365878389162042910302106837749_<49>

Fri Apr 17 22:03:47 2009 Msieve v. 1.41 Fri Apr 17 22:03:47 2009 random seeds: e488b000 c6788c06 Fri Apr 17 22:03:47 2009 factoring 211078149363589963815116393190719711120312274320994824021579216883462998082421755858953483683133 (96 digits) Fri Apr 17 22:03:48 2009 searching for 15-digit factors Fri Apr 17 22:03:50 2009 commencing quadratic sieve (96-digit input) Fri Apr 17 22:03:50 2009 using multiplier of 3 Fri Apr 17 22:03:50 2009 using 32kb Intel Core sieve core Fri Apr 17 22:03:50 2009 sieve interval: 36 blocks of size 32768 Fri Apr 17 22:03:50 2009 processing polynomials in batches of 6 Fri Apr 17 22:03:50 2009 using a sieve bound of 2221733 (82353 primes) Fri Apr 17 22:03:50 2009 using large prime bound of 333259950 (28 bits) Fri Apr 17 22:03:50 2009 using double large prime bound of 2192853470339550 (43-51 bits) Fri Apr 17 22:03:50 2009 using trial factoring cutoff of 51 bits Fri Apr 17 22:03:50 2009 polynomial 'A' values have 12 factors Sat Apr 18 02:35:33 2009 82536 relations (20005 full + 62531 combined from 1235511 partial), need 82449 Sat Apr 18 02:35:35 2009 begin with 1255516 relations Sat Apr 18 02:35:36 2009 reduce to 216093 relations in 10 passes Sat Apr 18 02:35:36 2009 attempting to read 216093 relations Sat Apr 18 02:35:39 2009 recovered 216093 relations Sat Apr 18 02:35:39 2009 recovered 202007 polynomials Sat Apr 18 02:35:40 2009 attempting to build 82536 cycles Sat Apr 18 02:35:40 2009 found 82536 cycles in 6 passes Sat Apr 18 02:35:40 2009 distribution of cycle lengths: Sat Apr 18 02:35:40 2009 length 1 : 20005 Sat Apr 18 02:35:40 2009 length 2 : 14414 Sat Apr 18 02:35:40 2009 length 3 : 13967 Sat Apr 18 02:35:40 2009 length 4 : 11178 Sat Apr 18 02:35:40 2009 length 5 : 8393 Sat Apr 18 02:35:40 2009 length 6 : 5707 Sat Apr 18 02:35:40 2009 length 7 : 3677 Sat Apr 18 02:35:40 2009 length 9+: 5195 Sat Apr 18 02:35:40 2009 largest cycle: 20 relations Sat Apr 18 02:35:40 2009 matrix is 82353 x 82536 (23.0 MB) with weight 5698494 (69.04/col) Sat Apr 18 02:35:40 2009 sparse part has weight 5698494 (69.04/col) Sat Apr 18 02:35:42 2009 filtering completed in 3 passes Sat Apr 18 02:35:42 2009 matrix is 78705 x 78769 (22.1 MB) with weight 5470954 (69.46/col) Sat Apr 18 02:35:42 2009 sparse part has weight 5470954 (69.46/col) Sat Apr 18 02:35:42 2009 saving the first 48 matrix rows for later Sat Apr 18 02:35:42 2009 matrix is 78657 x 78769 (15.6 MB) with weight 4510774 (57.27/col) Sat Apr 18 02:35:42 2009 sparse part has weight 3628703 (46.07/col) Sat Apr 18 02:35:42 2009 matrix includes 64 packed rows Sat Apr 18 02:35:42 2009 using block size 31507 for processor cache size 1024 kB Sat Apr 18 02:35:43 2009 commencing Lanczos iteration Sat Apr 18 02:35:43 2009 memory use: 14.0 MB Sat Apr 18 02:36:32 2009 lanczos halted after 1245 iterations (dim = 78657) Sat Apr 18 02:36:32 2009 recovered 19 nontrivial dependencies Sat Apr 18 02:36:33 2009 prp47 factor: 42936148687473484273728024786408390015437208617 Sat Apr 18 02:36:33 2009 prp49 factor: 4916094149477628730365878389162042910302106837749 Sat Apr 18 02:36:33 2009 elapsed time 04:32:46

Apr 18, 2009 (3rd)

By Jeff Gilchrist / GGNFS, Msieve 1.41 / Apr 18, 2009
(32·10¹⁷⁰+31)/9 = 3(5)₁₆₉9_<171> = 3449 · 15128611 · 23008033 · C153
C153 = P52 · P102
P52 = 1528216471097860021313334111063020163874176813026371_<52>
P102 = 193798696059930635413390537724663298714890396659618435429067607489207334036908047360384278676186052967_<102>

Number: 35559_170 N=296166359396073944683160485101585851681443934301671987655522323564543253916503976987487165849021699261332677580008470890265619918699850211710956573792757 ( 153 digits) SNFS difficulty: 171 digits. Divisors found: r1=1528216471097860021313334111063020163874176813026371 (pp52) r2=193798696059930635413390537724663298714890396659618435429067607489207334036908047360384278676186052967 (pp102) Version: Msieve-1.41 Total time: 90.66 hours. Scaled time: 68.27 units (timescale=0.753). Factorization parameters were as follows: n: 296166359396073944683160485101585851681443934301671987655522323564543253916503976987487165849021699261332677580008470890265619918699850211710956573792757 m: 20000000000000000000000000000000000 deg: 5 c5: 1 c0: 31 skew: 1.99 type: snfs lss: 1 rlim: 5100000 alim: 5100000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 5100000/5100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2550000, 5050001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 794466 x 794714 Total sieving time: 90.66 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,171.000,5,0,0,0,0,0,0,0,0,5100000,5100000,27,27,52,52,2.4,2.4,100000 total time: 90.66 hours. --------- CPU info (if available) ----------

Apr 18, 2009 (2nd)

By Wataru Sakai / GMP-ECM 6.2.1 / Apr 17, 2009
(17·10¹⁹⁰+1)/9 = 1(8)₁₈₉9_<191> = 13 · 649123 · 707912267722698978623_<21> · 24592951456281913764228758669239_<32> · C132
C132 = P37 · P95
P37 = 7213700843439887344632470841269291957_<37>
P95 = 17823288757233023573682324129309601544137069773637839144377564166930756298795605248649159083659_<95>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=87697117 Step 1 took 38211ms Step 2 took 13867ms ********** Factor found in step 2: 7213700843439887344632470841269291957 Found probable prime factor of 37 digits: 7213700843439887344632470841269291957 Probable prime cofactor 17823288757233023573682324129309601544137069773637839144377564166930756298795605248649159083659 has 95 digits

(49·10¹⁹⁷+41)/9 = 5(4)₁₉₆9_<198> = 3 · 103 · 229 · 693483587 · 106035242108839020242123_<24> · 2001264824074391733510725271041_<31> · C131
C131 = P40 · P91
P40 = 7753115765111063522021142552571754477947_<40>
P91 = 6743608649761494883582317379979859049540910030066178214889108592918675243582982981900750267_<91>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2900669674 Step 1 took 41286ms Step 2 took 15713ms ********** Factor found in step 2: 7753115765111063522021142552571754477947 Found probable prime factor of 40 digits: 7753115765111063522021142552571754477947 Probable prime cofactor 6743608649761494883582317379979859049540910030066178214889108592918675243582982981900750267 has 91 digits

Apr 18, 2009

By Max Dettweiler / GMP-ECM, YAFU v1.10, Msieve / Apr 17, 2009
(34·10¹⁷⁰-7)/9 = 3(7)_170<171> = 13 · 29 · 33490275305670749792334851887141_<32> · C137
C137 = P41 · P96
P41 = 34681276407981177103088346208185521753173_<41>
P96 = 862742647641399005036569351298107041173106291055284796151924344953422830786304949874008936124657_<96>

P41=34681276407981177103088346208185521753173 P96=862742647641399005036569351298107041173106291055284796151924344953422830786304949874008936124657 B1=3000000 B2=(unknown--might be 760000000?) Method=ECM Found by the ECM "workers" at http://factorization.ath.cx

(53·10¹²³-71)/9 = 5(8)₁₂₂1_<124> = 90943231 · 77869883783146913142335509_<26> · C90
C90 = P36 · P55
P36 = 202264546609434854254852740781297727_<36>
P55 = 4111248127642512233539893307565579092523923938001118957_<55>

04/16/09 16:34:17 v1.10 @ Core2Duo, starting SIQS on c90: 831559738536500690691743153345461801909511644511260916432349884974767033138555344560710739 04/16/09 16:34:17 v1.10 @ Core2Duo, random seeds: 597820055, 1786273408 04/16/09 16:34:18 v1.10 @ Core2Duo, ==== sieve params ==== 04/16/09 16:34:18 v1.10 @ Core2Duo, n = 90 digits, 299 bits 04/16/09 16:34:18 v1.10 @ Core2Duo, factor base: 66328 primes (max prime = 1764199) 04/16/09 16:34:18 v1.10 @ Core2Duo, single large prime cutoff: 211703880 (120 * pmax) 04/16/09 16:34:18 v1.10 @ Core2Duo, double large prime range from 43 to 50 bits 04/16/09 16:34:18 v1.10 @ Core2Duo, double large prime cutoff: 968973437116546 04/16/09 16:34:18 v1.10 @ Core2Duo, using 10 large prime slices of factor base 04/16/09 16:34:18 v1.10 @ Core2Duo, buckets hold 1024 elements 04/16/09 16:34:18 v1.10 @ Core2Duo, sieve interval: 22 blocks of size 32768 04/16/09 16:34:18 v1.10 @ Core2Duo, polynomial A has ~ 12 factors 04/16/09 16:34:18 v1.10 @ Core2Duo, using multiplier of 1 04/16/09 16:34:18 v1.10 @ Core2Duo, using small prime variation correction of 20 bits 04/16/09 16:34:18 v1.10 @ Core2Duo, using SSE2 for trial division and x128 sieve scanning 04/16/09 16:34:18 v1.10 @ Core2Duo, trial factoring cutoff at 97 bits 04/16/09 16:34:18 v1.10 @ Core2Duo, ==== sieving started ==== 04/16/09 17:40:00 v1.10 @ Core2Duo, sieve time = 1211.2770, relation time = 637.2920, poly_time = 2089.8140 04/16/09 17:40:00 v1.10 @ Core2Duo, 66408 relations found: 18863 full + 47545 from 811249 partial, using 443534 polys (223 A polys) 04/16/09 17:40:00 v1.10 @ Core2Duo, on average, sieving found 1.87 rels/poly and 210.54 rels/sec 04/16/09 17:40:00 v1.10 @ Core2Duo, trial division touched 26209823 sieve locations out of 639483772928 04/16/09 17:40:00 v1.10 @ Core2Duo, ==== post processing stage (msieve-1.38) ==== 04/16/09 17:40:00 v1.10 @ Core2Duo, begin with 830112 relations 04/16/09 17:40:01 v1.10 @ Core2Duo, reduce to 156592 relations in 9 passes 04/16/09 17:40:03 v1.10 @ Core2Duo, recovered 156592 relations 04/16/09 17:40:03 v1.10 @ Core2Duo, recovered 132068 polynomials 04/16/09 17:40:04 v1.10 @ Core2Duo, attempting to build 66408 cycles 04/16/09 17:40:04 v1.10 @ Core2Duo, found 66408 cycles in 5 passes 04/16/09 17:40:04 v1.10 @ Core2Duo, distribution of cycle lengths: 04/16/09 17:40:04 v1.10 @ Core2Duo, length 1 : 18863 04/16/09 17:40:04 v1.10 @ Core2Duo, length 2 : 14095 04/16/09 17:40:04 v1.10 @ Core2Duo, length 3 : 11947 04/16/09 17:40:04 v1.10 @ Core2Duo, length 4 : 8470 04/16/09 17:40:04 v1.10 @ Core2Duo, length 5 : 5531 04/16/09 17:40:04 v1.10 @ Core2Duo, length 6 : 3328 04/16/09 17:40:04 v1.10 @ Core2Duo, length 7 : 2009 04/16/09 17:40:04 v1.10 @ Core2Duo, length 9+: 2165 04/16/09 17:40:04 v1.10 @ Core2Duo, largest cycle: 19 relations 04/16/09 17:40:04 v1.10 @ Core2Duo, matrix is 66328 x 66408 (15.3 MB) with weight 3748888 (56.45/col) 04/16/09 17:40:04 v1.10 @ Core2Duo, sparse part has weight 3748888 (56.45/col) 04/16/09 17:40:04 v1.10 @ Core2Duo, filtering completed in 3 passes 04/16/09 17:40:04 v1.10 @ Core2Duo, matrix is 61551 x 61614 (14.4 MB) with weight 3515995 (57.06/col) 04/16/09 17:40:04 v1.10 @ Core2Duo, sparse part has weight 3515995 (57.06/col) 04/16/09 17:40:04 v1.10 @ Core2Duo, saving the first 48 matrix rows for later 04/16/09 17:40:04 v1.10 @ Core2Duo, matrix is 61503 x 61614 (9.0 MB) with weight 2658612 (43.15/col) 04/16/09 17:40:04 v1.10 @ Core2Duo, sparse part has weight 1991948 (32.33/col) 04/16/09 17:40:04 v1.10 @ Core2Duo, matrix includes 64 packed rows 04/16/09 17:40:04 v1.10 @ Core2Duo, using block size 24645 for processor cache size 2048 kB 04/16/09 17:40:05 v1.10 @ Core2Duo, commencing Lanczos iteration 04/16/09 17:40:05 v1.10 @ Core2Duo, memory use: 9.0 MB 04/16/09 17:40:23 v1.10 @ Core2Duo, lanczos halted after 974 iterations (dim = 61500) 04/16/09 17:40:23 v1.10 @ Core2Duo, recovered 16 nontrivial dependencies 04/16/09 17:40:24 v1.10 @ Core2Duo, prp36 = 202264546609434854254852740781297727 04/16/09 17:40:28 v1.10 @ Core2Duo, prp55 = 4111248127642512233539893307565579092523923938001118957 04/16/09 17:40:28 v1.10 @ Core2Duo, Lanczos elapsed time = 22.7030 seconds. 04/16/09 17:40:28 v1.10 @ Core2Duo, Sqrt elapsed time = 4.9220 seconds. 04/16/09 17:40:28 v1.10 @ Core2Duo, SIQS elapsed time = 3970.3590 seconds.

(53·10¹²¹-71)/9 = 5(8)₁₂₀1_<122> = 3 · 194659 · 384621067 · 207102242897777867_<18> · C91
C91 = P34 · P58
P34 = 1133539780530774666049337268862213_<34>
P58 = 1116819481169900334059112170711297777323250963240946700829_<58>

04/16/09 16:35:26 v1.10 @ Core2Duo, starting SIQS on c91: 1265959309577822454446640479059957214320018167680776045410923986160203316835382572933874577 04/16/09 16:35:26 v1.10 @ Core2Duo, random seeds: 1414385627, 1486820648 04/16/09 16:35:27 v1.10 @ Core2Duo, ==== sieve params ==== 04/16/09 16:35:27 v1.10 @ Core2Duo, n = 91 digits, 305 bits 04/16/09 16:35:27 v1.10 @ Core2Duo, factor base: 67412 primes (max prime = 1799261) 04/16/09 16:35:27 v1.10 @ Core2Duo, single large prime cutoff: 215911320 (120 * pmax) 04/16/09 16:35:27 v1.10 @ Core2Duo, double large prime range from 43 to 50 bits 04/16/09 16:35:27 v1.10 @ Core2Duo, double large prime cutoff: 1003912224363295 04/16/09 16:35:27 v1.10 @ Core2Duo, using 10 large prime slices of factor base 04/16/09 16:35:27 v1.10 @ Core2Duo, buckets hold 1024 elements 04/16/09 16:35:27 v1.10 @ Core2Duo, sieve interval: 22 blocks of size 32768 04/16/09 16:35:27 v1.10 @ Core2Duo, polynomial A has ~ 12 factors 04/16/09 16:35:27 v1.10 @ Core2Duo, using multiplier of 29 04/16/09 16:35:27 v1.10 @ Core2Duo, using small prime variation correction of 23 bits 04/16/09 16:35:27 v1.10 @ Core2Duo, using SSE2 for trial division and x128 sieve scanning 04/16/09 16:35:27 v1.10 @ Core2Duo, trial factoring cutoff at 96 bits 04/16/09 16:35:27 v1.10 @ Core2Duo, ==== sieving started ==== 04/16/09 17:38:42 v1.10 @ Core2Duo, sieve time = 1146.0730, relation time = 650.4160, poly_time = 1994.7900 04/16/09 17:38:42 v1.10 @ Core2Duo, 67497 relations found: 19809 full + 47688 from 813125 partial, using 414687 polys (202 A polys) 04/16/09 17:38:42 v1.10 @ Core2Duo, on average, sieving found 2.01 rels/poly and 219.41 rels/sec 04/16/09 17:38:42 v1.10 @ Core2Duo, trial division touched 29489564 sieve locations out of 597892399104 04/16/09 17:38:42 v1.10 @ Core2Duo, ==== post processing stage (msieve-1.38) ==== 04/16/09 17:38:44 v1.10 @ Core2Duo, begin with 832934 relations 04/16/09 17:38:45 v1.10 @ Core2Duo, reduce to 156443 relations in 10 passes 04/16/09 17:38:47 v1.10 @ Core2Duo, recovered 156443 relations 04/16/09 17:38:47 v1.10 @ Core2Duo, recovered 130277 polynomials 04/16/09 17:38:48 v1.10 @ Core2Duo, attempting to build 67497 cycles 04/16/09 17:38:48 v1.10 @ Core2Duo, found 67497 cycles in 5 passes 04/16/09 17:38:48 v1.10 @ Core2Duo, distribution of cycle lengths: 04/16/09 17:38:48 v1.10 @ Core2Duo, length 1 : 19809 04/16/09 17:38:48 v1.10 @ Core2Duo, length 2 : 14671 04/16/09 17:38:48 v1.10 @ Core2Duo, length 3 : 12452 04/16/09 17:38:48 v1.10 @ Core2Duo, length 4 : 8410 04/16/09 17:38:48 v1.10 @ Core2Duo, length 5 : 5369 04/16/09 17:38:48 v1.10 @ Core2Duo, length 6 : 3216 04/16/09 17:38:48 v1.10 @ Core2Duo, length 7 : 1758 04/16/09 17:38:48 v1.10 @ Core2Duo, length 9+: 1812 04/16/09 17:38:48 v1.10 @ Core2Duo, largest cycle: 19 relations 04/16/09 17:38:48 v1.10 @ Core2Duo, matrix is 67412 x 67497 (15.8 MB) with weight 3859261 (57.18/col) 04/16/09 17:38:48 v1.10 @ Core2Duo, sparse part has weight 3859261 (57.18/col) 04/16/09 17:38:48 v1.10 @ Core2Duo, filtering completed in 3 passes 04/16/09 17:38:48 v1.10 @ Core2Duo, matrix is 62004 x 62068 (14.7 MB) with weight 3599837 (58.00/col) 04/16/09 17:38:48 v1.10 @ Core2Duo, sparse part has weight 3599837 (58.00/col) 04/16/09 17:38:49 v1.10 @ Core2Duo, saving the first 48 matrix rows for later 04/16/09 17:38:49 v1.10 @ Core2Duo, matrix is 61956 x 62068 (9.8 MB) with weight 2860904 (46.09/col) 04/16/09 17:38:49 v1.10 @ Core2Duo, sparse part has weight 2204854 (35.52/col) 04/16/09 17:38:49 v1.10 @ Core2Duo, matrix includes 64 packed rows 04/16/09 17:38:49 v1.10 @ Core2Duo, using block size 24827 for processor cache size 2048 kB 04/16/09 17:38:49 v1.10 @ Core2Duo, commencing Lanczos iteration 04/16/09 17:38:49 v1.10 @ Core2Duo, memory use: 9.4 MB 04/16/09 17:39:10 v1.10 @ Core2Duo, lanczos halted after 982 iterations (dim = 61955) 04/16/09 17:39:10 v1.10 @ Core2Duo, recovered 17 nontrivial dependencies 04/16/09 17:39:11 v1.10 @ Core2Duo, prp58 = 1116819481169900334059112170711297777323250963240946700829 04/16/09 17:39:12 v1.10 @ Core2Duo, prp34 = 1133539780530774666049337268862213 04/16/09 17:39:12 v1.10 @ Core2Duo, Lanczos elapsed time = 27.3910 seconds. 04/16/09 17:39:12 v1.10 @ Core2Duo, Sqrt elapsed time = 2.2500 seconds. 04/16/09 17:39:12 v1.10 @ Core2Duo, SIQS elapsed time = 3825.8750 seconds.

Apr 16, 2009 (4th)

Factorizations of 588...881 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Apr 16, 2009 (3rd)

By Ignacio Santos / GGNFS, Msieve / Apr 16, 2009
(52·10¹⁷⁴-61)/9 = 5(7)₁₇₃1_<175> = 15749 · C171
C171 = P34 · P51 · P87
P34 = 4456418495820421423482950428914067_<34>
P51 = 586089258996949155306651521414790973265453349486223_<51>
P87 = 140461764836441451075909139943636759414509330131265327498354115378476241498359801842619_<87>

Number: 57771_174 N=366866326609802386042147296830133835657995922139677298735016685362739080435442109199173139740794830006843468015605929124247747652408265780543385470682441918710888169266479 ( 171 digits) SNFS difficulty: 176 digits. Divisors found: r1=4456418495820421423482950428914067 (pp34) r2=586089258996949155306651521414790973265453349486223 (pp51) r3=140461764836441451075909139943636759414509330131265327498354115378476241498359801842619 (pp87) Version: Msieve-1.39 Total time: 81.98 hours. Scaled time: 142.24 units (timescale=1.735). Factorization parameters were as follows: n: 366866326609802386042147296830133835657995922139677298735016685362739080435442109199173139740794830006843468015605929124247747652408265780543385470682441918710888169266479 m: 100000000000000000000000000000000000 deg: 5 c5: 26 c0: -305 skew: 1.64 type: snfs lss: 1 rlim: 6100000 alim: 6100000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 6100000/6100000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3050000, 7050001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1314040 x 1314288 Total sieving time: 81.98 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,176,5,0,0,0,0,0,0,0,0,6100000,6100000,28,28,53,53,2.5,2.5,100000 total time: 81.98 hours. --------- CPU info (if available) ----------

(52·10¹⁶⁸-61)/9 = 5(7)₁₆₇1_<169> = 113 · C167
C167 = P47 · P51 · P71
P47 = 19594909439998386601697728948481069367588129493_<47>
P51 = 227202190339783073222336540223881606408474505882161_<51>
P71 = 11484884081582197425900107097665164509550167084613358848553590701850079_<71>

Number: 57771_168 N=51130776794493608652900688298918387413962635201573254670599803343166175024582104228121927236971484759095378564405113077679449360865290068829891838741396263520157325467 ( 167 digits) SNFS difficulty: 171 digits. Divisors found: r1=19594909439998386601697728948481069367588129493 (pp47) r2=227202190339783073222336540223881606408474505882161 (pp51) r3=11484884081582197425900107097665164509550167084613358848553590701850079 (pp71) Version: Msieve-1.39 Total time: 70.05 hours. Scaled time: 180.81 units (timescale=2.581). Factorization parameters were as follows: n: 51130776794493608652900688298918387413962635201573254670599803343166175024582104228121927236971484759095378564405113077679449360865290068829891838741396263520157325467 m: 10000000000000000000000000000000000 deg: 5 c5: 13 c0: -1525 skew: 2.59 type: snfs lss: 1 rlim: 5000000 alim: 5000000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2500000, 6100001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1040706 x 1040954 Total sieving time: 70.05 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,100000 total time: 70.05 hours. --------- CPU info (if available) ----------

(37·10¹⁷⁸+17)/9 = 4(1)₁₇₇3_<179> = 13752402607_<11> · 4488398865557_<13> · 10792876087603367_<17> · 7049599458449368393_<19> · C121
C121 = P57 · P64
P57 = 901053580759546473335733195289088783980467426146667758137_<57>
P64 = 9714868865503115801159431371805518306707962321967502211308133021_<64>

Number: 41113_178 N=8753617377871015379501280731640734720391420036927883299454746453053412071345125172976838459344035255267627866305051141877 ( 121 digits) Divisors found: r1=901053580759546473335733195289088783980467426146667758137 (pp57) r2=9714868865503115801159431371805518306707962321967502211308133021 (pp64) Version: Msieve-1.39 Total time: 42.93 hours. Scaled time: 74.87 units (timescale=1.744). Factorization parameters were as follows: n: 8753617377871015379501280731640734720391420036927883299454746453053412071345125172976838459344035255267627866305051141877 Y0: -232444750578107045732042 Y1: 18042078346271 c0: -88669467322140490833982108215 c1: -3045316310392554112648423 c2: 33782754219691244909 c3: -10726229016841 c4: -330767170 c5: 12900 skew: 121095.13 type: gnfs Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [3000000, 5280001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 713270 x 713518 Total sieving time: 42.93 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,120,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,6000000,6000000,27,27,50,50,2.4,2.4,60000 total time: 42.93 hours. --------- CPU info (if available) ----------

(47·10¹⁸⁷+61)/9 = 5(2)₁₈₆9_<188> = 472333 · 17123431378539583_<17> · 3005422296029909783_<19> · 229120334047763623675514957_<27> · C121
C121 = P33 · P45 · P45
P33 = 418959790849984109280420085898543_<33>
P45 = 130459351366153640145461498845742658269799017_<45>
P45 = 171553492944694353363214986772791976579824851_<45>

Number: 52229_187 N=9376637445301894692630526042340308089577381927812760651326578892014175084978443337190895669157712510157322717408832872581 ( 121 digits) Divisors found: r1=418959790849984109280420085898543 (pp33) r2=130459351366153640145461498845742658269799017 (pp45) r3=171553492944694353363214986772791976579824851 (pp45) Version: Msieve-1.39 Total time: 44.72 hours. Scaled time: 115.52 units (timescale=2.583). Factorization parameters were as follows: n: 9376637445301894692630526042340308089577381927812760651326578892014175084978443337190895669157712510157322717408832872581 Y0: -235662499711423574126299 Y1: 7140679275653 c0: 3616806725893284226991581464 c1: 3136244370186715815288714 c2: -77509608345842470109 c3: -1117609557837509 c4: 4914956575 c5: 12900 skew: 113010.98 type: gnfs Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2500000, 4720001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 640055 x 640303 Total sieving time: 44.72 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,120,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.4,2.4,60000 total time: 44.72 hours. --------- CPU info (if available) ----------

Apr 16, 2009 (2nd)

By Robert Backstrom / GGNFS, Msieve / Apr 16, 2009
(29·10¹⁶⁹+43)/9 = 3(2)₁₆₈7_<170> = 37 · 67 · 89 · 219274245089_<12> · 7009215964631_<13> · 11889948082870718027_<20> · C121
C121 = P50 · P72
P50 = 32583084617094617615042603090346568972351851388073_<50>
P72 = 245278642849600244520859043647749948902552614694651833843364433822233153_<72>

Number: n N=7991934774734654452054356447725718770084016035191644948179308728459372861636901877233956143656618879080281199811689384169 ( 121 digits) SNFS difficulty: 171 digits. Divisors found: Thu Apr 16 21:15:03 2009 prp50 factor: 32583084617094617615042603090346568972351851388073 Thu Apr 16 21:15:03 2009 prp72 factor: 245278642849600244520859043647749948902552614694651833843364433822233153 Thu Apr 16 21:15:03 2009 elapsed time 01:37:35 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 65.88 hours. Scaled time: 175.23 units (timescale=2.660). Factorization parameters were as follows: name: KA_3_2_168_7 n: 7991934774734654452054356447725718770084016035191644948179308728459372861636901877233956143656618879080281199811689384169 m: 10000000000000000000000000000000000 deg: 5 c5: 29 c0: 430 skew: 1.71 type: snfs lss: 1 rlim: 5000000 alim: 5000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2500000, 6403351) Primes: RFBsize:348513, AFBsize:348691, largePrimes:18018717 encountered Relations: rels:18137376, finalFF:707077 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 2444613 hash collisions in 20202113 relations Msieve: matrix is 880336 x 880584 (232.9 MB) Total sieving time: 64.94 hours. Total relation processing time: 0.94 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.4,2.4,100000 total time: 65.88 hours. --------- CPU info (if available) ----------

Apr 16, 2009

By Jo Yeong Uk / GMP-ECM, GGNFS, Msieve v1.39 / Apr 16, 2009
2·10¹⁹³-1 = 1(9)_193<194> = 61 · 3011 · 3019 · 2630399 · 1921011481_<10> · 5467489597378404813936108409_<28> · C142
C142 = P33 · C109
P33 = 394666621455911984281003929471901_<33>
C109 = [3307930204406174659160459281208577919156483154925588805331903346568937950394323661593005058106900251722779881_<109>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 1305529637784949287620571177887970771289520181235731640907698902880282231900498703097479220981210951629363692688397047212888405051383997623781 (142 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1344099513 Step 1 took 4654ms Step 2 took 2600ms ********** Factor found in step 2: 394666621455911984281003929471901 Found probable prime factor of 33 digits: 394666621455911984281003929471901 Composite cofactor 3307930204406174659160459281208577919156483154925588805331903346568937950394323661593005058106900251722779881 has 109 digits

(8·10¹⁹³+1)/9 = (8)₁₉₂9_<193> = 3 · 2418067 · C187
C187 = P58 · P59 · P71
P58 = 1681578303467735333201104967483311312998583427691180027389_<58>
P59 = 35884535642448250237342854660843058641051045981390093667103_<59>
P71 = 20306424780177190474846958704671361567809643262574547068456307082537867_<71>

Number: 88889_193 N=1225343616600765389446596377587123501111823188920308230898053264431036428255694719361772425231791742314403597155481201704900221111723936087363568901508090124451871252104661683469880265089 ( 187 digits) SNFS difficulty: 195 digits. Divisors found: r1=1681578303467735333201104967483311312998583427691180027389 r2=35884535642448250237342854660843058641051045981390093667103 r3=20306424780177190474846958704671361567809643262574547068456307082537867 Version: Total time: 208.79 hours. Scaled time: 499.02 units (timescale=2.390). Factorization parameters were as follows: n: 1225343616600765389446596377587123501111823188920308230898053264431036428255694719361772425231791742314403597155481201704900221111723936087363568901508090124451871252104661683469880265089 m: 1000000000000000000000000000000000000000 deg: 5 c5: 2 c0: 25 skew: 1.66 type: snfs lss: 1 rlim: 12000000 alim: 12000000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5 Factor base limits: 12000000/12000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [6000000, 11100001) Primes: rational ideals reading, algebraic ideals reading, Relations: 22616652 Max relations in full relation-set: Initial matrix: Pruned matrix : 2153331 x 2153578 Total sieving time: 188.60 hours. Total relation processing time: 6.21 hours. Matrix solve time: 12.83 hours. Time per square root: 1.16 hours. Prototype def-par.txt line would be: snfs,195,5,0,0,0,0,0,0,0,0,12000000,12000000,28,28,55,55,2.5,2.5,100000 total time: 208.79 hours. --------- CPU info (if available) ----------

Apr 15, 2009 (2nd)

By Jeff Gilchrist / GGNFS, Msieve 1.41 / Apr 15, 2009
(47·10¹⁸²+61)/9 = 5(2)₁₈₁9_<183> = 613 · 3677 · 5851441249_<10> · 530965497313_<12> · 10585881510667_<14> · 2179431821107410771893_<22> · C121
C121 = P44 · P78
P44 = 17506708982877796590471231654665554196604017_<44>
P78 = 184627872613379352806475438960335967278715754772741368162582062046769524215971_<78>

Number: 52229_182 N=3232226435970265846236451757188221400714438709580553767065174279795300964396998306487207820154993202004200696972674155507 ( 121 digits) Divisors found: r1=17506708982877796590471231654665554196604017 (pp44) r2=184627872613379352806475438960335967278715754772741368162582062046769524215971 (pp78) Version: Msieve-1.41 Total time: 24.87 hours. Scaled time: 92.16 units (timescale=3.706). Factorization parameters were as follows: n: 3232226435970265846236451757188221400714438709580553767065174279795300964396998306487207820154993202004200696972674155507 Y0: -185237779331646459172495 Y1: 7107011474677 c0: 55561197852791414195499475416 c1: -4782340600789847977395504 c2: -149176072421321140560 c3: 896428011026213 c4: 5109382940 c5: 14820 skew: 114386.69 type: gnfs Factor base limits: 4400000/4400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 53/53 Sieved algebraic special-q in [2200000, 4000001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 721051 x 721299 Total sieving time: 24.28 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.42 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: gnfs,120,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4400000,4400000,27,27,53,53,2.5,2.5,100000 total time: 24.87 hours. --------- CPU info (if available) ----------

(43·10¹⁸⁰+11)/9 = 4(7)₁₇₉9_<181> = 3 · 123341 · 44408731 · 85698463 · 4608479822817881_<16> · 101634239042663041733027_<24> · C121
C121 = P59 · P63
P59 = 18676433807687590180365272544953252176843032508168358289251_<59>
P63 = 387850313579850484085035039843960807035642431536398508046292593_<63>

Number: 47779_180 N=7243660708864952842040160790748686888826709453225422267548583677017716601532894954117510926890870537131075823270472817843 ( 121 digits) Divisors found: r1=18676433807687590180365272544953252176843032508168358289251 (pp59) r2=387850313579850484085035039843960807035642431536398508046292593 (pp63) Version: Msieve-1.41 Total time: 27.88 hours. Scaled time: 99.14 units (timescale=3.556). Factorization parameters were as follows: n: 7243660708864952842040160790748686888826709453225422267548583677017716601532894954117510926890870537131075823270472817843 Y0: -238635564021888899190086 Y1: 10660975489501 c0: 3060659713647717335169676087065 c1: 77381263460365481918711579 c2: -243420606357591876439 c3: -1951509855053695 c4: 3094543218 c5: 9360 skew: 286689.37 type: gnfs Factor base limits: 4400000/4400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 53/53 Sieved algebraic special-q in [2200000, 4200001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 733879 x 734127 Total sieving time: 26.99 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.50 hours. Time per square root: 0.31 hours. Prototype def-par.txt line would be: gnfs,120,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4400000,4400000,27,27,53,53,2.5,2.5,100000 total time: 27.88 hours. --------- CPU info (if available) ----------

Apr 15, 2009

By Robert Backstrom / GGNFS, Msieve / Apr 15, 2009
(46·10¹⁶⁴+53)/9 = 5(1)₁₆₃7_<165> = 11² · 9511 · 1759886443463004645030568229_<28> · C132
C132 = P44 · P89
P44 = 11285753184776442856762752555140164277069129_<44>
P89 = 22360863791807806952061637322870117280197298346250658978177527581370911848085145743419727_<89>

Number: n N=252359189752747203387481007806132642014097328260445368426717671665279502548365537787656106881257387644151261259364816582589241307783 ( 132 digits) SNFS difficulty: 166 digits. Divisors found: Wed Apr 15 16:30:13 2009 prp44 factor: 11285753184776442856762752555140164277069129 Wed Apr 15 16:30:13 2009 prp89 factor: 22360863791807806952061637322870117280197298346250658978177527581370911848085145743419727 Wed Apr 15 16:30:13 2009 elapsed time 00:57:06 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 28.65 hours. Scaled time: 74.34 units (timescale=2.595). Factorization parameters were as follows: name: KA_5_1_163_7 n: 252359189752747203387481007806132642014097328260445368426717671665279502548365537787656106881257387644151261259364816582589241307783 m: 1000000000000000000000000000000000 deg: 5 c5: 23 c0: 265 skew: 1.63 type: snfs lss: 1 rlim: 4100000 alim: 4100000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4100000/4100000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2050000, 3645899) Primes: RFBsize:289774, AFBsize:289682, largePrimes:14524305 encountered Relations: rels:13480818, finalFF:556526 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1314584 hash collisions in 15355401 relations Msieve: matrix is 675331 x 675579 (181.4 MB) Total sieving time: 28.29 hours. Total relation processing time: 0.36 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,4100000,4100000,28,28,56,56,2.4,2.4,100000 total time: 28.65 hours. --------- CPU info (if available) ----------

Apr 14, 2009 (5th)

By Robert Backstrom / GGNFS, Msieve / Apr 14, 2009
(2·10¹⁷¹+7)/9 = (2)₁₇₀3_<171> = 151 · 599 · 4139 · 147729150559_<12> · C151
C151 = P65 · P87
P65 = 25253094403184544346171495882979001456863037424443302102508569041_<65>
P87 = 159113667900210245746532907667701881096819030984060918003028803426828497942798849216147_<87>

Number: n N=4018112476320963647194617559312925511372532354290249565022495815523720386385026834556628042670177642790261114138766659873405014576266701042753481505027 ( 151 digits) SNFS difficulty: 171 digits. Divisors found: Tue Apr 14 12:01:12 2009 prp65 factor: 25253094403184544346171495882979001456863037424443302102508569041 Tue Apr 14 12:01:12 2009 prp87 factor: 159113667900210245746532907667701881096819030984060918003028803426828497942798849216147 Tue Apr 14 12:01:12 2009 elapsed time 01:23:33 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 35.03 hours. Scaled time: 91.29 units (timescale=2.606). Factorization parameters were as follows: name: KA_2_170_3 n: 4018112476320963647194617559312925511372532354290249565022495815523720386385026834556628042670177642790261114138766659873405014576266701042753481505027 m: 10000000000000000000000000000000000 deg: 5 c5: 20 c0: 7 skew: 0.81 type: snfs lss: 1 rlim: 5000000 alim: 5000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2500000, 4422959) Primes: RFBsize:348513, AFBsize:347941, largePrimes:15922524 encountered Relations: rels:14992231, finalFF:680601 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1379854 hash collisions in 16218455 relations Msieve: matrix is 860413 x 860661 (232.8 MB) Total sieving time: 34.59 hours. Total relation processing time: 0.44 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.4,2.4,100000 total time: 35.03 hours. --------- CPU info (if available) ----------

(47·10¹⁶⁴+7)/9 = 5(2)₁₆₃3_<165> = 23 · 43 · 21759131 · 3120834083_<10> · 3374993773673_<13> · C133
C133 = P65 · P69
P65 = 20398266286980159421404905123974135815941181589412331885179004209_<65>
P69 = 112948533588779377061204194941043083851885494268137274349596053865987_<69>

Number: n N=2303954264867844524330553774540163037301266630240816352596872696898564697965909487259971496062975076341497274290832388187297394939283 ( 133 digits) SNFS difficulty: 166 digits. Divisors found: Wed Apr 15 00:44:52 2009 prp65 factor: 20398266286980159421404905123974135815941181589412331885179004209 Wed Apr 15 00:44:52 2009 prp69 factor: 112948533588779377061204194941043083851885494268137274349596053865987 Wed Apr 15 00:44:52 2009 elapsed time 01:02:06 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 46.09 hours. Scaled time: 122.59 units (timescale=2.660). Factorization parameters were as follows: name: KA_5_2_163_3 n: 2303954264867844524330553774540163037301266630240816352596872696898564697965909487259971496062975076341497274290832388187297394939283 m: 1000000000000000000000000000000000 deg: 5 c5: 47 c0: 70 skew: 1.08 type: snfs lss: 1 rlim: 4200000 alim: 4200000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4200000/4200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2100000, 4872583) Primes: RFBsize:296314, AFBsize:296696, largePrimes:16186740 encountered Relations: rels:15719737, finalFF:550036 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1974808 hash collisions in 17758903 relations Msieve: matrix is 759246 x 759494 (201.2 MB) Total sieving time: 45.52 hours. Total relation processing time: 0.57 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,4200000,4200000,28,28,56,56,2.4,2.4,100000 total time: 46.09 hours. --------- CPU info (if available) ----------

Apr 14, 2009 (4th)

By Wataru Sakai / Msieve / Apr 14, 2009
(82·10¹⁹⁵+71)/9 = 9(1)₁₉₄9_<196> = 11 · C195
C195 = P44 · P53 · P99
P44 = 26817179798988518160368430220371768368944123_<44>
P53 = 41336149253678642884740626247977819067177540825049981_<53>
P99 = 747197718833206552292925059686568743196749345648134372526995569692687022286641164505132635390259683_<99>

Number: 91119_195 N=828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282829 ( 195 digits) SNFS difficulty: 196 digits. Divisors found: r1=26817179798988518160368430220371768368944123 r2=41336149253678642884740626247977819067177540825049981 r3=747197718833206552292925059686568743196749345648134372526995569692687022286641164505132635390259683 Version: Total time: 729.76 hours. Scaled time: 1444.92 units (timescale=1.980). Factorization parameters were as follows: n: 828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282828282829 m: 1000000000000000000000000000000000000000 deg: 5 c5: 82 c0: 71 skew: 0.97 type: snfs lss: 1 rlim: 13400000 alim: 13400000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5 Factor base limits: 13400000/13400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [6700000, 15200001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2253396 x 2253644 Total sieving time: 729.76 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,196,5,0,0,0,0,0,0,0,0,13400000,13400000,28,28,55,55,2.5,2.5,100000 total time: 729.76 hours. --------- CPU info (if available) ----------

(52·10¹⁸⁶-61)/9 = 5(7)₁₈₅1_<187> = C187
C187 = P52 · P54 · P83
P52 = 1482475847766385096562505037464122985100924080834529_<52>
P54 = 192860932423855597241429916466095224241530870434302299_<54>
P83 = 20208261142197016589293170339084167717687793242636949187506813175574959234255083601_<83>

Number: 57771_186 N=5777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777771 ( 187 digits) SNFS difficulty: 188 digits. Divisors found: r1=1482475847766385096562505037464122985100924080834529 r2=192860932423855597241429916466095224241530870434302299 r3=20208261142197016589293170339084167717687793242636949187506813175574959234255083601 Version: Total time: 393.88 hours. Scaled time: 684.17 units (timescale=1.737). Factorization parameters were as follows: n: 5777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777771 m: 20000000000000000000000000000000000000 deg: 5 c5: 65 c0: -244 skew: 1.30 type: snfs lss: 1 rlim: 9600000 alim: 9600000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5Factor base limits: 9600000/9600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [4800000, 9100001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1926902 x 1927149 Total sieving time: 393.88 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,188,5,0,0,0,0,0,0,0,0,9600000,9600000,28,28,54,54,2.5,2.5,100000 total time: 393.88 hours. --------- CPU info (if available) ----------

Apr 14, 2009 (3rd)

By Ignacio Santos / GGNFS, Msieve / Apr 14, 2009
(7·10¹⁹⁴+17)/3 = 2(3)₁₉₃9_<195> = 1709 · C192
C192 = P63 · P129
P63 = 346829221976324092618801102438231038737439780793265937700693079_<63>
P129 = 393657963022806093903868529787748043691165968836977987683147655420299632252039577434692218103776328441087411740739267406602236849_<129>

Number: 23339_194 N=136532085039984396333138287497561927052857421494051102008972108445484688901891944606982640920616344841037643846303881412131850984981470645601716403354788375268188024185683635654378779013068071 ( 192 digits) SNFS difficulty: 195 digits. Divisors found: r1=346829221976324092618801102438231038737439780793265937700693079 (pp63) r2=393657963022806093903868529787748043691165968836977987683147655420299632252039577434692218103776328441087411740739267406602236849 (pp129) Version: Msieve-1.39 Total time: 525.40 hours. Scaled time: 916.30 units (timescale=1.744). Factorization parameters were as follows: n: 136532085039984396333138287497561927052857421494051102008972108445484688901891944606982640920616344841037643846303881412131850984981470645601716403354788375268188024185683635654378779013068071 m: 500000000000000000000000000000000000000 deg: 5 c5: 112 c0: 85 skew: 0.95 type: snfs lss: 1 rlim: 12700000 alim: 12700000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5Factor base limits: 12700000/12700000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [6350000, 14950001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2537985 x 2538232 Total sieving time: 525.40 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,195,5,0,0,0,0,0,0,0,0,12700000,12700000,28,28,55,55,2.5,2.5,100000 total time: 525.40 hours. --------- CPU info (if available) ----------

(29·10¹⁶⁷+43)/9 = 3(2)₁₆₆7_<168> = 3² · 9067 · 55143554263432152331343_<23> · C140
C140 = P37 · P104
P37 = 4800573794884051481511926497391306549_<37>
P104 = 14916311979172569492728684520219784207270861744830265394871640637715056063809315699069363930229167578787_<104>

Number: 32227_167 N=71606856403530898614318803019976572490320678307484085258590318918033797130638183025963493447882757092868811532376557010544452763536826576063 ( 140 digits) SNFS difficulty: 169 digits. Divisors found: r1=4800573794884051481511926497391306549 (pp37) r2=14916311979172569492728684520219784207270861744830265394871640637715056063809315699069363930229167578787 (pp104) Version: Msieve-1.39 Total time: 59.66 hours. Scaled time: 103.75 units (timescale=1.739). Factorization parameters were as follows: n: 71606856403530898614318803019976572490320678307484085258590318918033797130638183025963493447882757092868811532376557010544452763536826576063 m: 2000000000000000000000000000000000 deg: 5 c5: 725 c0: 344 skew: 0.86 type: snfs lss: 1 rlim: 4700000 alim: 4700000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 4700000/4700000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2350000, 5750001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 974006 x 974254 Total sieving time: 59.66 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,169,5,0,0,0,0,0,0,0,0,4700000,4700000,27,27,52,52,2.4,2.4,100000 total time: 59.66 hours. --------- CPU info (if available) ----------

Apr 14, 2009 (2nd)

By Jeff Gilchrist / GGNFS & Msieve 1.41 / Apr 14, 2009
(29·10¹⁷⁰-11)/9 = 3(2)₁₆₉1_<171> = 3² · 257 · 3307 · 22121849 · C157
C157 = P50 · P108
P50 = 12128123182634994286036427814173335412207095123621_<50>
P108 = 157011201819375816815738752111265025210257283065238438120187834665257869938723695758458452814451628310344539_<108>

Number: 32221_170 N=1904251196718953636692162604583969903297314220743772932280383376864559932289145597338154925039823123268209183786578507255925998331853435869770613657307255719 ( 157 digits) SNFS difficulty: 171 digits. Divisors found: r1=12128123182634994286036427814173335412207095123621 (pp50) r2=157011201819375816815738752111265025210257283065238438120187834665257869938723695758458452814451628310344539 (pp108) Version: Msieve-1.41 Total time: 34.88 hours. Scaled time: 129.51 units (timescale=3.713). Factorization parameters were as follows: n: 1904251196718953636692162604583969903297314220743772932280383376864559932289145597338154925039823123268209183786578507255925998331853435869770613657307255719 m: 10000000000000000000000000000000000 deg: 5 c5: 29 c0: -11 skew: 0.82 type: snfs lss: 1 rlim: 5000000 alim: 5000000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2500000, 5000001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 805085 x 805333 Total sieving time: 34.08 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.53 hours. Time per square root: 0.18 hours. Prototype def-par.txt line would be: snfs,171.000,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,100000 total time: 34.88 hours. --------- CPU info (if available) ----------

(43·10¹⁷⁷-61)/9 = 4(7)₁₇₆1_<178> = 13 · 2593 · 357583 · 127558727 · 458872771789_<12> · 2367916363141745435233386787_<28> · C121
C121 = P44 · P78
P44 = 23458394311309179842266062524539260421928509_<44>
P78 = 121909095092311908628611882099805127119896107845918011449043507752877570553757_<78>

Number: 47771_177 N=2859791622810339532002420199806141256086331750290755724214138455762859858329326969029525125381588126101060803108995358313 ( 121 digits) Divisors found: r1=23458394311309179842266062524539260421928509 (pp44) r2=121909095092311908628611882099805127119896107845918011449043507752877570553757 (pp78) Version: Msieve-1.41 Total time: 29.33 hours. Scaled time: 108.98 units (timescale=3.716). Factorization parameters were as follows: n: 2859791622810339532002420199806141256086331750290755724214138455762859858329326969029525125381588126101060803108995358313 Y0: -174568903292024692763149 Y1: 10713486627859 c0: 3999749289757025257324102518 c1: -90701164448737131225067 c2: -14051139356920072819 c3: -43072998826651 c4: 920786306 c5: 17640 skew: 58874.87 type: gnfs Factor base limits: 4400000/4400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 53/53 Sieved algebraic special-q in [2200000, 4300001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 766054 x 766302 Total sieving time: 28.49 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.49 hours. Time per square root: 0.27 hours. Prototype def-par.txt line would be: gnfs,120,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4400000,4400000,27,27,53,53,2.5,2.5,100000 total time: 29.33 hours. --------- CPU info (if available) ----------

Apr 14, 2009

By Andreas Tete / GMP-ECM 6.2.1 / Apr 14, 2009
(46·10¹⁶⁴+71)/9 = 5(1)₁₆₃9_<165> = 3 · 17 · 79 · 179 · 233 · 41244039563019883_<17> · 38761045063606867373_<20> · C121
C121 = P37 · P84
P37 = 2085491164318326769316061631065415687_<37>
P84 = 912313446682833428261016780631623637749006006146390104272853716796969509502773150281_<84>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=983803196 ********** Factor found in step 2: 2085491164318326769316061631065415687 Found probable prime factor of 37 digits: 2085491164318326769316061631065415687 Probable prime cofactor 912313446682833428261016780631623637749006006146390104272853716796969509502773150281 has 84 digits

Apr 13, 2009 (3rd)

By Robert Backstrom / GGNFS, Msieve / Apr 13, 2009
(32·10¹⁶⁷+31)/9 = 3(5)₁₆₆9_<168> = 983 · 9337 · 1179789025019489_<16> · C146
C146 = P61 · P85
P61 = 5463215511259409267862691359715547396629804846074347587647637_<61>
P85 = 6010268966830633552407442674646264717255365729873344812447062941431439165340265027253_<85>

Number: n N=32835394646430181205812761282197698125513991593693821482034452227895325294651015157181683388666833151226627373344575666356437173478223009966051161 ( 146 digits) SNFS difficulty: 168 digits. Divisors found: Mon Apr 13 20:51:07 2009 prp61 factor: 5463215511259409267862691359715547396629804846074347587647637 Mon Apr 13 20:51:07 2009 prp85 factor: 6010268966830633552407442674646264717255365729873344812447062941431439165340265027253 Mon Apr 13 20:51:07 2009 elapsed time 01:21:47 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 38.37 hours. Scaled time: 97.99 units (timescale=2.554). Factorization parameters were as follows: name: KA_3_5_166_9 n: 32835394646430181205812761282197698125513991593693821482034452227895325294651015157181683388666833151226627373344575666356437173478223009966051161 m: 2000000000000000000000000000000000 deg: 5 c5: 100 c0: 31 skew: 0.79 type: snfs lss: 1 rlim: 4500000 alim: 4500000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2250000, 4453171) Primes: RFBsize:315948, AFBsize:316592, largePrimes:15819911 encountered Relations: rels:15045685, finalFF:641270 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1549571 hash collisions in 16281834 relations Msieve: matrix is 826261 x 826509 (221.8 MB) Total sieving time: 37.90 hours. Total relation processing time: 0.47 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,168,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,56,56,2.4,2.4,100000 total time: 38.37 hours. --------- CPU info (if available) ----------

Apr 13, 2009 (2nd)

By Jeff Gilchrist / GGNFS, Msieve 1.41 / Apr 13, 2009
5·10¹⁷⁰-7 = 4(9)₁₆₉3_<171> = 29 · 371840101717736949659_<21> · C149
C149 = P47 · P103
P47 = 36186346361901794734149614174823118926381921601_<47>
P103 = 1281359654549060281898606138184287341774636409267856035278076719876171866019239509683237360176741662263_<103>

Number: 49993_170 N=46367724273679128016875371673688962314473643710346808216784893586777456121488913841522626515505467594301778975907422007305297498445090108152886243063 ( 149 digits) SNFS difficulty: 170 digits. Divisors found: r1=36186346361901794734149614174823118926381921601 (pp47) r2=1281359654549060281898606138184287341774636409267856035278076719876171866019239509683237360176741662263 (pp103) Version: Msieve-1.41 Total time: 33.32 hours. Scaled time: 122.77 units (timescale=3.685). Factorization parameters were as follows: n: 46367724273679128016875371673688962314473643710346808216784893586777456121488913841522626515505467594301778975907422007305297498445090108152886243063 m: 10000000000000000000000000000000000 deg: 5 c5: 5 c0: -7 skew: 1.07 type: snfs lss: 1 rlim: 4900000 alim: 4900000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 4900000/4900000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2450000, 5250001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 860100 x 860348 Total sieving time: 32.47 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.63 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: snfs,170.000,5,0,0,0,0,0,0,0,0,4900000,4900000,27,27,52,52,2.4,2.4,100000 total time: 33.32 hours. --------- CPU info (if available) ----------

3·10¹⁷¹+7 = 3(0)₁₇₀7_<172> = 31620332097111024989233352721851562907652707_<44> · C128
C128 = P54 · P75
P54 = 119542069001731768208656345412449977669924073427695871_<54>
P75 = 793659208661801859516537543036477671956372358203480550399351605739016658931_<75>

Number: 30007_171 N=94875663885708949340722098875716958576811202800602452263648706419261724778781975587671373398601569684090092604704674588003973901 ( 128 digits) SNFS difficulty: 171 digits. Divisors found: r1=119542069001731768208656345412449977669924073427695871 (pp54) r2=793659208661801859516537543036477671956372358203480550399351605739016658931 (pp75) Version: Msieve-1.41 Total time: 44.42 hours. Scaled time: 163.50 units (timescale=3.681). Factorization parameters were as follows: n: 94875663885708949340722098875716958576811202800602452263648706419261724778781975587671373398601569684090092604704674588003973901 m: 10000000000000000000000000000000000 deg: 5 c5: 30 c0: 7 skew: 0.75 type: snfs lss: 1 rlim: 5000000 alim: 5000000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2500000, 5700001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 982062 x 982310 Total sieving time: 43.42 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.84 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,171.000,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,100000 total time: 44.42 hours. --------- CPU info (if available) ----------

Apr 13, 2009

By Sinkiti Sibata / GGNFS / Apr 13, 2009
(17·10¹⁸⁰+7)/3 = 5(6)₁₇₉9_<181> = 239 · C179
C179 = P48 · P49 · P83
P48 = 554926436167528943257699327435205874475108632793_<48>
P49 = 3523835766306910904207910803375786328587724571921_<49>
P83 = 12124914694059309969702016472528715477560656576791053322559643089873095090003003307_<83>

Number: 56669_180 N=23709902370990237099023709902370990237099023709902370990237099023709902370990237099023709902370990237099023709902370990237099023709902370990237099023709902370990237099023709902371 ( 179 digits) SNFS difficulty: 181 digits. Divisors found: r1=554926436167528943257699327435205874475108632793 (pp48) r2=3523835766306910904207910803375786328587724571921 (pp49) r3=12124914694059309969702016472528715477560656576791053322559643089873095090003003307 (pp83) Version: GGNFS-0.77.1-20060513-nocona Total time: 266.79 hours. Scaled time: 678.70 units (timescale=2.544). Factorization parameters were as follows: name: 56669_180 n: 23709902370990237099023709902370990237099023709902370990237099023709902370990237099023709902370990237099023709902370990237099023709902370990237099023709902370990237099023709902371 m: 1000000000000000000000000000000000000 deg: 5 c5: 17 c0: 7 skew: 0.84 type: snfs rlim: 6000000 alim: 6000000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved algebraic special-q in [3000000, 6300001) Primes: RFBsize:412849, AFBsize:413446, largePrimes:18103909 encountered Relations: rels:19163581, finalFF:1171199 Max relations in full relation-set: 28 Initial matrix: 826360 x 1171199 with sparse part having weight 155619666. Pruned matrix : 656224 x 660419 with weight 152393023. Total sieving time: 254.35 hours. Total relation processing time: 0.44 hours. Matrix solve time: 11.67 hours. Time per square root: 0.32 hours. Prototype def-par.txt line would be: snfs,181,5,0,0,0,0,0,0,0,0,6000000,6000000,28,28,53,53,2.5,2.5,100000 total time: 266.79 hours. --------- CPU info (if available) ----------

Apr 12, 2009 (2nd)

By Jeff Gilchrist / GGNFS & Msieve 1.41 / Apr 12, 2009
(17·10¹⁶⁴-11)/3 = 5(6)₁₆₃3_<165> = 31 · 383069 · 1593268421_<10> · 12235022127066387424376957_<26> · C124
C124 = P42 · P82
P42 = 450081134598038991950517876062431432323767_<42>
P82 = 5438817017371359971306142994586362267552757887934854040958910381842538227187462283_<82>

Number: 56663_164 N=2447908934049624041479766689351333818597811560902790473946582004995814104101521660195361352308148553703338584975482356980061 ( 124 digits) SNFS difficulty: 166 digits. Divisors found: r1=450081134598038991950517876062431432323767 (pp42) r2=5438817017371359971306142994586362267552757887934854040958910381842538227187462283 (pp82) Version: Msieve-1.41 Total time: 21.95 hours. Scaled time: 80.85 units (timescale=3.683). Factorization parameters were as follows: n: 2447908934049624041479766689351333818597811560902790473946582004995814104101521660195361352308148553703338584975482356980061 m: 1000000000000000000000000000000000 deg: 5 c5: 17 c0: -110 skew: 1.45 type: snfs lss: 1 rlim: 4100000 alim: 4100000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 4100000/4100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [2050000, 3850001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 753801 x 754049 Total sieving time: 21.38 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.46 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,166.000,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000 total time: 21.95 hours. --------- CPU info (if available) ----------

Apr 12, 2009

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / Apr 12, 2009
(52·10¹⁶¹+11)/9 = 5(7)₁₆₀9_<162> = 3² · 8664553 · C154
C154 = P47 · P108
P47 = 18928489948339749847018632028593340878665991563_<47>
P108 = 391431879723808945338088267301885408398292615483568378380918267204298704333073286676905854436479613341848329_<108>

Number: n N=7409214400811851559358864890571681062392662479437488681089206894365760226084084298889686619055539375683607782674712805634350769647035555578866083939648227 ( 154 digits) SNFS difficulty: 163 digits. Divisors found: Sun Apr 12 04:53:40 2009 prp47 factor: 18928489948339749847018632028593340878665991563 Sun Apr 12 04:53:40 2009 prp108 factor: 391431879723808945338088267301885408398292615483568378380918267204298704333073286676905854436479613341848329 Sun Apr 12 04:53:40 2009 elapsed time 00:55:48 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 22.58 hours. Scaled time: 59.57 units (timescale=2.638). Factorization parameters were as follows: name: KA_5_7_160_9 n: 7409214400811851559358864890571681062392662479437488681089206894365760226084084298889686619055539375683607782674712805634350769647035555578866083939648227 m: 200000000000000000000000000000000 deg: 5 c5: 65 c0: 44 skew: 0.92 type: snfs lss: 1 rlim: 3700000 alim: 3700000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 3700000/3700000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [1850000, 3250123) Primes: RFBsize:263397, AFBsize:263373, largePrimes:13742240 encountered Relations: rels:12753845, finalFF:533425 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1099106 hash collisions in 13613282 relations Msieve: matrix is 678552 x 678800 (183.0 MB) Total sieving time: 22.26 hours. Total relation processing time: 0.32 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,163,5,0,0,0,0,0,0,0,0,3700000,3700000,28,28,56,56,2.4,2.4,100000 total time: 22.58 hours. --------- CPU info (if available) ----------

(52·10¹⁶²+11)/9 = 5(7)₁₆₁9_<163> = 7 · 23 · C161
C161 = P42 · P120
P42 = 321519970820085608181037744328588516697743_<42>
P120 = 111616141305248804803400290837173564328599235003578090047986807312818902456903064735501933589562639357218054538297354173_<120>

Number: n N=35886818495514147688060731538992408557625948930296756383712905452035886818495514147688060731538992408557625948930296756383712905452035886818495514147688060731539 ( 161 digits) SNFS difficulty: 164 digits. Divisors found: Sun Apr 12 06:15:36 2009 prp42 factor: 321519970820085608181037744328588516697743 Sun Apr 12 06:15:36 2009 prp120 factor: 111616141305248804803400290837173564328599235003578090047986807312818902456903064735501933589562639357218054538297354173 Sun Apr 12 06:15:36 2009 elapsed time 00:52:55 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 30.70 hours. Scaled time: 81.32 units (timescale=2.649). Factorization parameters were as follows: name: KA_5_7_161_9 n: 35886818495514147688060731538992408557625948930296756383712905452035886818495514147688060731538992408557625948930296756383712905452035886818495514147688060731539 m: 200000000000000000000000000000000 deg: 5 c5: 325 c0: 22 skew: 0.58 type: snfs lss: 1 rlim: 3800000 alim: 3800000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 3800000/3800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved special-q in [1900000, 3800113) Primes: RFBsize:269987, AFBsize:269688, largePrimes:8808225 encountered Relations: rels:8644280, finalFF:545089 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 881198 hash collisions in 9436045 relations Msieve: matrix is 699430 x 699678 (186.3 MB) Total sieving time: 30.47 hours. Total relation processing time: 0.23 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,164,5,0,0,0,0,0,0,0,0,3800000,3800000,27,27,51,51,2.4,2.4,100000 total time: 30.70 hours. --------- CPU info (if available) ----------

(52·10¹⁶³+11)/9 = 5(7)₁₆₂9_<164> = 97 · 87931 · 876568187833930289_<18> · C139
C139 = P54 · P86
P54 = 285499687981964450229006620431228817065494664829635261_<54>
P86 = 27067973613206102904512248875476135325093088787990227833361756111499707732578188978893_<86>

Number: n N=7727898020874389273633226675969318827671185863144042247840595857996178908012693244379155722125782899946146998056281826623324143363217546073 ( 139 digits) SNFS difficulty: 166 digits. Divisors found: Sun Apr 12 13:31:34 2009 prp54 factor: 285499687981964450229006620431228817065494664829635261 Sun Apr 12 13:31:34 2009 prp86 factor: 27067973613206102904512248875476135325093088787990227833361756111499707732578188978893 Sun Apr 12 13:31:34 2009 elapsed time 01:05:41 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 30.87 hours. Scaled time: 82.12 units (timescale=2.660). Factorization parameters were as follows: name: KA_5_7_162_9 n: 7727898020874389273633226675969318827671185863144042247840595857996178908012693244379155722125782899946146998056281826623324143363217546073 m: 1000000000000000000000000000000000 deg: 5 c5: 13 c0: 275 skew: 1.84 type: snfs lss: 1 rlim: 4100000 alim: 4100000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4100000/4100000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2050000, 3861203) Primes: RFBsize:289774, AFBsize:290078, largePrimes:14963521 encountered Relations: rels:14071940, finalFF:586784 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1356936 hash collisions in 15148444 relations Msieve: matrix is 754434 x 754682 (201.5 MB) Total sieving time: 30.49 hours. Total relation processing time: 0.39 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,4100000,4100000,28,28,56,56,2.4,2.4,100000 total time: 30.87 hours. --------- CPU info (if available) ----------

(52·10¹⁶⁵+11)/9 = 5(7)₁₆₄9_<166> = 17 · 86761097 · 592224781 · 124457150677_<12> · 190862997763738379_<18> · C120
C120 = P39 · P81
P39 = 947603373792569765729573937197287389869_<39>
P81 = 293854339940673288307735977122722469845978112409126167654289550189645063181598133_<81>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM] Input number is 278457363931370693256810083723809311549125447635796682650235234084816134689205258661992118672738189311298709411653514577 (120 digits) Using B1=2136000, B2=2854078510, polynomial Dickson(6), sigma=2890840773 Step 1 took 23758ms ********** Factor found in step 1: 947603373792569765729573937197287389869 Found probable prime factor of 39 digits: 947603373792569765729573937197287389869 Probable prime cofactor 293854339940673288307735977122722469845978112409126167654289550189645063181598133 has 81 digits

Apr 11, 2009 (2nd)

By Andreas Tete / GMP-ECM 6.2.2 / Apr 11, 2009
(47·10¹⁶⁴+43)/9 = 5(2)₁₆₃7_<165> = 21031 · 56099 · 9480603531462587241575906463236513_<34> · C122
C122 = P37 · P86
P37 = 1925457966905235846156525388783627303_<37>
P86 = 24247684792636549715927770946748662555654899363148036016451038975272737398252341068097_<86>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=17151464 ********** Factor found in step 2: 1925457966905235846156525388783627303 Found probable prime factor of 37 digits: 1925457966905235846156525388783627303 Probable prime cofactor 24247684792636549715927770946748662555654899363148036016451038975272737398252341068097 has 86 digits

(49·10¹⁶⁶+23)/9 = 5(4)₁₆₅7_<167> = 3 · 29 · 193 · 955469 · 4188451 · 622422253 · 1830545011_<10> · 15678994369_<11> · C122
C122 = P32 · P91
P32 = 29197910954985748593465543486977_<32>
P91 = 1553357653460083080407321738143405658573231909383968797372397037983792553040705001133212217_<91>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=15830070 ********** Factor found in step 2: 29197910954985748593465543486977 Found probable prime factor of 32 digits: 29197910954985748593465543486977 Probable prime cofactor 1553357653460083080407321738143405658573231909383968797372397037983792553040705001133212217 has 91 digits

Apr 11, 2009

By Robert Backstrom / GGNFS / Apr 11, 2009
(52·10¹⁶⁰+11)/9 = 5(7)₁₅₉9_<161> = 3331 · C158
C158 = P40 · P52 · P66
P40 = 1984602862159222328197712995842323139233_<40>
P52 = 8995729372655953524904434979327475766365640628552961_<52>
P66 = 971574720881561621643707317580907592723358162775265761540357497393_<66>

Number: n N=17345475165949497981920677807798792488074985823409720137429534007138330164448447246405817405517195370092398011941692518096000533706928183061476366790086393809 ( 158 digits) SNFS difficulty: 161 digits. Divisors found: r1=1984602862159222328197712995842323139233 (pp40) r2=8995729372655953524904434979327475766365640628552961 (pp52) r3=971574720881561621643707317580907592723358162775265761540357497393 (pp66) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 20.60 hours. Scaled time: 54.79 units (timescale=2.660). Factorization parameters were as follows: name: KA_5_7_159_9 n: 17345475165949497981920677807798792488074985823409720137429534007138330164448447246405817405517195370092398011941692518096000533706928183061476366790086393809 m: 100000000000000000000000000000000 deg: 5 c5: 52 c0: 11 skew: 0.73 type: snfs lss: 1 rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved rational special-q in [1750000, 2850001) Primes: RFBsize:250150, AFBsize:249882, largePrimes:13781805 encountered Relations: rels:13310814, finalFF:645052 Max relations in full relation-set: 28 Initial matrix: 500100 x 645052 with sparse part having weight 68070186. Pruned matrix : 420473 x 423037 with weight 45366021. Total sieving time: 18.84 hours. Total relation processing time: 0.30 hours. Matrix solve time: 1.15 hours. Total square root time: 0.31 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,56,56,2.4,2.4,100000 total time: 20.60 hours. --------- CPU info (if available) ----------

Apr 10, 2009 (4th)

By Sinkiti Sibata / Msieve / Apr 10, 2009
(52·10¹⁵¹+11)/9 = 5(7)₁₅₀9_<152> = C152
C152 = P64 · P89
P64 = 3953535681244358031390387279802526646473653843971170017410808979_<64>
P89 = 14614204205080672347139781653275652403689134613732690915539647764779044145671465056087201_<89>

Number: 57779_151 N=57777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779 ( 152 digits) SNFS difficulty: 153 digits. Divisors found: r1=3953535681244358031390387279802526646473653843971170017410808979 (pp64) r2=14614204205080672347139781653275652403689134613732690915539647764779044145671465056087201 (pp89) Version: Msieve-1.40 Total time: 15.17 hours. Scaled time: 39.07 units (timescale=2.575). Factorization parameters were as follows: name: 57779_151 n: 57777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779 m: 2000000000000000000000000000000 deg: 5 c5: 65 c0: 44 skew: 0.92 type: snfs lss: 1 rlim: 2500000 alim: 2500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1250000, 1950001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 416304 x 416552 Total sieving time: 15.17 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,153.000,5,0,0,0,0,0,0,0,0,2500000,2500000,27,27,50,50,2.4,2.4,100000 total time: 15.17 hours. --------- CPU info (if available) ----------

Apr 10, 2009 (3rd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve / Apr 10, 2009
(52·10¹⁵⁴+11)/9 = 5(7)₁₅₃9_<155> = 1009 · 1873 · 1780071853727_<13> · C137
C137 = P41 · P96
P41 = 93050385464681516500046281914738043499239_<41>
P96 = 184576404077904571046705571397602099672425078097604346576358124523939748687222923404111884169099_<96>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM] Input number is 17174905547133833686201829165853188941164294376020559094629779979976178551279987548468323356118519181871603715021418206048713273953815661 (137 digits) Using B1=1262000, B2=1426326730, polynomial Dickson(6), sigma=2614469203 Step 1 took 17378ms Step 2 took 6412ms ********** Factor found in step 2: 93050385464681516500046281914738043499239 Found probable prime factor of 41 digits: 93050385464681516500046281914738043499239 Probable prime cofactor 184576404077904571046705571397602099672425078097604346576358124523939748687222923404111884169099 has 96 digits

(52·10¹⁶⁶+11)/9 = 5(7)₁₆₅9_<167> = 19 · 313 · 1543 · 83115250284832640411_<20> · 12632594670057892169047869846613_<32> · C109
C109 = P47 · P63
P47 = 42691128655357150982468169102793571554807074883_<47>
P63 = 140470799532314444373497792586935413113578875626021083297673571_<63>

Number: n N=5996856975154919058724890468413883408998447325094790249647861377749782830297948367090644019881202485487017193 ( 109 digits) Divisors found: r1=42691128655357150982468169102793571554807074883 (pp47) r2=140470799532314444373497792586935413113578875626021083297673571 (pp63) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 13.47 hours. Scaled time: 35.25 units (timescale=2.616). Factorization parameters were as follows: name: KA_5_7_165_9 n:5996856975154919058724890468413883408998447325094790249647861377749782830297948367090644019881202485487017193 Y0: -1067795297988797501616 Y1: 164264666753 c0: 8530558915607398247347346489 c1: 242316730277730117495673 c2: -1667914485931205175 c3: -70391702544601 c4: -4927106 c5: 4320 skew: 77192.47 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved algebraic special-q in [1600000, 2900001) Primes: RFBsize:230209, AFBsize:230575, largePrimes:16977985 encountered Relations: rels:15492064, finalFF:690402 Max relations in full relation-set: 28 Initial matrix: 460861 x 690402 with sparse part having weight 64012452. Pruned matrix : 306082 x 308450 with weight 37318507. Total sieving time: 11.29 hours. Total relation processing time: 0.51 hours. Matrix solve time: 0.52 hours. Total square root time: 1.16 hours, sqrts: 5. Prototype def-par.txt line would be: gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,28,28,56,56,2.6,2.6,100000 total time: 13.47 hours. --------- CPU info (if available) ----------

(41·10¹⁶⁶-23)/9 = 4(5)₁₆₅3_<167> = 439 · 2586919225049507147_<19> · C146
C146 = P52 · P95
P52 = 1065505954138455564238719164964882682924840493039843_<52>
P95 = 37647667807395859819607873997112941704493623479901923145975021806996208571696732038445830885287_<95>

Number: n N=40113814208206942961286412653651200042765317891904117999505219090653791939685124936497665627919725179282174773415014399429404984085252766453489941 ( 146 digits) SNFS difficulty: 167 digits. Divisors found: Fri Apr 10 12:32:01 2009 prp52 factor: 1065505954138455564238719164964882682924840493039843 Fri Apr 10 12:32:01 2009 prp95 factor: 37647667807395859819607873997112941704493623479901923145975021806996208571696732038445830885287 Fri Apr 10 12:32:01 2009 elapsed time 01:07:27 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 44.86 hours. Scaled time: 115.97 units (timescale=2.585). Factorization parameters were as follows: name: KA_4_5_165_3 n: 40113814208206942961286412653651200042765317891904117999505219090653791939685124936497665627919725179282174773415014399429404984085252766453489941 m: 1000000000000000000000000000000000 deg: 5 c5: 410 c0: -23 skew: 0.56 type: snfs lss: 1 rlim: 4400000 alim: 4400000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4400000/4400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2200000, 4801133) Primes: RFBsize:309335, AFBsize:309429, largePrimes:16673429 encountered Relations: rels:16590378, finalFF:596243 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1931330 hash collisions in 18160482 relations Msieve: matrix is 738140 x 738388 (196.1 MB) Total sieving time: 44.21 hours. Total relation processing time: 0.65 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,4400000,4400000,28,28,56,56,2.4,2.4,100000 total time: 44.86 hours. --------- CPU info (if available) ----------

Apr 10, 2009 (2nd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Apr 10, 2009
(52·10¹⁵³+11)/9 = 5(7)₁₅₂9_<154> = 29 · 40543 · 710027 · 470818507 · C134
C134 = P35 · P99
P35 = 19627040332408708604436682113596563_<35>
P99 = 748968841027261409761188316700947313844944317053127062144103065053216914230007485726769694669513251_<99>

Number: 57779_153 N=14700041650559466010672832813381002063469358855134283947591049880295228687855696994256445000105441634400101420815978396489308196556313 ( 134 digits) SNFS difficulty: 156 digits. Divisors found: r1=19627040332408708604436682113596563 r2=748968841027261409761188316700947313844944317053127062144103065053216914230007485726769694669513251 Version: Total time: 9.99 hours. Scaled time: 23.80 units (timescale=2.383). Factorization parameters were as follows: n: 14700041650559466010672832813381002063469358855134283947591049880295228687855696994256445000105441634400101420815978396489308196556313 m: 10000000000000000000000000000000 deg: 5 c5: 13 c0: 275 skew: 1.84 type: snfs lss: 1 rlim: 2400000 alim: 2400000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1200000, 2100001) Primes: rational ideals reading, algebraic ideals reading, Relations: 7814054 Max relations in full relation-set: Initial matrix: Pruned matrix : 480721 x 480969 Total sieving time: 9.06 hours. Total relation processing time: 0.35 hours. Matrix solve time: 0.51 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,50,50,2.4,2.4,100000 total time: 9.99 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797) Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Apr 10, 2009

By Andreas Tete / Msieve v1.41, GGNFS / Apr 10, 2009
(52·10¹⁷²+11)/9 = 5(7)₁₇₁9_<173> = 3951719 · 13380499109519_<14> · 36282474114511_<14> · 309043953890409714925505897364313_<33> · C107
C107 = P51 · P57
P51 = 118145920262199525963524190015546715838352113676563_<51>
P57 = 824834068673450927934822305182677949265824343092447793071_<57>

Thu Apr 09 17:24:45 2009 Msieve v. 1.41 Thu Apr 09 17:24:45 2009 random seeds: ae9280b0 10196da0 Thu Apr 09 17:24:45 2009 factoring 97450780107039141260457072613462534480633327041513829548037360610763669539962170088778288463915365246494973 (107 digits) Thu Apr 09 17:24:47 2009 searching for 15-digit factors Thu Apr 09 17:24:49 2009 commencing number field sieve (107-digit input) Thu Apr 09 17:24:49 2009 R0: -583560684231641996834 Thu Apr 09 17:24:49 2009 R1: 78488406179 Thu Apr 09 17:24:49 2009 A0: -27278358361861303319170275 Thu Apr 09 17:24:50 2009 A1: 3917602922717724100809 Thu Apr 09 17:24:50 2009 A2: 311529443604860231 Thu Apr 09 17:24:50 2009 A3: -1660678779952 Thu Apr 09 17:24:50 2009 A4: -179866821 Thu Apr 09 17:24:50 2009 A5: 1440 Thu Apr 09 17:24:50 2009 skew 39860.96, size 3.272186e-010, alpha -4.805594, combined = 1.441065e-009 Thu Apr 09 17:24:50 2009 Thu Apr 09 17:24:50 2009 commencing relation filtering Thu Apr 09 17:24:50 2009 commencing duplicate removal, pass 1 Thu Apr 09 17:26:03 2009 found 423914 hash collisions in 5084040 relations Thu Apr 09 17:26:30 2009 added 34695 free relations Thu Apr 09 17:26:30 2009 commencing duplicate removal, pass 2 Thu Apr 09 17:26:42 2009 found 407648 duplicates and 4711086 unique relations Thu Apr 09 17:26:42 2009 memory use: 41.3 MB Thu Apr 09 17:26:42 2009 reading rational ideals above 2949120 Thu Apr 09 17:26:42 2009 reading algebraic ideals above 2949120 Thu Apr 09 17:26:42 2009 commencing singleton removal, pass 1 Thu Apr 09 17:27:46 2009 relations with 0 large ideals: 116858 Thu Apr 09 17:27:46 2009 relations with 1 large ideals: 738043 Thu Apr 09 17:27:46 2009 relations with 2 large ideals: 1692634 Thu Apr 09 17:27:46 2009 relations with 3 large ideals: 1613036 Thu Apr 09 17:27:46 2009 relations with 4 large ideals: 515175 Thu Apr 09 17:27:46 2009 relations with 5 large ideals: 2472 Thu Apr 09 17:27:46 2009 relations with 6 large ideals: 32868 Thu Apr 09 17:27:46 2009 relations with 7+ large ideals: 0 Thu Apr 09 17:27:46 2009 4711086 relations and about 4612394 large ideals Thu Apr 09 17:27:46 2009 commencing singleton removal, pass 2 Thu Apr 09 17:28:51 2009 found 2070067 singletons Thu Apr 09 17:28:51 2009 current dataset: 2641019 relations and about 2113480 large ideals Thu Apr 09 17:28:51 2009 commencing singleton removal, pass 3 Thu Apr 09 17:29:29 2009 found 489447 singletons Thu Apr 09 17:29:29 2009 current dataset: 2151572 relations and about 1588891 large ideals Thu Apr 09 17:29:29 2009 commencing singleton removal, final pass Thu Apr 09 17:30:04 2009 memory use: 33.4 MB Thu Apr 09 17:30:04 2009 commencing in-memory singleton removal Thu Apr 09 17:30:04 2009 begin with 2151572 relations and 1635870 unique ideals Thu Apr 09 17:30:08 2009 reduce to 1811566 relations and 1286231 ideals in 14 passes Thu Apr 09 17:30:08 2009 max relations containing the same ideal: 42 Thu Apr 09 17:30:08 2009 reading rational ideals above 100000 Thu Apr 09 17:30:08 2009 reading algebraic ideals above 100000 Thu Apr 09 17:30:08 2009 commencing singleton removal, final pass Thu Apr 09 17:30:48 2009 keeping 1637389 ideals with weight <= 25, new excess is 128075 Thu Apr 09 17:30:52 2009 memory use: 47.7 MB Thu Apr 09 17:30:52 2009 commencing in-memory singleton removal Thu Apr 09 17:30:53 2009 begin with 1820656 relations and 1637389 unique ideals Thu Apr 09 17:30:56 2009 reduce to 1801170 relations and 1573710 ideals in 11 passes Thu Apr 09 17:30:56 2009 max relations containing the same ideal: 25 Thu Apr 09 17:30:58 2009 removing 290398 relations and 250951 ideals in 39447 cliques Thu Apr 09 17:30:58 2009 commencing in-memory singleton removal Thu Apr 09 17:30:58 2009 begin with 1510772 relations and 1573710 unique ideals Thu Apr 09 17:31:01 2009 reduce to 1480022 relations and 1291204 ideals in 9 passes Thu Apr 09 17:31:01 2009 max relations containing the same ideal: 25 Thu Apr 09 17:31:02 2009 removing 217191 relations and 177744 ideals in 39447 cliques Thu Apr 09 17:31:02 2009 commencing in-memory singleton removal Thu Apr 09 17:31:02 2009 begin with 1262831 relations and 1291204 unique ideals Thu Apr 09 17:31:04 2009 reduce to 1240337 relations and 1090388 ideals in 8 passes Thu Apr 09 17:31:04 2009 max relations containing the same ideal: 25 Thu Apr 09 17:31:05 2009 relations with 0 large ideals: 5419 Thu Apr 09 17:31:05 2009 relations with 1 large ideals: 46967 Thu Apr 09 17:31:05 2009 relations with 2 large ideals: 172417 Thu Apr 09 17:31:05 2009 relations with 3 large ideals: 329391 Thu Apr 09 17:31:05 2009 relations with 4 large ideals: 356668 Thu Apr 09 17:31:05 2009 relations with 5 large ideals: 223079 Thu Apr 09 17:31:05 2009 relations with 6 large ideals: 85257 Thu Apr 09 17:31:05 2009 relations with 7+ large ideals: 21139 Thu Apr 09 17:31:05 2009 commencing 2-way merge Thu Apr 09 17:31:07 2009 reduce to 751009 relation sets and 601060 unique ideals Thu Apr 09 17:31:07 2009 commencing full merge Thu Apr 09 17:31:23 2009 memory use: 50.7 MB Thu Apr 09 17:31:24 2009 found 355008 cycles, need 335260 Thu Apr 09 17:31:24 2009 weight of 335260 cycles is about 23712374 (70.73/cycle) Thu Apr 09 17:31:24 2009 distribution of cycle lengths: Thu Apr 09 17:31:24 2009 1 relations: 32881 Thu Apr 09 17:31:24 2009 2 relations: 33611 Thu Apr 09 17:31:24 2009 3 relations: 33970 Thu Apr 09 17:31:24 2009 4 relations: 31832 Thu Apr 09 17:31:24 2009 5 relations: 30348 Thu Apr 09 17:31:24 2009 6 relations: 26986 Thu Apr 09 17:31:24 2009 7 relations: 24661 Thu Apr 09 17:31:24 2009 8 relations: 21895 Thu Apr 09 17:31:24 2009 9 relations: 19028 Thu Apr 09 17:31:24 2009 10+ relations: 80048 Thu Apr 09 17:31:24 2009 heaviest cycle: 19 relations Thu Apr 09 17:31:24 2009 commencing cycle optimization Thu Apr 09 17:31:25 2009 start with 2173536 relations Thu Apr 09 17:31:35 2009 pruned 66094 relations Thu Apr 09 17:31:35 2009 memory use: 55.2 MB Thu Apr 09 17:31:35 2009 distribution of cycle lengths: Thu Apr 09 17:31:35 2009 1 relations: 32881 Thu Apr 09 17:31:35 2009 2 relations: 34444 Thu Apr 09 17:31:35 2009 3 relations: 35444 Thu Apr 09 17:31:35 2009 4 relations: 32852 Thu Apr 09 17:31:35 2009 5 relations: 31506 Thu Apr 09 17:31:35 2009 6 relations: 27645 Thu Apr 09 17:31:35 2009 7 relations: 25198 Thu Apr 09 17:31:35 2009 8 relations: 22193 Thu Apr 09 17:31:35 2009 9 relations: 19286 Thu Apr 09 17:31:35 2009 10+ relations: 73811 Thu Apr 09 17:31:35 2009 heaviest cycle: 19 relations Thu Apr 09 17:31:36 2009 RelProcTime: 305 Thu Apr 09 17:31:36 2009 Thu Apr 09 17:31:36 2009 commencing linear algebra Thu Apr 09 17:31:36 2009 read 335260 cycles Thu Apr 09 17:31:37 2009 cycles contain 1123030 unique relations Thu Apr 09 17:31:54 2009 read 1123030 relations Thu Apr 09 17:31:57 2009 using 20 quadratic characters above 87500574 Thu Apr 09 17:32:07 2009 building initial matrix Thu Apr 09 17:32:32 2009 memory use: 125.5 MB Thu Apr 09 17:32:33 2009 read 335260 cycles Thu Apr 09 17:32:34 2009 matrix is 335062 x 335260 (94.9 MB) with weight 31928740 (95.24/col) Thu Apr 09 17:32:34 2009 sparse part has weight 22524397 (67.18/col) Thu Apr 09 17:32:41 2009 filtering completed in 2 passes Thu Apr 09 17:32:41 2009 matrix is 333741 x 333937 (94.7 MB) with weight 31851832 (95.38/col) Thu Apr 09 17:32:41 2009 sparse part has weight 22487289 (67.34/col) Thu Apr 09 17:32:42 2009 read 333937 cycles Thu Apr 09 17:32:43 2009 matrix is 333741 x 333937 (94.7 MB) with weight 31851832 (95.38/col) Thu Apr 09 17:32:43 2009 sparse part has weight 22487289 (67.34/col) Thu Apr 09 17:32:43 2009 saving the first 48 matrix rows for later Thu Apr 09 17:32:44 2009 matrix is 333693 x 333937 (91.4 MB) with weight 25249537 (75.61/col) Thu Apr 09 17:32:44 2009 sparse part has weight 21955093 (65.75/col) Thu Apr 09 17:32:44 2009 matrix includes 64 packed rows Thu Apr 09 17:32:44 2009 using block size 65536 for processor cache size 3072 kB Thu Apr 09 17:32:49 2009 commencing Lanczos iteration Thu Apr 09 17:32:49 2009 memory use: 88.4 MB Thu Apr 09 17:49:15 2009 lanczos halted after 5279 iterations (dim = 333693) Thu Apr 09 17:49:16 2009 recovered 33 nontrivial dependencies Thu Apr 09 17:49:16 2009 BLanczosTime: 1060 Thu Apr 09 17:49:16 2009 Thu Apr 09 17:49:16 2009 commencing square root phase Thu Apr 09 17:49:16 2009 reading relations for dependency 1 Thu Apr 09 17:49:17 2009 read 166851 cycles Thu Apr 09 17:49:17 2009 cycles contain 696453 unique relations Thu Apr 09 17:49:26 2009 read 696453 relations Thu Apr 09 17:49:29 2009 multiplying 561498 relations Thu Apr 09 17:50:54 2009 multiply complete, coefficients have about 21.70 million bits Thu Apr 09 17:50:55 2009 initial square root is modulo 1709443 Thu Apr 09 17:52:58 2009 reading relations for dependency 2 Thu Apr 09 17:52:58 2009 read 167207 cycles Thu Apr 09 17:52:59 2009 cycles contain 697067 unique relations Thu Apr 09 17:53:07 2009 read 697067 relations Thu Apr 09 17:53:11 2009 multiplying 561526 relations Thu Apr 09 17:54:35 2009 multiply complete, coefficients have about 21.70 million bits Thu Apr 09 17:54:36 2009 initial square root is modulo 1712237 Thu Apr 09 17:56:39 2009 sqrtTime: 443 Thu Apr 09 17:56:39 2009 prp51 factor: 118145920262199525963524190015546715838352113676563 Thu Apr 09 17:56:39 2009 prp57 factor: 824834068673450927934822305182677949265824343092447793071 Thu Apr 09 17:56:39 2009 elapsed time 00:31:54 total time for Polysearch + Sieving + factorization ~ 10 hours

Apr 9, 2009 (4th)

By Robert Backstrom / GGNFS / Apr 9, 2009
(52·10¹⁴⁰+11)/9 = 5(7)₁₃₉9_<141> = 3 · 23 · 113 · 1439 · 2821728461_<10> · C125
C125 = P43 · P82
P43 = 1858703100709054768133619754033983334336277_<43>
P82 = 9818547917634304819287024108448651704534852780908499389251702140960977795402014729_<82>

Number: n N=18249765458967315251100758570354262987161550021582943083881949385207687813350351661755670150068944041437021726912929793023933 ( 125 digits) SNFS difficulty: 141 digits. Divisors found: r1=1858703100709054768133619754033983334336277 (pp43) r2=9818547917634304819287024108448651704534852780908499389251702140960977795402014729 (pp82) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 3.60 hours. Scaled time: 9.55 units (timescale=2.649). Factorization parameters were as follows: name: KA_5_7_139_9 n: 18249765458967315251100758570354262987161550021582943083881949385207687813350351661755670150068944041437021726912929793023933 m: 10000000000000000000000000000 deg: 5 c5: 52 c0: 11 skew: 0.73 type: snfs lss: 1 rlim: 1600000 alim: 1600000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.3 alambda: 2.3 qintsize: 100000 Factor base limits: 1600000/1600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved rational special-q in [800000, 1400001) Primes: RFBsize:121127, AFBsize:120941, largePrimes:5917320 encountered Relations: rels:5319702, finalFF:317067 Max relations in full relation-set: 28 Initial matrix: 242136 x 317067 with sparse part having weight 24371004. Pruned matrix : 208945 x 210219 with weight 12742149. Total sieving time: 3.16 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.11 hours. Total square root time: 0.24 hours, sqrts: 4. Prototype def-par.txt line would be: snfs,141,5,0,0,0,0,0,0,0,0,1600000,1600000,28,28,56,56,2.3,2.3,100000 total time: 3.60 hours. --------- CPU info (if available) ----------

(52·10¹³⁹+11)/9 = 5(7)₁₃₈9_<140> = 353 · 2894867749_<10> · C128
C128 = P60 · P69
P60 = 106562174939360003911367421423355456729232756135646331248841_<60>
P69 = 530584214402232516348340135462445847762080807588416523417975808079327_<69>

Number: n N=56540207875193597111760613217706491076129293855908752726056959507882390115350784593308042957937614467659848751785382557504810007 ( 128 digits) SNFS difficulty: 141 digits. Divisors found: r1=106562174939360003911367421423355456729232756135646331248841 (pp60) r2=530584214402232516348340135462445847762080807588416523417975808079327 (pp69) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 4.78 hours. Scaled time: 12.72 units (timescale=2.660). Factorization parameters were as follows: name: KA_5_7_138_9 n: 56540207875193597111760613217706491076129293855908752726056959507882390115350784593308042957937614467659848751785382557504810007 m: 10000000000000000000000000000 deg: 5 c5: 26 c0: 55 skew: 1.16 type: snfs lss: 1 rlim: 1600000 alim: 1600000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.3 alambda: 2.3 qintsize: 100000 Factor base limits: 1600000/1600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved rational special-q in [800000, 1700001) Primes: RFBsize:121127, AFBsize:121466, largePrimes:6325858 encountered Relations: rels:5753045, finalFF:323128 Max relations in full relation-set: 28 Initial matrix: 242659 x 323128 with sparse part having weight 28887173. Pruned matrix : 217171 x 218448 with weight 16093286. Total sieving time: 4.48 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.15 hours. Total square root time: 0.07 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,141,5,0,0,0,0,0,0,0,0,1600000,1600000,28,28,56,56,2.3,2.3,100000 total time: 4.78 hours. --------- CPU info (if available) ----------

Apr 9, 2009 (3rd)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Apr 9, 2009
(52·10¹⁴⁴+11)/9 = 5(7)₁₄₃9_<145> = 7 · 103 · 167 · 653 · 2954611865092757_<16> · C122
C122 = P39 · P83
P39 = 724290725579767305836091030202155649537_<39>
P83 = 34338597671396579436444177778028131407510991420689462672723960428011307199603139061_<83>

Number: 57779_144 N=24871127822807536540677308893737853256793987719707497098779318903928078213373681114319761189526515069860939915500591264757 ( 122 digits) SNFS difficulty: 146 digits. Divisors found: r1=724290725579767305836091030202155649537 r2=34338597671396579436444177778028131407510991420689462672723960428011307199603139061 Version: Total time: 5.51 hours. Scaled time: 13.14 units (timescale=2.384). Factorization parameters were as follows: n: 24871127822807536540677308893737853256793987719707497098779318903928078213373681114319761189526515069860939915500591264757 m: 100000000000000000000000000000 deg: 5 c5: 26 c0: 55 skew: 1.16 type: snfs lss: 1 rlim: 1350000 alim: 1350000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1350000/1350000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [675000, 1275001) Primes: rational ideals reading, algebraic ideals reading, Relations: 4442108 Max relations in full relation-set: Initial matrix: Pruned matrix : 236109 x 236357 Total sieving time: 5.21 hours. Total relation processing time: 0.17 hours. Matrix solve time: 0.12 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1350000,1350000,27,27,49,49,2.3,2.3,75000 total time: 5.51 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797) Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

(52·10¹⁴⁵+11)/9 = 5(7)₁₄₄9_<146> = 223 · 145617467609_<12> · C133
C133 = P35 · P45 · P53
P35 = 56954380313470557383476264133069369_<35>
P45 = 877944135394782865480706076381912796258246379_<45>
P53 = 35583485323197678203373839989701525841764457126274647_<53>

Number: 57779_145 N=1779272625363021460612243496577185608423839199881627329550077736603303475175902484372231463577430300728043315288438234114262937132597 ( 133 digits) SNFS difficulty: 146 digits. Divisors found: r1=56954380313470557383476264133069369 r2=877944135394782865480706076381912796258246379 r3=35583485323197678203373839989701525841764457126274647 Version: Total time: 4.23 hours. Scaled time: 10.09 units (timescale=2.384). Factorization parameters were as follows: n: 1779272625363021460612243496577185608423839199881627329550077736603303475175902484372231463577430300728043315288438234114262937132597 m: 100000000000000000000000000000 deg: 5 c5: 52 c0: 11 skew: 0.73 type: snfs lss: 1 rlim: 1350000 alim: 1350000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1350000/1350000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [675000, 1125001) Primes: rational ideals reading, algebraic ideals reading, Relations: 4184175 Max relations in full relation-set: Initial matrix: Pruned matrix : 215777 x 216025 Total sieving time: 3.95 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.10 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1350000,1350000,27,27,49,49,2.3,2.3,75000 total time: 4.23 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797) Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Apr 9, 2009 (2nd)

By Andreas Tete / Msieve v1.41, GGNFS / Apr 9, 2009
(52·10¹⁴²+11)/9 = 5(7)₁₄₁9_<143> = 33937 · 58603297 · 850234538894121437711_<21> · C110
C110 = P31 · P80
P31 = 3343047086365563711398608131791_<31>
P80 = 10220781380272666838366366338702762386870049984758453088533674483692999433547011_<80>

Thu Apr 09 03:03:15 2009 Msieve v. 1.41 Thu Apr 09 03:03:15 2009 random seeds: 0244d728 35297466 Thu Apr 09 03:03:15 2009 factoring 34168553413699943534215778841743330944560565854995941012155248657561572877659329534745682232709216307282126701 (110 digits) Thu Apr 09 03:03:16 2009 searching for 15-digit factors Thu Apr 09 03:03:18 2009 commencing number field sieve (110-digit input) Thu Apr 09 03:03:18 2009 R0: -1700913657140603924940 Thu Apr 09 03:03:18 2009 R1: 198739532677 Thu Apr 09 03:03:18 2009 A0: 2785491139512664258540157293 Thu Apr 09 03:03:18 2009 A1: 403368444129627968520825 Thu Apr 09 03:03:18 2009 A2: 728029085584517419 Thu Apr 09 03:03:18 2009 A3: -89078160501357 Thu Apr 09 03:03:18 2009 A4: 189651940 Thu Apr 09 03:03:18 2009 A5: 2400 Thu Apr 09 03:03:18 2009 skew 104086.27, size 1.972286e-010, alpha -6.860694, combined = 1.100483e-009 Thu Apr 09 03:03:19 2009 Thu Apr 09 03:03:19 2009 commencing relation filtering Thu Apr 09 03:03:19 2009 commencing duplicate removal, pass 1 Thu Apr 09 03:04:30 2009 found 550305 hash collisions in 5661426 relations Thu Apr 09 03:04:47 2009 added 42618 free relations Thu Apr 09 03:04:47 2009 commencing duplicate removal, pass 2 Thu Apr 09 03:05:13 2009 found 539667 duplicates and 5164376 unique relations Thu Apr 09 03:05:13 2009 memory use: 41.3 MB Thu Apr 09 03:05:13 2009 reading rational ideals above 3080192 Thu Apr 09 03:05:13 2009 reading algebraic ideals above 3080192 Thu Apr 09 03:05:13 2009 commencing singleton removal, pass 1 Thu Apr 09 03:06:09 2009 relations with 0 large ideals: 111892 Thu Apr 09 03:06:09 2009 relations with 1 large ideals: 725947 Thu Apr 09 03:06:09 2009 relations with 2 large ideals: 1725109 Thu Apr 09 03:06:09 2009 relations with 3 large ideals: 1771461 Thu Apr 09 03:06:09 2009 relations with 4 large ideals: 711542 Thu Apr 09 03:06:09 2009 relations with 5 large ideals: 76946 Thu Apr 09 03:06:09 2009 relations with 6 large ideals: 41477 Thu Apr 09 03:06:09 2009 relations with 7+ large ideals: 2 Thu Apr 09 03:06:09 2009 5164376 relations and about 5234055 large ideals Thu Apr 09 03:06:09 2009 commencing singleton removal, pass 2 Thu Apr 09 03:07:05 2009 found 2269372 singletons Thu Apr 09 03:07:05 2009 current dataset: 2895004 relations and about 2370513 large ideals Thu Apr 09 03:07:05 2009 commencing singleton removal, pass 3 Thu Apr 09 03:07:46 2009 found 592847 singletons Thu Apr 09 03:07:46 2009 current dataset: 2302157 relations and about 1730815 large ideals Thu Apr 09 03:07:46 2009 commencing singleton removal, pass 4 Thu Apr 09 03:08:23 2009 found 185711 singletons Thu Apr 09 03:08:23 2009 current dataset: 2116446 relations and about 1539384 large ideals Thu Apr 09 03:08:23 2009 commencing singleton removal, final pass Thu Apr 09 03:09:01 2009 memory use: 33.3 MB Thu Apr 09 03:09:01 2009 commencing in-memory singleton removal Thu Apr 09 03:09:01 2009 begin with 2116446 relations and 1590336 unique ideals Thu Apr 09 03:09:03 2009 reduce to 1885716 relations and 1355557 ideals in 14 passes Thu Apr 09 03:09:03 2009 max relations containing the same ideal: 39 Thu Apr 09 03:09:03 2009 reading rational ideals above 720000 Thu Apr 09 03:09:03 2009 reading algebraic ideals above 720000 Thu Apr 09 03:09:03 2009 commencing singleton removal, final pass Thu Apr 09 03:09:43 2009 keeping 1723978 ideals with weight <= 20, new excess is 193681 Thu Apr 09 03:09:45 2009 memory use: 47.9 MB Thu Apr 09 03:09:45 2009 commencing in-memory singleton removal Thu Apr 09 03:09:45 2009 begin with 1905859 relations and 1723978 unique ideals Thu Apr 09 03:09:47 2009 reduce to 1875377 relations and 1595193 ideals in 11 passes Thu Apr 09 03:09:47 2009 max relations containing the same ideal: 20 Thu Apr 09 03:09:48 2009 removing 235209 relations and 207452 ideals in 27757 cliques Thu Apr 09 03:09:48 2009 commencing in-memory singleton removal Thu Apr 09 03:09:48 2009 begin with 1640168 relations and 1595193 unique ideals Thu Apr 09 03:09:50 2009 reduce to 1620757 relations and 1367935 ideals in 8 passes Thu Apr 09 03:09:50 2009 max relations containing the same ideal: 20 Thu Apr 09 03:09:51 2009 removing 174444 relations and 146687 ideals in 27757 cliques Thu Apr 09 03:09:51 2009 commencing in-memory singleton removal Thu Apr 09 03:09:51 2009 begin with 1446313 relations and 1367935 unique ideals Thu Apr 09 03:09:52 2009 reduce to 1432880 relations and 1207596 ideals in 7 passes Thu Apr 09 03:09:52 2009 max relations containing the same ideal: 20 Thu Apr 09 03:09:53 2009 relations with 0 large ideals: 15040 Thu Apr 09 03:09:53 2009 relations with 1 large ideals: 103426 Thu Apr 09 03:09:53 2009 relations with 2 large ideals: 299605 Thu Apr 09 03:09:53 2009 relations with 3 large ideals: 441521 Thu Apr 09 03:09:53 2009 relations with 4 large ideals: 358753 Thu Apr 09 03:09:53 2009 relations with 5 large ideals: 163345 Thu Apr 09 03:09:53 2009 relations with 6 large ideals: 44150 Thu Apr 09 03:09:53 2009 relations with 7+ large ideals: 7040 Thu Apr 09 03:09:53 2009 commencing 2-way merge Thu Apr 09 03:09:54 2009 reduce to 864816 relation sets and 639532 unique ideals Thu Apr 09 03:09:54 2009 commencing full merge Thu Apr 09 03:10:04 2009 memory use: 49.4 MB Thu Apr 09 03:10:05 2009 found 403958 cycles, need 375732 Thu Apr 09 03:10:05 2009 weight of 375732 cycles is about 26631272 (70.88/cycle) Thu Apr 09 03:10:05 2009 distribution of cycle lengths: Thu Apr 09 03:10:05 2009 1 relations: 40847 Thu Apr 09 03:10:05 2009 2 relations: 37918 Thu Apr 09 03:10:05 2009 3 relations: 37801 Thu Apr 09 03:10:05 2009 4 relations: 35042 Thu Apr 09 03:10:05 2009 5 relations: 32630 Thu Apr 09 03:10:05 2009 6 relations: 29567 Thu Apr 09 03:10:05 2009 7 relations: 26654 Thu Apr 09 03:10:05 2009 8 relations: 23522 Thu Apr 09 03:10:05 2009 9 relations: 20609 Thu Apr 09 03:10:05 2009 10+ relations: 91142 Thu Apr 09 03:10:05 2009 heaviest cycle: 20 relations Thu Apr 09 03:10:05 2009 commencing cycle optimization Thu Apr 09 03:10:05 2009 start with 2428548 relations Thu Apr 09 03:10:12 2009 pruned 77505 relations Thu Apr 09 03:10:12 2009 memory use: 61.7 MB Thu Apr 09 03:10:12 2009 distribution of cycle lengths: Thu Apr 09 03:10:12 2009 1 relations: 40847 Thu Apr 09 03:10:12 2009 2 relations: 39017 Thu Apr 09 03:10:12 2009 3 relations: 39486 Thu Apr 09 03:10:12 2009 4 relations: 36367 Thu Apr 09 03:10:12 2009 5 relations: 33787 Thu Apr 09 03:10:12 2009 6 relations: 30392 Thu Apr 09 03:10:12 2009 7 relations: 27261 Thu Apr 09 03:10:12 2009 8 relations: 23779 Thu Apr 09 03:10:12 2009 9 relations: 20663 Thu Apr 09 03:10:12 2009 10+ relations: 84133 Thu Apr 09 03:10:12 2009 heaviest cycle: 20 relations Thu Apr 09 03:10:13 2009 RelProcTime: 321 Thu Apr 09 03:10:13 2009 Thu Apr 09 03:10:13 2009 commencing linear algebra Thu Apr 09 03:10:13 2009 read 375732 cycles Thu Apr 09 03:10:14 2009 cycles contain 1262361 unique relations Thu Apr 09 03:10:36 2009 read 1262361 relations Thu Apr 09 03:10:38 2009 using 20 quadratic characters above 129051674 Thu Apr 09 03:10:46 2009 building initial matrix Thu Apr 09 03:11:03 2009 memory use: 140.2 MB Thu Apr 09 03:11:03 2009 read 375732 cycles Thu Apr 09 03:11:04 2009 matrix is 375495 x 375732 (108.0 MB) with weight 35920809 (95.60/col) Thu Apr 09 03:11:04 2009 sparse part has weight 25294481 (67.32/col) Thu Apr 09 03:11:09 2009 filtering completed in 3 passes Thu Apr 09 03:11:10 2009 matrix is 373450 x 373650 (107.6 MB) with weight 35776280 (95.75/col) Thu Apr 09 03:11:10 2009 sparse part has weight 25215452 (67.48/col) Thu Apr 09 03:11:11 2009 read 373650 cycles Thu Apr 09 03:11:11 2009 matrix is 373450 x 373650 (107.6 MB) with weight 35776280 (95.75/col) Thu Apr 09 03:11:11 2009 sparse part has weight 25215452 (67.48/col) Thu Apr 09 03:11:11 2009 saving the first 48 matrix rows for later Thu Apr 09 03:11:12 2009 matrix is 373402 x 373650 (102.5 MB) with weight 28487580 (76.24/col) Thu Apr 09 03:11:12 2009 sparse part has weight 24633976 (65.93/col) Thu Apr 09 03:11:12 2009 matrix includes 64 packed rows Thu Apr 09 03:11:12 2009 using block size 65536 for processor cache size 3072 kB Thu Apr 09 03:11:15 2009 commencing Lanczos iteration Thu Apr 09 03:11:15 2009 memory use: 99.6 MB Thu Apr 09 03:30:38 2009 lanczos halted after 5906 iterations (dim = 373402) Thu Apr 09 03:30:39 2009 recovered 31 nontrivial dependencies Thu Apr 09 03:30:39 2009 BLanczosTime: 1226 Thu Apr 09 03:30:39 2009 Thu Apr 09 03:30:39 2009 commencing square root phase Thu Apr 09 03:30:39 2009 reading relations for dependency 1 Thu Apr 09 03:30:39 2009 read 186146 cycles Thu Apr 09 03:30:40 2009 cycles contain 777166 unique relations Thu Apr 09 03:30:58 2009 read 777166 relations Thu Apr 09 03:31:03 2009 multiplying 628388 relations Thu Apr 09 03:32:32 2009 multiply complete, coefficients have about 25.11 million bits Thu Apr 09 03:32:33 2009 initial square root is modulo 16293239 Thu Apr 09 03:34:38 2009 sqrtTime: 239 Thu Apr 09 03:34:38 2009 prp31 factor: 3343047086365563711398608131791 Thu Apr 09 03:34:38 2009 prp80 factor: 10220781380272666838366366338702762386870049984758453088533674483692999433547011 Thu Apr 09 03:34:38 2009 elapsed time 00:31:23

Apr 9, 2009

By Sinkiti Sibata / GGNFS, Msieve / Apr 9, 2009
(52·10¹⁵⁷-43)/9 = 5(7)₁₅₆3_<158> = 23 · 53 · 1213 · 29567 · 12658876837_<11> · 135348159141181289_<18> · C120
C120 = P34 · P87
P34 = 1563245310616346305114141976356471_<34>
P87 = 493417335839288436508758464426809943832532907598333625203510886400945640369114348815759_<87>

Number: 57773_157 N=771332336427578513933358574990653834345535965729313032742009229397885912124919989008537968701911759932297553236486426489 ( 120 digits) SNFS difficulty: 159 digits. Divisors found: r1=1563245310616346305114141976356471 (pp34) r2=493417335839288436508758464426809943832532907598333625203510886400945640369114348815759 (pp87) Version: GGNFS-0.77.1-20060513-k8 Total time: 65.25 hours. Scaled time: 129.14 units (timescale=1.979). Factorization parameters were as follows: name: 57773_157 n: 771332336427578513933358574990653834345535965729313032742009229397885912124919989008537968701911759932297553236486426489 m: 20000000000000000000000000000000 deg: 5 c5: 325 c0: -86 skew: 0.77 type: snfs rlim: 2000000 alim: 2000000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1000000, 3500001) Primes: RFBsize:148933, AFBsize:148895, largePrimes:8955379 encountered Relations: rels:10119563, finalFF:424072 Max relations in full relation-set: 28 Initial matrix: 297894 x 424072 with sparse part having weight 61358057. Pruned matrix : 267588 x 269141 with weight 42138672. Total sieving time: 63.24 hours. Total relation processing time: 0.31 hours. Matrix solve time: 1.54 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,159,5,0,0,0,0,0,0,0,0,2000000,2000000,27,27,50,50,2.4,2.4,100000 total time: 65.25 hours. --------- CPU info (if available) ----------

(52·10¹⁶⁹-43)/9 = 5(7)₁₆₈3_<170> = 5153 · C167
C167 = P30 · P137
P30 = 141123905140081748758439889157_<30>
P137 = 79451135073637208062710826844545700257591647268293500083720115297127311011627099148183218921499931962868099751915326230940533150055049513_<137>

Number: 57773_169 N=11212454449403799297065355671992582530133471332772710610863143368480065549733704206826659766694697802790176164909330055846648122992000344998598443193824525087866830541 ( 167 digits) SNFS difficulty: 171 digits. Divisors found: r1=141123905140081748758439889157 (pp30) r2=79451135073637208062710826844545700257591647268293500083720115297127311011627099148183218921499931962868099751915326230940533150055049513 (pp137) Version: GGNFS-0.77.1-20060513-nocona Total time: 129.59 hours. Scaled time: 329.68 units (timescale=2.544). Factorization parameters were as follows: name: 57773_169 n: 11212454449403799297065355671992582530133471332772710610863143368480065549733704206826659766694697802790176164909330055846648122992000344998598443193824525087866830541 m: 10000000000000000000000000000000000 deg: 5 c5: 26 c0: -215 skew: 1.53 type: snfs rlim: 5000000 alim: 5000000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved algebraic special-q in [2500000, 7400001) Primes: RFBsize:348513, AFBsize:348441, largePrimes:10507710 encountered Relations: rels:11670776, finalFF:884620 Max relations in full relation-set: 28 Initial matrix: 697020 x 884620 with sparse part having weight 117081634. Pruned matrix : 600360 x 603909 with weight 99044012. Total sieving time: 122.70 hours. Total relation processing time: 0.27 hours. Matrix solve time: 6.37 hours. Time per square root: 0.25 hours. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,100000 total time: 129.59 hours. --------- CPU info (if available) ----------

(52·10¹³⁶+11)/9 = 5(7)₁₃₅9_<137> = C137
C137 = P39 · P42 · P58
P39 = 162327654977075883402432607143510339247_<39>
P42 = 225516353255079604804093456753934845067833_<42>
P58 = 1578302626785572386446896929818689186951420900821885917029_<58>

Number: 57779_136 N=57777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779 ( 137 digits) SNFS difficulty: 138 digits. Divisors found: r1=162327654977075883402432607143510339247 (pp39) r2=225516353255079604804093456753934845067833 (pp42) r3=1578302626785572386446896929818689186951420900821885917029 (pp58) Version: Msieve-1.40 Total time: 5.82 hours. Scaled time: 11.40 units (timescale=1.960). Factorization parameters were as follows: name: 57779_136 n: 57777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779 m: 2000000000000000000000000000 deg: 5 c5: 65 c0: 44 skew: 0.92 type: snfs lss: 1 rlim: 1410000 alim: 1410000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1410000/1410000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [705000, 1305001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 195509 x 195757 Total sieving time: 5.82 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,138.000,5,0,0,0,0,0,0,0,0,1410000,1410000,26,26,48,48,2.3,2.3,75000 total time: 5.82 hours. --------- CPU info (if available) ----------

Apr 8, 2009 (5th)

By Andreas Tete / Msieve, GGNFS / Apr 8, 2009
(52·10¹⁴⁹+11)/9 = 5(7)₁₄₈9_<150> = 3 · 17 · 1783 · 628363 · 8825785487_<10> · 213641945483460762505333_<24> · C106
C106 = P48 · P59
P48 = 449254024867847727675909476262097732256487477847_<48>
P59 = 11937045302486433091318474345081585284330222063528243378473_<59>

Wed Apr 08 15:53:47 2009 Msieve v. 1.41 Wed Apr 08 15:53:47 2009 random seeds: 55fce73c e1f53e2b Wed Apr 08 15:53:47 2009 factoring 5362765647171864912608824510227527182258184685704261834523201022179084754944556645341581873430918024187631 (106 digits) Wed Apr 08 15:53:49 2009 searching for 15-digit factors Wed Apr 08 15:53:52 2009 commencing number field sieve (106-digit input) Wed Apr 08 15:53:52 2009 R0: -271133063771250244924 Wed Apr 08 15:53:52 2009 R1: 100195085147 Wed Apr 08 15:53:52 2009 A0: -59425125008032265936367375 Wed Apr 08 15:53:52 2009 A1: 5255982720263690813535 Wed Apr 08 15:53:52 2009 A2: 111647876233073929 Wed Apr 08 15:53:52 2009 A3: -15196907018525 Wed Apr 08 15:53:52 2009 A4: -106597328 Wed Apr 08 15:53:52 2009 A5: 3660 Wed Apr 08 15:53:52 2009 skew 36177.73, size 5.317563e-010, alpha -6.255835, combined = 1.903280e-009 Wed Apr 08 15:53:52 2009 Wed Apr 08 15:53:52 2009 commencing relation filtering Wed Apr 08 15:53:52 2009 commencing duplicate removal, pass 1 Wed Apr 08 15:54:41 2009 found 351678 hash collisions in 4591979 relations Wed Apr 08 15:55:04 2009 added 31407 free relations Wed Apr 08 15:55:04 2009 commencing duplicate removal, pass 2 Wed Apr 08 15:55:11 2009 found 335788 duplicates and 4287597 unique relations Wed Apr 08 15:55:11 2009 memory use: 40.3 MB Wed Apr 08 15:55:11 2009 reading rational ideals above 2555904 Wed Apr 08 15:55:11 2009 reading algebraic ideals above 2555904 Wed Apr 08 15:55:11 2009 commencing singleton removal, pass 1 Wed Apr 08 15:55:58 2009 relations with 0 large ideals: 94646 Wed Apr 08 15:55:58 2009 relations with 1 large ideals: 617918 Wed Apr 08 15:55:58 2009 relations with 2 large ideals: 1486882 Wed Apr 08 15:55:58 2009 relations with 3 large ideals: 1505950 Wed Apr 08 15:55:58 2009 relations with 4 large ideals: 534854 Wed Apr 08 15:55:58 2009 relations with 5 large ideals: 17526 Wed Apr 08 15:55:58 2009 relations with 6 large ideals: 29821 Wed Apr 08 15:55:58 2009 relations with 7+ large ideals: 0 Wed Apr 08 15:55:58 2009 4287597 relations and about 4323015 large ideals Wed Apr 08 15:55:58 2009 commencing singleton removal, pass 2 Wed Apr 08 15:56:45 2009 found 1956078 singletons Wed Apr 08 15:56:45 2009 current dataset: 2331519 relations and about 1946125 large ideals Wed Apr 08 15:56:45 2009 commencing singleton removal, pass 3 Wed Apr 08 15:57:13 2009 found 481565 singletons Wed Apr 08 15:57:13 2009 current dataset: 1849954 relations and about 1424840 large ideals Wed Apr 08 15:57:13 2009 commencing singleton removal, final pass Wed Apr 08 15:57:38 2009 memory use: 33.3 MB Wed Apr 08 15:57:38 2009 commencing in-memory singleton removal Wed Apr 08 15:57:38 2009 begin with 1849954 relations and 1464090 unique ideals Wed Apr 08 15:57:43 2009 reduce to 1493132 relations and 1095577 ideals in 17 passes Wed Apr 08 15:57:43 2009 max relations containing the same ideal: 15 Wed Apr 08 15:57:43 2009 reading rational ideals above 100000 Wed Apr 08 15:57:43 2009 reading algebraic ideals above 100000 Wed Apr 08 15:57:43 2009 commencing singleton removal, final pass Wed Apr 08 15:58:20 2009 keeping 1381232 ideals with weight <= 25, new excess is 104356 Wed Apr 08 15:58:23 2009 memory use: 46.6 MB Wed Apr 08 15:58:23 2009 commencing in-memory singleton removal Wed Apr 08 15:58:23 2009 begin with 1496135 relations and 1381232 unique ideals Wed Apr 08 15:58:27 2009 reduce to 1480368 relations and 1350857 ideals in 12 passes Wed Apr 08 15:58:27 2009 max relations containing the same ideal: 25 Wed Apr 08 15:58:29 2009 relations with 0 large ideals: 3762 Wed Apr 08 15:58:29 2009 relations with 1 large ideals: 37480 Wed Apr 08 15:58:29 2009 relations with 2 large ideals: 160886 Wed Apr 08 15:58:29 2009 relations with 3 large ideals: 359726 Wed Apr 08 15:58:29 2009 relations with 4 large ideals: 446278 Wed Apr 08 15:58:29 2009 relations with 5 large ideals: 312236 Wed Apr 08 15:58:29 2009 relations with 6 large ideals: 127460 Wed Apr 08 15:58:29 2009 relations with 7+ large ideals: 32540 Wed Apr 08 15:58:29 2009 commencing 2-way merge Wed Apr 08 15:58:32 2009 reduce to 831906 relation sets and 702521 unique ideals Wed Apr 08 15:58:32 2009 ignored 126 oversize relation sets Wed Apr 08 15:58:32 2009 commencing full merge Wed Apr 08 15:58:48 2009 memory use: 53.8 MB Wed Apr 08 15:58:49 2009 found 362928 cycles, need 348721 Wed Apr 08 15:58:49 2009 weight of 348721 cycles is about 24522820 (70.32/cycle) Wed Apr 08 15:58:49 2009 distribution of cycle lengths: Wed Apr 08 15:58:49 2009 1 relations: 38690 Wed Apr 08 15:58:49 2009 2 relations: 37640 Wed Apr 08 15:58:49 2009 3 relations: 37108 Wed Apr 08 15:58:49 2009 4 relations: 33406 Wed Apr 08 15:58:49 2009 5 relations: 30118 Wed Apr 08 15:58:49 2009 6 relations: 26528 Wed Apr 08 15:58:49 2009 7 relations: 23071 Wed Apr 08 15:58:49 2009 8 relations: 19577 Wed Apr 08 15:58:49 2009 9 relations: 16983 Wed Apr 08 15:58:49 2009 10+ relations: 85600 Wed Apr 08 15:58:49 2009 heaviest cycle: 23 relations Wed Apr 08 15:58:49 2009 commencing cycle optimization Wed Apr 08 15:58:50 2009 start with 2308529 relations Wed Apr 08 15:59:03 2009 pruned 63973 relations Wed Apr 08 15:59:03 2009 memory use: 59.7 MB Wed Apr 08 15:59:03 2009 distribution of cycle lengths: Wed Apr 08 15:59:03 2009 1 relations: 38690 Wed Apr 08 15:59:03 2009 2 relations: 38619 Wed Apr 08 15:59:03 2009 3 relations: 38562 Wed Apr 08 15:59:03 2009 4 relations: 34268 Wed Apr 08 15:59:03 2009 5 relations: 31073 Wed Apr 08 15:59:03 2009 6 relations: 26924 Wed Apr 08 15:59:03 2009 7 relations: 23273 Wed Apr 08 15:59:03 2009 8 relations: 19526 Wed Apr 08 15:59:03 2009 9 relations: 17009 Wed Apr 08 15:59:03 2009 10+ relations: 80777 Wed Apr 08 15:59:03 2009 heaviest cycle: 23 relations Wed Apr 08 15:59:04 2009 RelProcTime: 258 Wed Apr 08 15:59:05 2009 Wed Apr 08 15:59:05 2009 commencing linear algebra Wed Apr 08 15:59:05 2009 read 348721 cycles Wed Apr 08 15:59:07 2009 cycles contain 1241197 unique relations Wed Apr 08 15:59:29 2009 read 1241197 relations Wed Apr 08 15:59:33 2009 using 20 quadratic characters above 67107102 Wed Apr 08 15:59:44 2009 building initial matrix Wed Apr 08 16:00:16 2009 memory use: 133.6 MB Wed Apr 08 16:00:16 2009 read 348721 cycles Wed Apr 08 16:00:18 2009 matrix is 348372 x 348721 (98.2 MB) with weight 32653745 (93.64/col) Wed Apr 08 16:00:18 2009 sparse part has weight 23311371 (66.85/col) Wed Apr 08 16:00:25 2009 filtering completed in 3 passes Wed Apr 08 16:00:25 2009 matrix is 345226 x 345426 (97.5 MB) with weight 32393005 (93.78/col) Wed Apr 08 16:00:25 2009 sparse part has weight 23152847 (67.03/col) Wed Apr 08 16:00:27 2009 read 345426 cycles Wed Apr 08 16:00:28 2009 matrix is 345226 x 345426 (97.5 MB) with weight 32393005 (93.78/col) Wed Apr 08 16:00:28 2009 sparse part has weight 23152847 (67.03/col) Wed Apr 08 16:00:28 2009 saving the first 48 matrix rows for later Wed Apr 08 16:00:28 2009 matrix is 345178 x 345426 (93.6 MB) with weight 25761950 (74.58/col) Wed Apr 08 16:00:28 2009 sparse part has weight 22474477 (65.06/col) Wed Apr 08 16:00:28 2009 matrix includes 64 packed rows Wed Apr 08 16:00:28 2009 using block size 65536 for processor cache size 3072 kB Wed Apr 08 16:00:33 2009 commencing Lanczos iteration Wed Apr 08 16:00:33 2009 memory use: 91.0 MB Wed Apr 08 16:20:55 2009 lanczos halted after 5461 iterations (dim = 345178) Wed Apr 08 16:20:56 2009 recovered 30 nontrivial dependencies Wed Apr 08 16:20:56 2009 BLanczosTime: 1311 Wed Apr 08 16:20:56 2009 Wed Apr 08 16:20:56 2009 commencing square root phase Wed Apr 08 16:20:56 2009 reading relations for dependency 1 Wed Apr 08 16:20:56 2009 read 172900 cycles Wed Apr 08 16:20:57 2009 cycles contain 761657 unique relations Wed Apr 08 16:21:06 2009 read 761657 relations Wed Apr 08 16:21:10 2009 multiplying 618710 relations Wed Apr 08 16:22:39 2009 multiply complete, coefficients have about 24.39 million bits Wed Apr 08 16:22:40 2009 initial square root is modulo 10105189 Wed Apr 08 16:24:44 2009 sqrtTime: 228 Wed Apr 08 16:24:44 2009 prp48 factor: 449254024867847727675909476262097732256487477847 Wed Apr 08 16:24:44 2009 prp59 factor: 11937045302486433091318474345081585284330222063528243378473 Wed Apr 08 16:24:44 2009 elapsed time 00:30:57

Apr 8, 2009 (4th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Apr 8, 2009
(8·10¹⁸⁴+1)/9 = (8)₁₈₃9_<184> = 3 · 19603 · 172173708801163613627_<21> · 27179099398845119796776615939_<29> · C131
C131 = P54 · P77
P54 = 655200614742021634033184493527939976327840479083596331_<54>
P77 = 49297794490247366498009769287197835197566546266043480968889690856371958296947_<77>

Number: 88889_184 N=32299945255435921563264500910223759473383544543244622969530356135443820563047187110300569176110925997216606362828072402522777701457 ( 131 digits) SNFS difficulty: 185 digits. Divisors found: r1=655200614742021634033184493527939976327840479083596331 r2=49297794490247366498009769287197835197566546266043480968889690856371958296947 Version: Total time: 90.35 hours. Scaled time: 215.67 units (timescale=2.387). Factorization parameters were as follows: n: 32299945255435921563264500910223759473383544543244622969530356135443820563047187110300569176110925997216606362828072402522777701457 m: 10000000000000000000000000000000000000 deg: 5 c5: 4 c0: 5 skew: 1.05 type: snfs lss: 1 rlim: 7400000 alim: 7400000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [3700000, 6100001) Primes: rational ideals reading, algebraic ideals reading, Relations: 19738380 Max relations in full relation-set: Initial matrix: Pruned matrix : 1439655 x 1439903 Total sieving time: 82.17 hours. Total relation processing time: 2.51 hours. Matrix solve time: 5.15 hours. Time per square root: 0.52 hours. Prototype def-par.txt line would be: snfs,185,5,0,0,0,0,0,0,0,0,7400000,7400000,28,28,54,54,2.5,2.5,100000 total time: 90.35 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047004k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673797) Calibrating delay using timer specific routine.. 5148.57 BogoMIPS (lpj=2574285) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672337) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672389)

Apr 8, 2009 (3rd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM / Apr 8, 2009
(64·10³²¹-1)/9 = 7(1)_321<322> = 13 · 557 · 3163 · 48947 · 10809769 · 1731548410507_<13> · 261280146756814062538507318913686335068158574151673052598829302142577942835385969_<81> · C211
C211 = P57 · P154
P57 = 136920528458324437784046746620817633432816773555317196129_<57>
P154 = 9473001739252911590386140919918219522378832016848880341270650479366213030853894032663349942975658310158914485340068110000467344258703110989631095198989717_<154>

Number: n N=1297048404225135176763377838306703308284086026735410232090598831035125692096921942005723226083643408967468407954149338910641471501414593415858038052157558954903248295597331322908306784373809350097683957943205493 ( 211 digits) SNFS difficulty: 216 digits. Divisors found: Wed Apr 8 03:01:28 2009 prp57 factor: 136920528458324437784046746620817633432816773555317196129 Wed Apr 8 03:01:28 2009 prp154 factor: 9473001739252911590386140919918219522378832016848880341270650479366213030853894032663349942975658310158914485340068110000467344258703110989631095198989717 Wed Apr 8 03:01:28 2009 elapsed time 37:00:40 (Msieve 1.40 - dependency 1) Version: GGNFS-0.77.1-20050930-k8 Total time: 164.17 hours. Scaled time: 330.47 units (timescale=2.013). Factorization parameters were as follows: name: KA_7_1_321 n: 1297048404225135176763377838306703308284086026735410232090598831035125692096921942005723226083643408967468407954149338910641471501414593415858038052157558954903248295597331322908306784373809350097683957943205493 m: 1000000000000000000000000000000000000 deg: 6 c6: 4 c3: 10 c0: 25 skew: 1.36 type: snfs lss: 1 rlim: 29000000 alim: 29000000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.6 alambda: 2.6 Factor base limits: 29000000/29000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [14500000, 43099990) Primes: RFBsize:1799676, AFBsize:1800414, largePrimes:38190043 encountered Relations: rels:35567012, finalFF:1582831 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 10222882 hash collisions in 53039926 relations Msieve: matrix is 4419521 x 4419769 (1191.6 MB) Total sieving time: 162.85 hours. Total relation processing time: 1.32 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,216,6,0,0,0,0,0,0,0,0,29000000,29000000,29,29,58,58,2.6,2.6,100000 total time: 164.17 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU1: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU2: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU3: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 Memory: 3368972k/3407296k available (2746k kernel code, 36964k reserved, 1423k data, 416k init, 2489792k highmem) Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.94 BogoMIPS (lpj=2830471) Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830448) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830456) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830456) Total of 4 processors activated (22643.66 BogoMIPS).

(52·10¹²¹+11)/9 = 5(7)₁₂₀9_<122> = 2131 · 364423 · 26234906906371_<14> · C100
C100 = P30 · P70
P30 = 364380770250394223205085702913_<30>
P70 = 7782813588336038236590157745377257175997742877047838277174240662961821_<70>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 2835907610033120194199551806236055848179990717764081780027871686218836290400926117700635184267484573 (100 digits) Using B1=410000, B2=258309880, polynomial Dickson(3), sigma=1875643875 Step 1 took 2844ms Step 2 took 1547ms ********** Factor found in step 2: 364380770250394223205085702913 Found probable prime factor of 30 digits: 364380770250394223205085702913 Probable prime cofactor 7782813588336038236590157745377257175997742877047838277174240662961821 has 70 digits

(52·10¹³¹+11)/9 = 5(7)₁₃₀9_<132> = 3 · 156615616223844733_<18> · C115
C115 = P43 · P72
P43 = 7763687498449931812059462700396020833572123_<43>
P72 = 158393177019022554878786757562711332700651832607685626917554728976969727_<72>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 1229715128262352446646479717712916921331965604795480595127657762873153975570827675722018351807183853308813442120421 (115 digits) Using B1=3016000, B2=5707048630, polynomial Dickson(6), sigma=776505955 Step 1 took 23656ms Step 2 took 10813ms ********** Factor found in step 2: 7763687498449931812059462700396020833572123 Found probable prime factor of 43 digits: 7763687498449931812059462700396020833572123 Probable prime cofactor 158393177019022554878786757562711332700651832607685626917554728976969727 has 72 digits

(52·10¹⁶³-43)/9 = 5(7)₁₆₂3_<164> = 68227 · 1064333 · 10051697 · C146
C146 = P50 · P97
P50 = 11345284585959792348128719462608562601664887183003_<50>
P97 = 6977056631564364741721701334882809627921614120837450546938867006111665296912706481813926549424033_<97>

Number: n N=79156693057455737307008940043409821123504830816174226754932381838488471827986295021737720124311306762782216540492587282060531047450730353517311099 ( 146 digits) SNFS difficulty: 166 digits. Divisors found: Wed Apr 08 12:35:24 2009 prp50 factor: 11345284585959792348128719462608562601664887183003 Wed Apr 08 12:35:24 2009 prp97 factor: 6977056631564364741721701334882809627921614120837450546938867006111665296912706481813926549424033 Wed Apr 08 12:35:24 2009 elapsed time 00:49:52 (Msieve 1.39 - dependency 3) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 38.25 hours. Scaled time: 100.47 units (timescale=2.627). Factorization parameters were as follows: name: KA_5_7_162_3 n: 79156693057455737307008940043409821123504830816174226754932381838488471827986295021737720124311306762782216540492587282060531047450730353517311099 m: 1000000000000000000000000000000000 deg: 5 c5: 13 c0: -1075 skew: 2.42 type: snfs lss: 1 rlim: 4100000 alim: 4100000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4100000/4100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved special-q in [2050000, 4350000) Primes: RFBsize:289774, AFBsize:289152, largePrimes:9241359 encountered Relations: rels:9588942, finalFF:654042 Max relations in full relation-set: 28 Initial matrix: 578992 x 654042 with sparse part having weight 71044949. Pruned matrix : 543963 x 546921 with weight 56786987. Msieve: found 1073917 hash collisions in 10559866 relations Msieve: matrix is 634107 x 634355 (168.3 MB) Total sieving time: 37.64 hours. Total relation processing time: 0.28 hours. Matrix solve time: 0.33 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000 total time: 38.25 hours. --------- CPU info (if available) ----------

(52·10¹⁵²+11)/9 = 5(7)₁₅₁9_<153> = 3² · 757 · C149
C149 = P38 · P111
P38 = 93808864550850625172985855237704776067_<38>
P111 = 904021097507399866702195420272204652716997344737015447439748923511012042343544803174140630732101383321666439749_<111>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 84805192687182999820604400084805192687182999820604400084805192687182999820604400084805192687182999820604400084805192687182999820604400084805192687183 (149 digits) Using B1=2012000, B2=2853999340, polynomial Dickson(6), sigma=853283790 Step 1 took 23687ms Step 2 took 9922ms ********** Factor found in step 2: 93808864550850625172985855237704776067 Found probable prime factor of 38 digits: 93808864550850625172985855237704776067 Probable prime cofactor 904021097507399866702195420272204652716997344737015447439748923511012042343544803174140630732101383321666439749 has 111 digits

(52·10¹⁶³-61)/9 = 5(7)₁₆₂1_<164> = 3 · 281 · 49559 · 154452407 · C148
C148 = P72 · P76
P72 = 985599952264306027024189286435490320222399984074792036487401000273442791_<72>
P76 = 9084799990658051214181652821663796864828696072835756124477903941113082320359_<76>

Number: n N=8953978437123343116951200201478548849810829379828748970302581367078882584804549791697998382013828361531770509760399305306292768437157835291721081969 ( 148 digits) SNFS difficulty: 166 digits. Divisors found: Wed Apr 08 16:56:58 2009 prp72 factor: 985599952264306027024189286435490320222399984074792036487401000273442791 Wed Apr 08 16:56:58 2009 prp76 factor: 9084799990658051214181652821663796864828696072835756124477903941113082320359 Wed Apr 08 16:56:58 2009 elapsed time 00:55:33 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 42.65 hours. Scaled time: 112.98 units (timescale=2.649). Factorization parameters were as follows: name: KA_5_7_162_1 n: 8953978437123343116951200201478548849810829379828748970302581367078882584804549791697998382013828361531770509760399305306292768437157835291721081969 m: 1000000000000000000000000000000000 deg: 5 c5: 13 c0: -1525 skew: 2.59 type: snfs lss: 1 rlim: 4100000 alim: 4100000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4100000/4100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved special-q in [2050000, 4750091) Primes: RFBsize:289774, AFBsize:290733, largePrimes:9093056 encountered Relations: rels:9165804, finalFF:598084 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1115970 hash collisions in 10198363 relations Msieve: matrix is 725226 x 725474 (192.8 MB) Total sieving time: 42.35 hours. Total relation processing time: 0.30 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000 total time: 42.65 hours. --------- CPU info (if available) ----------

(52·10¹⁵⁶-61)/9 = 5(7)₁₅₅1_<157> = 4937 · 114370423 · 18365093151893_<14> · C132
C132 = P50 · P83
P50 = 24695978014100333072677731977278205511815080160837_<50>
P83 = 22561325654314430046535809389320157194646910045717054254420912038014349179571854781_<83>

Number: n N=557174002327906975798769654208559431606013104752429834529952087837656117353644842339464494240064263927360215844965204480695887411697 ( 132 digits) SNFS difficulty: 158 digits. Divisors found: Wed Apr 08 21:24:46 2009 prp50 factor: 24695978014100333072677731977278205511815080160837 Wed Apr 08 21:24:46 2009 prp83 factor: 22561325654314430046535809389320157194646910045717054254420912038014349179571854781 Wed Apr 08 21:24:46 2009 elapsed time 00:52:14 (Msieve 1.39 - dependency 4) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 21.26 hours. Scaled time: 55.86 units (timescale=2.627). Factorization parameters were as follows: name: KA_5_7_155_1 n: 557174002327906975798769654208559431606013104752429834529952087837656117353644842339464494240064263927360215844965204480695887411697 m: 20000000000000000000000000000000 deg: 5 c5: 65 c0: -244 skew: 1.30 type: snfs lss: 1 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [1500000, 2900083) Primes: RFBsize:216816, AFBsize:216527, largePrimes:12681842 encountered Relations: rels:11727577, finalFF:433586 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1107459 hash collisions in 12643471 relations Msieve: matrix is 588100 x 588348 (157.8 MB) Total sieving time: 20.97 hours. Total relation processing time: 0.29 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,56,56,2.4,2.4,100000 total time: 21.26 hours. --------- CPU info (if available) ----------

Apr 8, 2009 (2nd)

By Max Dettweiler / GMP-ECM, msieve v1.40beta2, GGNFS, msieve v1.41, msieve v1.39 / Apr 8, 2009
(49·10¹⁹⁰-13)/9 = 5(4)₁₈₉3_<191> = 23 · 56783 · 3577949592990109125475959133_<28> · 10560005477046551407109442082543_<32> · C127
C127 = P36 · P41 · P51
P36 = 151384963804792601957076838327835443_<36>
P41 = 27247030603187965412926575051567284862283_<41>
P51 = 267489733874812578723107950256592587386798727120657_<51>

--------------------------------- P36=151384963804792601957076838327835443 B1=1000000 B2=900000000 Method=ECM Found by the ECM "workers" at http://factorization.ath.cx --------------------------------- Tue Apr 07 03:16:09 2009 Msieve v. 1.40 Tue Apr 07 03:16:09 2009 random seeds: 28de34d8 8bda56ae Tue Apr 07 03:16:09 2009 factoring 7288300964925622921639267800655225120410607285033175107865679394472800601695388603369479931 (91 digits) Tue Apr 07 03:16:10 2009 searching for 15-digit factors Tue Apr 07 03:16:11 2009 commencing quadratic sieve (91-digit input) Tue Apr 07 03:16:11 2009 using multiplier of 3 Tue Apr 07 03:16:11 2009 using 32kb Intel Core sieve core Tue Apr 07 03:16:11 2009 sieve interval: 36 blocks of size 32768 Tue Apr 07 03:16:11 2009 processing polynomials in batches of 6 Tue Apr 07 03:16:11 2009 using a sieve bound of 1713449 (64706 primes) Tue Apr 07 03:16:11 2009 using large prime bound of 164491104 (27 bits) Tue Apr 07 03:16:11 2009 using double large prime bound of 615256603721856 (42-50 bits) Tue Apr 07 03:16:11 2009 using trial factoring cutoff of 50 bits Tue Apr 07 03:16:11 2009 polynomial 'A' values have 12 factors Tue Apr 07 04:37:43 2009 64819 relations (16665 full + 48154 combined from 762683 partial), need 64802 Tue Apr 07 04:37:43 2009 begin with 779348 relations Tue Apr 07 04:37:44 2009 reduce to 162308 relations in 11 passes Tue Apr 07 04:37:44 2009 attempting to read 162308 relations Tue Apr 07 04:37:46 2009 recovered 162308 relations Tue Apr 07 04:37:46 2009 recovered 142998 polynomials Tue Apr 07 04:37:46 2009 attempting to build 64819 cycles Tue Apr 07 04:37:46 2009 found 64819 cycles in 5 passes Tue Apr 07 04:37:46 2009 distribution of cycle lengths: Tue Apr 07 04:37:46 2009 length 1 : 16665 Tue Apr 07 04:37:46 2009 length 2 : 11914 Tue Apr 07 04:37:46 2009 length 3 : 11364 Tue Apr 07 04:37:46 2009 length 4 : 8678 Tue Apr 07 04:37:46 2009 length 5 : 6457 Tue Apr 07 04:37:46 2009 length 6 : 4061 Tue Apr 07 04:37:46 2009 length 7 : 2502 Tue Apr 07 04:37:46 2009 length 9+: 3178 Tue Apr 07 04:37:46 2009 largest cycle: 22 relations Tue Apr 07 04:37:46 2009 matrix is 64706 x 64819 (16.1 MB) with weight 3957333 (61.05/col) Tue Apr 07 04:37:46 2009 sparse part has weight 3957333 (61.05/col) Tue Apr 07 04:37:47 2009 filtering completed in 3 passes Tue Apr 07 04:37:47 2009 matrix is 60951 x 61015 (15.3 MB) with weight 3763741 (61.69/col) Tue Apr 07 04:37:47 2009 sparse part has weight 3763741 (61.69/col) Tue Apr 07 04:37:47 2009 saving the first 48 matrix rows for later Tue Apr 07 04:37:47 2009 matrix is 60903 x 61015 (9.4 MB) with weight 2929803 (48.02/col) Tue Apr 07 04:37:47 2009 sparse part has weight 2100869 (34.43/col) Tue Apr 07 04:37:47 2009 matrix includes 64 packed rows Tue Apr 07 04:37:47 2009 using block size 24406 for processor cache size 2048 kB Tue Apr 07 04:37:47 2009 commencing Lanczos iteration Tue Apr 07 04:37:47 2009 memory use: 9.3 MB Tue Apr 07 04:38:04 2009 lanczos halted after 965 iterations (dim = 60897) Tue Apr 07 04:38:04 2009 recovered 14 nontrivial dependencies Tue Apr 07 04:38:04 2009 prp41 factor: 27247030603187965412926575051567284862283 Tue Apr 07 04:38:04 2009 prp51 factor: 267489733874812578723107950256592587386798727120657 Tue Apr 07 04:38:04 2009 elapsed time 01:21:55

(52·10¹¹²+11)/9 = 5(7)₁₁₁9_<113> = 19 · 1471 · 6203 · 244561123 · C97
C97 = P39 · P58
P39 = 342635300376985740079889564063862325331_<39>
P58 = 3977161757490024436199522761739823455145947091623722643189_<58>

Number: 57779_112 N=1362716013425455038269365465041655392090464515205357520408224328485283338132684220072647149320559 ( 97 digits) SNFS difficulty: 114 digits. Divisors found: r1=342635300376985740079889564063862325331 (pp40) r2=3977161757490024436199522761739823455145947091623722643189 (pp59) Version: Msieve-1.41 Total time: 0.95 hours. Scaled time: 1.03 units (timescale=1.088). Factorization parameters were as follows: n: 1362716013425455038269365465041655392090464515205357520408224328485283338132684220072647149320559 m: 20000000000000000000000 deg: 5 c5: 325 c0: 22 skew: 0.58 type: snfs lss: 1 rlim: 560000 alim: 560000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2Factor base limits: 560000/560000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [280000, 480001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 56708 x 56935 Total sieving time: 0.95 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,114,5,0,0,0,0,0,0,0,0,560000,560000,25,25,45,45,2.2,2.2,50000 total time: 0.95 hours. --------- CPU info (if available) ----------

(52·10¹¹³+11)/9 = 5(7)₁₁₂9_<114> = 3 · 797 · C111
C111 = P32 · P80
P32 = 21191076950997992778938517729283_<32>
P80 = 11403239072609000017840567548152233635496296586350682597719486296171078116689943_<80>

Number: 57779_113 N=241646916678284306891584181421069752311910404758585436126214043403503880291835122449927970630605511408522700869 ( 111 digits) SNFS difficulty: 116 digits. Divisors found: r1=21191076950997992778938517729283 (pp33) r2=11403239072609000017840567548152233635496296586350682597719486296171078116689943 (pp81) Version: Msieve-1.39 Total time: 1.01 hours. Scaled time: 1.09 units (timescale=1.085). Factorization parameters were as follows: n: 241646916678284306891584181421069752311910404758585436126214043403503880291835122449927970630605511408522700869 m: 100000000000000000000000 deg: 5 c5: 13 c0: 275 skew: 1.84 type: snfs lss: 1 rlim: 600000 alim: 600000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [300000, 500001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 59957 x 60198 Total sieving time: 1.01 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,116,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.2,2.2,50000 total time: 1.01 hours. --------- CPU info (if available) ----------

(52·10¹¹⁴+11)/9 = 5(7)₁₁₃9_<115> = 7 · 419 · 36721 · C107
C107 = P42 · P66
P42 = 156191211927687234042225904227266197684409_<42>
P66 = 343461195244667387875682227644599921552361260327667052031805907567_<66>

Number: 57779_114 N=53645620335396606821871926431568222512112838049256370755536983441795441250273823494624946636921862091022903 ( 107 digits) SNFS difficulty: 116 digits. Divisors found: r1=156191211927687234042225904227266197684409 (pp43) r2=343461195244667387875682227644599921552361260327667052031805907567 (pp67) Version: Msieve-1.39 Total time: 1.01 hours. Scaled time: 1.10 units (timescale=1.090). Factorization parameters were as follows: n: 53645620335396606821871926431568222512112838049256370755536983441795441250273823494624946636921862091022903 m: 100000000000000000000000 deg: 5 c5: 26 c0: 55 skew: 1.16 type: snfs lss: 1 rlim: 610000 alim: 610000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2Factor base limits: 610000/610000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [305000, 505001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 62274 x 62507 Total sieving time: 1.01 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,116,5,0,0,0,0,0,0,0,0,610000,610000,25,25,45,45,2.2,2.2,50000 total time: 1.01 hours. --------- CPU info (if available) ----------

(52·10¹⁰⁴+11)/9 = 5(7)₁₀₃9_<105> = 3 · 27103 · 997052731 · C91
C91 = P29 · P63
P29 = 19220610958847864530012111841_<29>
P63 = 370797586486105227102882427553203663841628754066639649741320861_<63>

Number: 57779_104 N=7126956154329172964190407581733579595542753084022720093873577878288167714232922899398415101 ( 91 digits) SNFS difficulty: 106 digits. Divisors found: r1=19220610958847864530012111841 (pp29) r2=370797586486105227102882427553203663841628754066639649741320861 (pp63) Version: GGNFS-0.77.1-VC8(Sat Total time: 0.35 hours. Scaled time: 0.38 units (timescale=1.092). Factorization parameters were as follows: n: 7126956154329172964190407581733579595542753084022720093873577878288167714232922899398415101 m: 200000000000000000000000000 deg: 4 c4: 13 c0: 44 skew: 1.36 type: snfs lss: 1 rlim: 410000 alim: 410000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2Factor base limits: 410000/410000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [205000, 265001) Primes: RFBsize:34614, AFBsize:34155, largePrimes:979903 encountered Relations: rels:899445, finalFF:86300 Max relations in full relation-set: 32 Initial matrix: 68836 x 86300 with sparse part having weight 3259399. Pruned matrix : 57430 x 57838 with weight 1677024. Total sieving time: 0.31 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.01 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,106,4,0,0,0,0,0,0,0,0,410000,410000,25,25,44,44,2.2,2.2,20000 total time: 0.35 hours. --------- CPU info (if available) ----------

(52·10¹¹⁷+11)/9 = 5(7)₁₁₆9_<118> = 17 · 59 · 10956842667605569320979_<23> · C93
C93 = P38 · P55
P38 = 71924007866618544951803639781410382773_<38>
P55 = 7309717546312534089494372288483167098053407071733225079_<55>

Number: 57779_117 N=525744182303742310034568486879758102100680007383383575604620876268515086518106958523153164067 ( 93 digits) SNFS difficulty: 119 digits. Divisors found: r1=71924007866618544951803639781410382773 (pp39) r2=7309717546312534089494372288483167098053407071733225079 (pp56) Version: Msieve-1.41 Total time: 1.23 hours. Scaled time: 1.34 units (timescale=1.088). Factorization parameters were as follows: n: 525744182303742310034568486879758102100680007383383575604620876268515086518106958523153164067 m: 200000000000000000000000 deg: 5 c5: 325 c0: 22 skew: 0.58 type: snfs lss: 1 rlim: 670000 alim: 670000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2Factor base limits: 670000/670000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [335000, 585001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 73690 x 73919 Total sieving time: 1.23 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,119,5,0,0,0,0,0,0,0,0,670000,670000,25,25,45,45,2.2,2.2,50000 total time: 1.23 hours. --------- CPU info (if available) ----------

(52·10¹¹⁹+11)/9 = 5(7)₁₁₈9_<120> = 3 · 1069 · 25044948075953116163_<20> · C97
C97 = P47 · P51
P47 = 65362022175359856796126919799848878544914687343_<47>
P51 = 110056642251239621825067197259113037041248732781833_<51>

Number: 57779_119 N=7193524691371170713641673802460032864647362592976192622799232625333131233825174851481483825439719 ( 97 digits) SNFS difficulty: 121 digits. Divisors found: r1=65362022175359856796126919799848878544914687343 (pp48) r2=110056642251239621825067197259113037041248732781833 (pp52) Version: Msieve-1.41 Total time: 1.25 hours. Scaled time: 1.35 units (timescale=1.081). Factorization parameters were as follows: n: 7193524691371170713641673802460032864647362592976192622799232625333131233825174851481483825439719 m: 1000000000000000000000000 deg: 5 c5: 26 c0: 55 skew: 1.16 type: snfs lss: 1 rlim: 740000 alim: 740000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2Factor base limits: 740000/740000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [370000, 620001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 83078 x 83303 Total sieving time: 1.25 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,121,5,0,0,0,0,0,0,0,0,740000,740000,25,25,46,46,2.2,2.2,50000 total time: 1.25 hours. --------- CPU info (if available) ----------

(52·10¹³³+11)/9 = 5(7)₁₃₂9_<134> = 17 · 5372303 · C126
C126 = P45 · P82
P45 = 552786152596759621451787350162034188925429337_<45>
P82 = 1144443240550567536987813732224100088589848122719187256363678808463144355031420117_<82>

Number: 57779_133 N=632632375809316105191624717695862274880643287462266870057488849072710396462327540718929685197421552487417492556979729043772429 ( 126 digits) SNFS difficulty: 136 digits. Divisors found: r1=552786152596759621451787350162034188925429337 (pp46) r2=1144443240550567536987813732224100088589848122719187256363678808463144355031420117 (pp83) Version: Msieve-1.39 Total time: 3.25 hours. Scaled time: 3.54 units (timescale=1.090). Factorization parameters were as follows: n: 632632375809316105191624717695862274880643287462266870057488849072710396462327540718929685197421552487417492556979729043772429 m: 1000000000000000000000000000 deg: 5 c5: 13 c0: 275 skew: 1.84 type: snfs lss: 1 rlim: 1300000 alim: 1300000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [650000, 1175001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 182164 x 182412 Total sieving time: 3.25 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,136,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,48,48,2.3,2.3,75000 total time: 3.25 hours. --------- CPU info (if available) ----------

Apr 8, 2009

By Serge Batalov / GMP-ECM 6.2.2 / Apr 8, 2009
(52·10¹¹⁶+11)/9 = 5(7)₁₁₅9_<117> = 3³ · 162618791 · C108
C108 = P37 · P71
P37 = 2645715604664475548380977250122717151_<37>
P71 = 49737411941327305141315767551566392120952692721970711669814872930052497_<71>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=2645698852 Step 1 took 6533ms Step 2 took 7036ms ********** Factor found in step 2: 2645715604664475548380977250122717151 Found probable prime factor of 37 digits: 2645715604664475548380977250122717151 Probable prime cofactor has 71 digits

(52·10¹⁴³+11)/9 = 5(7)₁₄₂9_<144> = 3³ · 83 · 357347 · C135
C135 = P31 · P105
P31 = 2627625558851476694029546636907_<31>
P105 = 274577761184714753670872305144563611669505000759721875940972634740657525851157819603161894138821807409811_<105>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=4099621279 Step 1 took 8108ms Step 2 took 7905ms ********** Factor found in step 2: 2627625558851476694029546636907 Found probable prime factor of 31 digits: 2627625558851476694029546636907 Probable prime cofactor has 105 digits

Apr 7, 2009 (6th)

Factorizations of 577...779 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Apr 7, 2009 (5th)

By Wataru Sakai / Msieve / Apr 7, 2009
(17·10¹⁸⁵-11)/3 = 5(6)₁₈₄3_<186> = C186
C186 = P70 · P117
P70 = 4925952720289718922267290651764752755426360242050366403515405657991967_<70>
P117 = 115036968246284402056838380084523901776546762863252344722745402064736836757750211510628015588193248445323115293824889_<117>

Number: 56663_185 N=566666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663 ( 186 digits) SNFS difficulty: 186 digits. Divisors found: r1=4925952720289718922267290651764752755426360242050366403515405657991967 r2=115036968246284402056838380084523901776546762863252344722745402064736836757750211510628015588193248445323115293824889 Version: Total time: 295.50 hours. Scaled time: 576.22 units (timescale=1.950). Factorization parameters were as follows: n: 566666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663 m: 10000000000000000000000000000000000000 deg: 5 c5: 17 c0: -11 skew: 0.92 type: snfs lss: 1 rlim: 8900000 alim: 8900000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 Factor base limits: 8900000/8900000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [4450000, 7350001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1351725 x 1351973 Total sieving time: 295.50 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.