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STUDIO KAMADA

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News and updates, June 2008

Jun 30, 2008 (4th)

By suberi / GMP-ECM
(64·10²⁴⁶+53)/9 = 7(1)₂₄₅7_<247> = 13 · 17 · 1160548621_<10> · C236
C236 = P40 · P196
P40 = 3653540712889564696115226712823703119009_<40>
P196 = 7588709004594473714701606971400814241433489374368336268700131770235266770437697694816355315610746815222410425117554914203426930343872298340279245942146302647290762688407537944247691411211636284693_<196>

Jun 30, 2008 (3rd)

By Serge Batalov / PRIMO 3.0.6
(11·10²¹³⁶+1)/3 = 3(6)₂₁₃₅7_<2137> is prime.
(22·10²²⁰⁴-1)/3 = 7(3)_2204<2205> is prime.

Jun 30, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve
(22·10¹⁶⁷-31)/9 = 2(4)₁₆₆1_<168> = 23 · 2539 · 37321 · C159
C159 = P44 · P115
P44 = 17383069455340930576859078822201728294481827_<44>
P115 = 6452230846702379390519960216544745384363065802954977313588048296249399827777355779886850218076924772405182266503159_<115>

Number: n N=112159576950120681443763221790573388303510799505846499774493764431806325745620236083497493365726993165082508258285562019154441967021394020693105366603163591493 ( 159 digits) SNFS difficulty: 168 digits. Divisors found: Mon Jun 30 13:30:40 2008 prp44 factor: 17383069455340930576859078822201728294481827 Mon Jun 30 13:30:40 2008 prp115 factor: 6452230846702379390519960216544745384363065802954977313588048296249399827777355779886850218076924772405182266503159 Mon Jun 30 13:30:40 2008 elapsed time 01:27:40 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 64.33 hours. Scaled time: 117.66 units (timescale=1.829). Factorization parameters were as follows: name: KA_2_4_166_1 n: 112159576950120681443763221790573388303510799505846499774493764431806325745620236083497493365726993165082508258285562019154441967021394020693105366603163591493 skew: 0.43 deg: 5 c5: 2200 c0: -31 m: 1000000000000000000000000000000000 type: snfs rlim: 5500000 alim: 5500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 5500000/5500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 3900000) Primes: RFBsize:380800, AFBsize:380504, largePrimes:8273794 encountered Relations: rels:7946017, finalFF:867342 Max relations in full relation-set: 28 Initial matrix: 761371 x 867342 with sparse part having weight 46178197. Pruned matrix : 664153 x 668023 with weight 29900504. Total sieving time: 63.98 hours. Total relation processing time: 0.35 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,168,5,0,0,0,0,0,0,0,0,5500000,5500000,28,28,48,48,2.5,2.5,100000 total time: 64.33 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

(22·10¹⁶⁶-31)/9 = 2(4)₁₆₅1_<167> = 3 · 71 · 64951 · C160
C160 = P49 · P112
P49 = 1054167195644633213538682942324589961665224175651_<49>
P112 = 1676120464464856575059394614578455426232363135439230363648406284394705342167031244505148822086872348576246745457_<112>

Number: n N=1766911209587497953093599302301376953102490078251437681439192871104381428198667673452673889623000339399549117991254544465513254335857550718764621943204454267507 ( 160 digits) SNFS difficulty: 167 digits. Divisors found: Mon Jun 30 13:57:25 2008 prp49 factor: 1054167195644633213538682942324589961665224175651 Mon Jun 30 13:57:25 2008 prp112 factor: 1676120464464856575059394614578455426232363135439230363648406284394705342167031244505148822086872348576246745457 Mon Jun 30 13:57:25 2008 elapsed time 01:54:07 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 64.73 hours. Scaled time: 93.66 units (timescale=1.447). Factorization parameters were as follows: name: KA_2_4_165_1 n: 1766911209587497953093599302301376953102490078251437681439192871104381428198667673452673889623000339399549117991254544465513254335857550718764621943204454267507 skew: 0.68 deg: 5 c5: 220 c0: -31 m: 1000000000000000000000000000000000 type: snfs rlim: 5200000 alim: 5200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 5200000/5200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 3000000) Primes: RFBsize:361407, AFBsize:361244, largePrimes:7999134 encountered Relations: rels:7698324, finalFF:845404 Max relations in full relation-set: 28 Initial matrix: 722718 x 845404 with sparse part having weight 44159497. Pruned matrix : 607145 x 610822 with weight 26410081. Total sieving time: 64.45 hours. Total relation processing time: 0.28 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,5200000,5200000,28,28,48,48,2.5,2.5,100000 total time: 64.73 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

Jun 30, 2008

By Serge Batalov / GMP-ECM
(13·10¹⁶⁹-31)/9 = 1(4)₁₆₈1_<170> = 11 · 233435160481_<12> · C157
C157 = P32 · P34 · P92
P32 = 23177318032476375616378164979441_<32>
P34 = 3889428202100559149737103058094361_<34>
P92 = 62401200909819595851686241736549279149882130176261860111226874344359239380766173789767518451_<92>

Jun 29, 2008 (4th)

By suberi / GMP-ECM
2·10¹⁷¹-3 = 1(9)₁₇₀7_<172> = 4691 · 2769503838393179_<16> · C153
C153 = P32 · P37 · P85
P32 = 56976208855415157152685472638791_<32>
P37 = 1494197448543319671819667216019537347_<37>
P85 = 1808260737095189373997972911343245292873628525108905125242459880129553110340203951049_<85>

Jun 29, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve
(22·10¹⁶²-31)/9 = 2(4)₁₆₁1_<163> = 63737 · 175819093 · C150
C150 = P47 · P104
P47 = 14301556867419987422995670262853271843431921849_<47>
P104 = 15252435624754255559351197971224772317866956646695045907287784752020816148507378065192759386215178367749_<104>

Number: n N=218133575454085489914759947173598865752402947025291892634882341632830313219197266117538854778381938634304794779037061562662852396167085943869950047901 ( 150 digits) SNFS difficulty: 163 digits. Divisors found: Sun Jun 29 16:01:24 2008 prp47 factor: 14301556867419987422995670262853271843431921849 Sun Jun 29 16:01:24 2008 prp104 factor: 15252435624754255559351197971224772317866956646695045907287784752020816148507378065192759386215178367749 Sun Jun 29 16:01:24 2008 elapsed time 00:52:21 (Msieve 1.34) Version: GGNFS-0.77.1-20050930-k8 Total time: 44.63 hours. Scaled time: 37.44 units (timescale=0.839). Factorization parameters were as follows: name: KA_2_4_161_1 n: 218133575454085489914759947173598865752402947025291892634882341632830313219197266117538854778381938634304794779037061562662852396167085943869950047901 type: snfs deg: 5 c5: 2200 c0: -31 skew: 0.43 m: 100000000000000000000000000000000 rlim: 4500000 alim: 4500000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 2500000 ) Primes: RFBsize:315948, AFBsize:315573, largePrimes:5606089 encountered Relations: rels:5690538, finalFF:717744 Max relations in full relation-set: 28 Initial matrix: 631588 x 717744 with sparse part having weight 42037180. Pruned matrix : 552185 x 555406 with weight 26967299. Total sieving time: 44.45 hours. Total relation processing time: 0.18 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,163,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.5,2.5,100000 total time: 44.63 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).

Jun 29, 2008 (2nd)

By Sinkiti Sibata / GGNFS
(22·10¹⁵²-31)/9 = 2(4)₁₅₁1_<153> = 241 · 33589 · 43063 · C141
C141 = P36 · P41 · P65
P36 = 267966650482880119367198545606586717_<36>
P41 = 31215354255566197538002781232347164771547_<41>
P65 = 83832565493279521861357860130355126983160895444458139420999716557_<65>

Number: 24441_152 N=701232074521790742830270859869370784937896181312621274744822033496199307723301462181157327064017251111525772069827393633543232268035105331843 ( 141 digits) SNFS difficulty: 153 digits. Divisors found: r1=267966650482880119367198545606586717 (pp36) r2=31215354255566197538002781232347164771547 (pp41) r3=83832565493279521861357860130355126983160895444458139420999716557 (pp65) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 44.29 hours. Scaled time: 29.94 units (timescale=0.676). Factorization parameters were as follows: name: 24441_152 n: 701232074521790742830270859869370784937896181312621274744822033496199307723301462181157327064017251111525772069827393633543232268035105331843 m: 1000000000000000000000000000000 c5: 2200 c0: -31 skew: 0.43 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2400001) Primes: RFBsize:176302, AFBsize:176210, largePrimes:5703677 encountered Relations: rels:5676502, finalFF:516785 Max relations in full relation-set: 28 Initial matrix: 352579 x 516785 with sparse part having weight 48496265. Pruned matrix : 293926 x 295752 with weight 26826377. Total sieving time: 40.17 hours. Total relation processing time: 0.27 hours. Matrix solve time: 3.70 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 44.29 hours. --------- CPU info (if available) ----------

Jun 29, 2008

By Serge Batalov / pol51, Msieve 1.36, GMP-ECM
(7·10¹⁸⁰+17)/3 = 2(3)₁₇₉9_<181> = 4739322601106537_<16> · 54789725825058929_<17> · 5635025408798334073151006813_<28> · C121
C121 = P47 · P74
P47 = 41874999678888405957858413767086436069870427179_<47>
P74 = 38081205768930982523881149611719815860882075982791143081161151118407749709_<74>

Number: 23339_180 N=1594650479345668205679297248996417788309645764071629470283797649136969454552884601269365941059206432039370206471942940911 (121 digits) Divisors found: r1=41874999678888405957858413767086436069870427179 (prp47) r2=38081205768930982523881149611719815860882075982791143081161151118407749709 (prp74) Version: Total time: 34 hours. Scaled time: 97.648 units (timescale=2.872). Factorization parameters were as follows: # poly selected by pol51 - 1.5 hours name: 23339_180 n: 1594650479345668205679297248996417788309645764071629470283797649136969454552884601269365941059206432039370206471942940911 skew: 35462.53 # norm 6.04e+16 c5: 38340 c4: -7645887822 c3: 2237821005459970 c2: 7602474157459019760 c1: -538696810513896633321935 c0: -1823549329867625284056766348 # alpha -5.80 Y1: 139319909443 Y0: -132985012360110909014155 # Murphy_E 2.48e-10 # M 788889806718177053534508787704877298154248623318878955959190838689725553459502855482663675053605970537986455887147354079 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, 4840001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 667726 x 667974 Total sieving time: 30:45:50 hours. Total relation processing time: 0.00 hours. Matrix solve time: 01:51:54 hours. Time per square root: 00:38:04 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: 0.00 hours. --------- CPU info (if available) ---------- Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init) Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618) Thu Jun 26 23:58:49 2008 Msieve v. 1.36 Thu Jun 26 23:58:49 2008 random seeds: 90f676d8 a0df0a85 Thu Jun 26 23:58:49 2008 factoring 1594650479345668205679297248996417788309645764071629470283797649136969454552884601269365941059206432039370206471942940911 (121 digits) Thu Jun 26 23:58:51 2008 no P-1/P+1/ECM available, skipping Thu Jun 26 23:58:51 2008 commencing number field sieve (121-digit input) Thu Jun 26 23:58:51 2008 R0: -132985012360110909014155 Thu Jun 26 23:58:51 2008 R1: 139319909443 Thu Jun 26 23:58:51 2008 A0: -1823549329867625284056766348 Thu Jun 26 23:58:51 2008 A1: -538696810513896633321935 Thu Jun 26 23:58:51 2008 A2: 7602474157459019760 Thu Jun 26 23:58:51 2008 A3: 2237821005459970 Thu Jun 26 23:58:51 2008 A4: -7645887822 Thu Jun 26 23:58:51 2008 A5: 38340 Thu Jun 26 23:58:51 2008 size score = 1.875082e-12, Murphy alpha = -5.801511, combined = 1.296806e-11 Thu Jun 26 23:58:51 2008 generating factor base Thu Jun 26 23:58:54 2008 factor base complete: Thu Jun 26 23:58:54 2008 348513 rational roots (max prime = 4999999) Thu Jun 26 23:58:54 2008 348157 algebraic roots (max prime = 4999999) Thu Jun 26 23:58:54 2008 a range: [-4000000, 4000000] Thu Jun 26 23:58:54 2008 b range: [1, 300] Thu Jun 26 23:58:54 2008 number of hash buckets: 77 Thu Jun 26 23:58:54 2008 sieve block size: 65536 Thu Jun 26 23:58:54 2008 Thu Jun 26 23:58:54 2008 maximum RFB prime: 4999999 Thu Jun 26 23:58:54 2008 RFB entries: 348513 Thu Jun 26 23:58:54 2008 medium RFB entries: 6542 Thu Jun 26 23:58:54 2008 resieved RFB entries: 6374 Thu Jun 26 23:58:54 2008 small RFB prime powers: 25 Thu Jun 26 23:58:54 2008 projective RFB roots: 5 Thu Jun 26 23:58:54 2008 RFB trial factoring cutoff: 58 or 87 bits Thu Jun 26 23:58:54 2008 single large prime RFB range: 22 - 27 bits Thu Jun 26 23:58:54 2008 double large prime RFB range: 45 - 52 bits Thu Jun 26 23:58:54 2008 triple large prime RFB range: 70 - 79 bits Thu Jun 26 23:58:54 2008 ... Sat Jun 28 14:45:50 2008 Sat Jun 28 14:45:50 2008 Msieve v. 1.36 Sat Jun 28 14:45:50 2008 random seeds: 6a3598f8 87614cc3 Sat Jun 28 14:45:50 2008 factoring 1594650479345668205679297248996417788309645764071629470283797649136969454552884601269365941059206432039370206471942940911 (121 digits) Sat Jun 28 14:45:51 2008 no P-1/P+1/ECM available, skipping Sat Jun 28 14:45:51 2008 commencing number field sieve (121-digit input) Sat Jun 28 14:45:51 2008 R0: -132985012360110909014155 Sat Jun 28 14:45:51 2008 R1: 139319909443 Sat Jun 28 14:45:51 2008 A0: -1823549329867625284056766348 Sat Jun 28 14:45:51 2008 A1: -538696810513896633321935 Sat Jun 28 14:45:51 2008 A2: 7602474157459019760 Sat Jun 28 14:45:51 2008 A3: 2237821005459970 Sat Jun 28 14:45:51 2008 A4: -7645887822 Sat Jun 28 14:45:51 2008 A5: 38340 Sat Jun 28 14:45:51 2008 size score = 1.875082e-12, Murphy alpha = -5.801511, combined = 1.296806e-11 Sat Jun 28 14:45:53 2008 restarting with 9447173 relations Sat Jun 28 14:45:53 2008 Sat Jun 28 14:45:53 2008 commencing relation filtering Sat Jun 28 14:45:53 2008 commencing duplicate removal, pass 1 Sat Jun 28 14:47:13 2008 found 1803884 hash collisions in 9447173 relations Sat Jun 28 14:47:13 2008 commencing duplicate removal, pass 2 Sat Jun 28 14:47:20 2008 found 1954127 duplicates and 7493046 unique relations Sat Jun 28 14:47:20 2008 memory use: 65.3 MB Sat Jun 28 14:47:22 2008 ignoring smallest 334421 rational and 334153 algebraic ideals Sat Jun 28 14:47:22 2008 filtering rational ideals above 4784128 Sat Jun 28 14:47:22 2008 filtering algebraic ideals above 4784128 Sat Jun 28 14:47:22 2008 need 1002861 more relations than ideals Sat Jun 28 14:47:22 2008 commencing singleton removal, pass 1 Sat Jun 28 14:48:31 2008 relations with 0 large ideals: 149207 Sat Jun 28 14:48:31 2008 relations with 1 large ideals: 1077069 Sat Jun 28 14:48:31 2008 relations with 2 large ideals: 2678793 Sat Jun 28 14:48:31 2008 relations with 3 large ideals: 2659073 Sat Jun 28 14:48:31 2008 relations with 4 large ideals: 899179 Sat Jun 28 14:48:31 2008 relations with 5 large ideals: 29496 Sat Jun 28 14:48:31 2008 relations with 6 large ideals: 229 Sat Jun 28 14:48:31 2008 relations with 7+ large ideals: 0 Sat Jun 28 14:48:31 2008 7493046 relations and about 7336098 large ideals Sat Jun 28 14:48:31 2008 commencing singleton removal, pass 2 Sat Jun 28 14:49:38 2008 found 3525823 singletons Sat Jun 28 14:49:38 2008 current dataset: 3967223 relations and about 3186249 large ideals Sat Jun 28 14:49:38 2008 commencing singleton removal, pass 3 Sat Jun 28 14:50:14 2008 found 677892 singletons Sat Jun 28 14:50:14 2008 current dataset: 3289331 relations and about 2463551 large ideals Sat Jun 28 14:50:14 2008 commencing singleton removal, pass 4 Sat Jun 28 14:50:44 2008 found 196603 singletons Sat Jun 28 14:50:44 2008 current dataset: 3092728 relations and about 2262445 large ideals Sat Jun 28 14:50:44 2008 commencing singleton removal, final pass Sat Jun 28 14:51:13 2008 memory use: 48.8 MB Sat Jun 28 14:51:14 2008 commencing in-memory singleton removal Sat Jun 28 14:51:14 2008 begin with 3092728 relations and 2380225 unique ideals Sat Jun 28 14:51:18 2008 reduce to 2697937 relations and 1977905 ideals in 14 passes Sat Jun 28 14:51:18 2008 max relations containing the same ideal: 39 Sat Jun 28 14:51:19 2008 filtering rational ideals above 720000 Sat Jun 28 14:51:19 2008 filtering algebraic ideals above 720000 Sat Jun 28 14:51:19 2008 need 116384 more relations than ideals Sat Jun 28 14:51:19 2008 commencing singleton removal, final pass Sat Jun 28 14:51:49 2008 keeping 2366367 ideals with weight <= 20, new excess is 279161 Sat Jun 28 14:51:50 2008 memory use: 67.1 MB Sat Jun 28 14:51:51 2008 commencing in-memory singleton removal Sat Jun 28 14:51:52 2008 begin with 2697937 relations and 2366367 unique ideals Sat Jun 28 14:51:57 2008 reduce to 2684931 relations and 2353350 ideals in 12 passes Sat Jun 28 14:51:57 2008 max relations containing the same ideal: 20 Sat Jun 28 14:52:00 2008 removing 147313 relations and 135061 ideals in 12252 cliques Sat Jun 28 14:52:00 2008 commencing in-memory singleton removal Sat Jun 28 14:52:00 2008 begin with 2537618 relations and 2353350 unique ideals Sat Jun 28 14:52:03 2008 reduce to 2532155 relations and 2212784 ideals in 7 passes Sat Jun 28 14:52:03 2008 max relations containing the same ideal: 20 Sat Jun 28 14:52:05 2008 removing 108716 relations and 96464 ideals in 12252 cliques Sat Jun 28 14:52:05 2008 commencing in-memory singleton removal Sat Jun 28 14:52:05 2008 begin with 2423439 relations and 2212784 unique ideals Sat Jun 28 14:52:08 2008 reduce to 2420149 relations and 2113014 ideals in 7 passes Sat Jun 28 14:52:08 2008 max relations containing the same ideal: 20 Sat Jun 28 14:52:09 2008 relations with 0 large ideals: 14446 Sat Jun 28 14:52:09 2008 relations with 1 large ideals: 117305 Sat Jun 28 14:52:09 2008 relations with 2 large ideals: 394599 Sat Jun 28 14:52:09 2008 relations with 3 large ideals: 691417 Sat Jun 28 14:52:09 2008 relations with 4 large ideals: 675705 Sat Jun 28 14:52:09 2008 relations with 5 large ideals: 376977 Sat Jun 28 14:52:09 2008 relations with 6 large ideals: 123053 Sat Jun 28 14:52:09 2008 relations with 7+ large ideals: 26647 Sat Jun 28 14:52:09 2008 commencing 2-way merge Sat Jun 28 14:52:11 2008 reduce to 1418089 relation sets and 1110954 unique ideals Sat Jun 28 14:52:11 2008 commencing full merge Sat Jun 28 14:52:32 2008 memory use: 108.3 MB Sat Jun 28 14:52:32 2008 found 697143 cycles, need 671154 Sat Jun 28 14:52:32 2008 weight of 671154 cycles is about 47207664 (70.34/cycle) Sat Jun 28 14:52:32 2008 distribution of cycle lengths: Sat Jun 28 14:52:32 2008 1 relations: 82867 Sat Jun 28 14:52:32 2008 2 relations: 77630 Sat Jun 28 14:52:32 2008 3 relations: 77110 Sat Jun 28 14:52:32 2008 4 relations: 70420 Sat Jun 28 14:52:32 2008 5 relations: 62652 Sat Jun 28 14:52:32 2008 6 relations: 53841 Sat Jun 28 14:52:32 2008 7 relations: 45748 Sat Jun 28 14:52:32 2008 8 relations: 39137 Sat Jun 28 14:52:32 2008 9 relations: 32448 Sat Jun 28 14:52:32 2008 10+ relations: 129301 Sat Jun 28 14:52:32 2008 heaviest cycle: 20 relations Sat Jun 28 14:52:32 2008 commencing cycle optimization Sat Jun 28 14:52:34 2008 start with 3953499 relations Sat Jun 28 14:52:43 2008 pruned 44706 relations Sat Jun 28 14:52:43 2008 memory use: 133.5 MB Sat Jun 28 14:52:43 2008 distribution of cycle lengths: Sat Jun 28 14:52:43 2008 1 relations: 82867 Sat Jun 28 14:52:43 2008 2 relations: 78135 Sat Jun 28 14:52:43 2008 3 relations: 78214 Sat Jun 28 14:52:43 2008 4 relations: 71049 Sat Jun 28 14:52:43 2008 5 relations: 63458 Sat Jun 28 14:52:43 2008 6 relations: 54339 Sat Jun 28 14:52:43 2008 7 relations: 46219 Sat Jun 28 14:52:43 2008 8 relations: 39107 Sat Jun 28 14:52:43 2008 9 relations: 32511 Sat Jun 28 14:52:43 2008 10+ relations: 125255 Sat Jun 28 14:52:43 2008 heaviest cycle: 20 relations Sat Jun 28 14:52:44 2008 elapsed time 00:06:54 Sat Jun 28 14:52:45 2008 Sat Jun 28 14:52:45 2008 Sat Jun 28 14:52:45 2008 Msieve v. 1.36 Sat Jun 28 14:52:45 2008 random seeds: 4fe81a4b 0280ad61 Sat Jun 28 14:52:45 2008 factoring 1594650479345668205679297248996417788309645764071629470283797649136969454552884601269365941059206432039370206471942940911 (121 digits) Sat Jun 28 14:52:46 2008 no P-1/P+1/ECM available, skipping Sat Jun 28 14:52:46 2008 commencing number field sieve (121-digit input) Sat Jun 28 14:52:46 2008 R0: -132985012360110909014155 Sat Jun 28 14:52:46 2008 R1: 139319909443 Sat Jun 28 14:52:46 2008 A0: -1823549329867625284056766348 Sat Jun 28 14:52:46 2008 A1: -538696810513896633321935 Sat Jun 28 14:52:46 2008 A2: 7602474157459019760 Sat Jun 28 14:52:46 2008 A3: 2237821005459970 Sat Jun 28 14:52:46 2008 A4: -7645887822 Sat Jun 28 14:52:46 2008 A5: 38340 Sat Jun 28 14:52:46 2008 size score = 1.875082e-12, Murphy alpha = -5.801511, combined = 1.296806e-11 Sat Jun 28 14:52:46 2008 Sat Jun 28 14:52:46 2008 commencing linear algebra Sat Jun 28 14:52:46 2008 read 671154 cycles Sat Jun 28 14:52:48 2008 cycles contain 2240490 unique relations Sat Jun 28 14:53:09 2008 read 2240490 relations Sat Jun 28 14:53:13 2008 using 32 quadratic characters above 134214782 Sat Jun 28 14:53:39 2008 building initial matrix Sat Jun 28 14:54:06 2008 memory use: 294.3 MB Sat Jun 28 14:54:09 2008 read 671154 cycles Sat Jun 28 14:54:10 2008 matrix is 670952 x 671154 (204.8 MB) with weight 68700036 (102.36/col) Sat Jun 28 14:54:10 2008 sparse part has weight 45644834 (68.01/col) Sat Jun 28 14:54:24 2008 filtering completed in 2 passes Sat Jun 28 14:54:24 2008 matrix is 667774 x 667974 (204.4 MB) with weight 68497158 (102.54/col) Sat Jun 28 14:54:24 2008 sparse part has weight 45560828 (68.21/col) Sat Jun 28 14:54:32 2008 read 667974 cycles Sat Jun 28 14:54:33 2008 matrix is 667774 x 667974 (204.4 MB) with weight 68497158 (102.54/col) Sat Jun 28 14:54:33 2008 sparse part has weight 45560828 (68.21/col) Sat Jun 28 14:54:33 2008 saving the first 48 matrix rows for later Sat Jun 28 14:54:34 2008 matrix is 667726 x 667974 (199.0 MB) with weight 53617419 (80.27/col) Sat Jun 28 14:54:34 2008 sparse part has weight 45486108 (68.10/col) Sat Jun 28 14:54:34 2008 matrix includes 64 packed rows Sat Jun 28 14:54:34 2008 using block size 43690 for processor cache size 1024 kB Sat Jun 28 14:54:38 2008 commencing Lanczos iteration Sat Jun 28 14:54:38 2008 memory use: 183.9 MB Sat Jun 28 16:44:37 2008 lanczos halted after 10561 iterations (dim = 667725) Sat Jun 28 16:44:39 2008 recovered 43 nontrivial dependencies Sat Jun 28 16:44:39 2008 elapsed time 01:51:54 Sat Jun 28 16:44:40 2008 Sat Jun 28 16:44:40 2008 Sat Jun 28 16:44:40 2008 Msieve v. 1.36 Sat Jun 28 16:44:40 2008 random seeds: 5793e7f0 d0222ab8 Sat Jun 28 16:44:40 2008 factoring 1594650479345668205679297248996417788309645764071629470283797649136969454552884601269365941059206432039370206471942940911 (121 digits) Sat Jun 28 16:44:40 2008 no P-1/P+1/ECM available, skipping Sat Jun 28 16:44:40 2008 commencing number field sieve (121-digit input) Sat Jun 28 16:44:40 2008 R0: -132985012360110909014155 Sat Jun 28 16:44:40 2008 R1: 139319909443 Sat Jun 28 16:44:40 2008 A0: -1823549329867625284056766348 Sat Jun 28 16:44:40 2008 A1: -538696810513896633321935 Sat Jun 28 16:44:40 2008 A2: 7602474157459019760 Sat Jun 28 16:44:40 2008 A3: 2237821005459970 Sat Jun 28 16:44:40 2008 A4: -7645887822 Sat Jun 28 16:44:40 2008 A5: 38340 Sat Jun 28 16:44:40 2008 size score = 1.875082e-12, Murphy alpha = -5.801511, combined = 1.296806e-11 Sat Jun 28 16:44:40 2008 Sat Jun 28 16:44:40 2008 commencing square root phase Sat Jun 28 16:44:40 2008 reading relations for dependency 1 Sat Jun 28 16:44:41 2008 read 333636 cycles Sat Jun 28 16:44:41 2008 cycles contain 1366577 unique relations Sat Jun 28 16:44:54 2008 read 1366577 relations Sat Jun 28 16:45:04 2008 multiplying 1949326 relations Sat Jun 28 16:52:18 2008 multiply complete, coefficients have about 89.97 million bits Sat Jun 28 16:52:21 2008 initial square root is modulo 2871293 Sat Jun 28 17:03:37 2008 reading relations for dependency 2 Sat Jun 28 17:03:37 2008 read 333906 cycles Sat Jun 28 17:03:38 2008 cycles contain 1370087 unique relations Sat Jun 28 17:03:51 2008 read 1370087 relations Sat Jun 28 17:04:00 2008 multiplying 1955116 relations Sat Jun 28 17:11:15 2008 multiply complete, coefficients have about 90.24 million bits Sat Jun 28 17:11:19 2008 initial square root is modulo 2999401 Sat Jun 28 17:22:44 2008 prp47 factor: 41874999678888405957858413767086436069870427179 Sat Jun 28 17:22:44 2008 prp74 factor: 38081205768930982523881149611719815860882075982791143081161151118407749709 Sat Jun 28 17:22:44 2008 elapsed time 00:38:04 Total time: 34 hours.

(8·10¹⁶⁸-17)/9 = (8)₁₆₇7_<168> = 3947 · 71699 · 373247252387_<12> · 1024799923094265919_<19> · C130
C130 = P41 · P90
P41 = 13086962130596681403157479104708270412239_<41>
P90 = 627469619736798457013692142254079987778839619064291230581747063260251518592308215913277437_<90>

Jun 28, 2008

By Sinkiti Sibata / GGNFS
(22·10¹⁵⁷-31)/9 = 2(4)₁₅₆1_<158> = 3 · 7³ · 18541 · 1732231 · 3794897 · C138
C138 = P44 · P94
P44 = 44098693698355178723007115893291109054904999_<44>
P94 = 4419774566759251381250748538579444137486855579222989929121298784868474730416401309522649387033_<94>

Number: 24441_157 N=194906284835296689056161059734252486653472926503376515699092856713705334417156440133625881676221606796262345126825254838818544669397477967 ( 138 digits) SNFS difficulty: 158 digits. Divisors found: r1=44098693698355178723007115893291109054904999 (pp44) r2=4419774566759251381250748538579444137486855579222989929121298784868474730416401309522649387033 (pp94) Version: GGNFS-0.77.1-20060513-k8 Total time: 54.43 hours. Scaled time: 108.85 units (timescale=2.000). Factorization parameters were as follows: name: 24441_157 n: 194906284835296689056161059734252486653472926503376515699092856713705334417156440133625881676221606796262345126825254838818544669397477967 m: 10000000000000000000000000000000 c5: 2200 c0: -31 skew: 0.43 type: snfs Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2000000, 3700001) Primes: RFBsize:283146, AFBsize:282969, largePrimes:5939096 encountered Relations: rels:6178732, finalFF:832302 Max relations in full relation-set: 28 Initial matrix: 566182 x 832302 with sparse part having weight 55094693. Pruned matrix : 372755 x 375649 with weight 39705875. Total sieving time: 52.04 hours. Total relation processing time: 0.19 hours. Matrix solve time: 2.03 hours. Time per square root: 0.17 hours. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 54.43 hours. --------- CPU info (if available) ----------

Jun 27, 2008 (4th)

By suberi / GMP-ECM
(16·10²⁴⁰-61)/9 = 1(7)₂₃₉1_<241> = 214259 · 45971639314341857839_<20> · C216
C216 = P43 · P173
P43 = 3635546933168771123588232262171985799019073_<43>
P173 = 49645358754231505271704520463941124503054131985354822418891186123680825347035422254985426027429954370789824305822464117472409850554663118163426845863590649176484170127543527_<173>

Jun 27, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve
(13·10¹⁷²+41)/9 = 1(4)₁₇₁9_<173> = 3547 · C169
C169 = P78 · P91
P78 = 695174701333859421685033528060504335793719122110800973735698497489652426318743_<78>
P91 = 5857950471415925447371678650915658511220611799017059207971764941934442613310213419314598469_<91>

Number: n N=4072298969395106976161388340694796854932180559471227641512389186479967421608244839144190708893274441625160542555524230178867900886508160260627134041286846474328853804467 ( 169 digits) SNFS difficulty: 173 digits. Divisors found: Thu Jun 26 22:17:23 2008 prp78 factor: 695174701333859421685033528060504335793719122110800973735698497489652426318743 Thu Jun 26 22:17:23 2008 prp91 factor: 5857950471415925447371678650915658511220611799017059207971764941934442613310213419314598469 Thu Jun 26 22:17:23 2008 elapsed time 01:59:04 (Msieve 1.34) Version: GGNFS-0.77.1-20050930-k8 Total time: 136.56 hours. Scaled time: 114.43 units (timescale=0.838). Factorization parameters were as follows: name: KA_1_4_171_9 n: 4072298969395106976161388340694796854932180559471227641512389186479967421608244839144190708893274441625160542555524230178867900886508160260627134041286846474328853804467 type: snfs deg: 5 c5: 1300 c0: 41 skew: 0.50 m: 10000000000000000000000000000000000 rlim: 6500000 alim: 6500000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 6500000/6500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 6800177) Primes: RFBsize:444757, AFBsize:445323, largePrimes:6021958 encountered Relations: rels:6219222, finalFF:891387 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 136.26 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,173,5,0,0,0,0,0,0,0,0,6500000,6500000,27,27,48,48,2.5,2.5,100000 total time: 136.56 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).

(19·10¹⁶⁰+71)/9 = 2(1)₁₅₉9_<161> = 7 · 379 · 593389409 · 559762404127_<12> · C137
C137 = P67 · P70
P67 = 3099176592679107542715695147437752731506212235694176436016316355489_<67>
P70 = 7730080230344753874735172128135993331930898349569035397737365097724549_<70>

Number: n N=23956883709415985088805146185238519992526664677894688593124161720632613338572606501599381490541484980237314702722541489720018966486199461 ( 137 digits) SNFS difficulty: 161 digits. Divisors found: Fri Jun 27 00:53:52 2008 prp67 factor: 3099176592679107542715695147437752731506212235694176436016316355489 Fri Jun 27 00:53:52 2008 prp70 factor: 7730080230344753874735172128135993331930898349569035397737365097724549 Fri Jun 27 00:53:52 2008 elapsed time 01:43:21 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 48.04 hours. Scaled time: 84.50 units (timescale=1.759). Factorization parameters were as follows: name: KA_2_1_159_9 n: 23956883709415985088805146185238519992526664677894688593124161720632613338572606501599381490541484980237314702722541489720018966486199461 type: snfs skew: 1.30 deg: 5 c5: 19 c0: 71 m: 100000000000000000000000000000000 rlim: 4200000 alim: 4200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 4200000/4200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2300131) Primes: RFBsize:296314, AFBsize:296822, largePrimes:7204240 encountered Relations: rels:6697074, finalFF:620996 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 47.72 hours. Total relation processing time: 0.33 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,4200000,4200000,28,28,48,48,2.3,2.3,100000 total time: 48.04 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Jun 27, 2008 (2nd)

By Serge Batalov / GMP-ECM
8·10¹⁷⁴-3 = 7(9)₁₇₃7_<175> = 73 · 383 · C171
C171 = P33 · C138
P33 = 804673696565514864785886378683159_<33>
C138 = [355589188251300183599349551020909011128214064008671840079518563313901833340223003003363699479461924771115130765652610192085570225362572237_<138>]

Jun 27, 2008

By Sinkiti Sibata / GGNFS
(22·10¹⁴³-31)/9 = 2(4)₁₄₂1_<144> = 1429 · 2131 · 8539 · 30697 · 101377089370163640052001_<24> · C106
C106 = P53 · P53
P53 = 51705751863367893367331438399782672546461708678915431_<53>
P53 = 58422867534690837233698901081105668200911196544155883_<53>

Number: 24441_143 N=3020798291895136359891852704095799554819730181878610339127208508607228112945999193267116836929465838130573 ( 106 digits) SNFS difficulty: 144 digits. Divisors found: r1=51705751863367893367331438399782672546461708678915431 (pp53) r2=58422867534690837233698901081105668200911196544155883 (pp53) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 21.09 hours. Scaled time: 14.26 units (timescale=0.676). Factorization parameters were as follows: name: 24441_143 n: 3020798291895136359891852704095799554819730181878610339127208508607228112945999193267116836929465838130573 m: 20000000000000000000000000000 c5: 1375 c0: -62 skew: 0.54 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [650000, 2650001) Primes: RFBsize:100021, AFBsize:99985, largePrimes:2812854 encountered Relations: rels:2793602, finalFF:225695 Max relations in full relation-set: 28 Initial matrix: 200072 x 225695 with sparse part having weight 25021839. Pruned matrix : 193287 x 194351 with weight 20050117. Total sieving time: 19.53 hours. Total relation processing time: 0.17 hours. Matrix solve time: 1.29 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,144,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 21.09 hours. --------- CPU info (if available) ----------

(22·10¹⁵⁴-31)/9 = 2(4)₁₅₃1_<155> = 3 · 179 · 1549 · 60258383 · 38677036373_<11> · C131
C131 = P35 · P96
P35 = 25070638326752702413568294387068201_<35>
P96 = 502942589916015173876187946749795727665325828159843838684451355988388130195810478642949230888423_<96>

Number: 24441_154 N=12609091770904717240693985056152712545732991754181146303169573493897991028211382495502130245846221909822164021358484594677522337023 ( 131 digits) SNFS difficulty: 156 digits. Divisors found: r1=25070638326752702413568294387068201 (pp35) r2=502942589916015173876187946749795727665325828159843838684451355988388130195810478642949230888423 (pp96) Version: GGNFS-0.77.1-20060513-k8 Total time: 37.39 hours. Scaled time: 73.43 units (timescale=1.964). Factorization parameters were as follows: name: 24441_154 n: 12609091770904717240693985056152712545732991754181146303169573493897991028211382495502130245846221909822164021358484594677522337023 m: 10000000000000000000000000000000 c5: 11 c0: -155 skew: 1.7 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2800001) Primes: RFBsize:216816, AFBsize:216508, largePrimes:6026421 encountered Relations: rels:6304162, finalFF:822234 Max relations in full relation-set: 28 Initial matrix: 433389 x 822234 with sparse part having weight 69650706. Pruned matrix : 285741 x 287971 with weight 37845723. Total sieving time: 35.53 hours. Total relation processing time: 0.17 hours. Matrix solve time: 1.54 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 37.39 hours. --------- CPU info (if available) ----------

Jun 26, 2008 (4th)

By suberi / GMP-ECM
2·10¹⁹²+3 = 2(0)₁₉₁3_<193> = 79 · 173 · 276519843869_<12> · 35108586452041_<14> · C164
C164 = P35 · C130
P35 = 10356144553255211560838847446569517_<35>
C130 = [1455522925575811754655315825187997365065439919940867408609722558444730235468189624497400802537194515833119641347147862725255416513_<130>]

Jun 26, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM
(7·10¹⁶⁴+17)/3 = 2(3)₁₆₃9_<165> = 96972986953_<11> · C154
C154 = P71 · P84
P71 = 20447108973637357731169193895657060177008590426856381850872885970740323_<71>
P84 = 117677680826937163671024204749611691538446639389633232890693130285209291102895498081_<84>

Number: n N=2406168363633299719066077856603911691342633210075679056961401519069627139871496470530434083135582234263916180531155483725562058518778534518235727395820163 ( 154 digits) SNFS difficulty: 165 digits. Divisors found: Thu Jun 26 13:04:03 2008 prp71 factor: 20447108973637357731169193895657060177008590426856381850872885970740323 Thu Jun 26 13:04:03 2008 prp84 factor: 117677680826937163671024204749611691538446639389633232890693130285209291102895498081 Thu Jun 26 13:04:03 2008 elapsed time 02:18:29 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 79.25 hours. Scaled time: 115.15 units (timescale=1.453). Factorization parameters were as follows: name: KA_2_3_163_9 n: 2406168363633299719066077856603911691342633210075679056961401519069627139871496470530434083135582234263916180531155483725562058518778534518235727395820163 skew: 1.89 deg: 5 c5: 7 c0: 170 m: 1000000000000000000000000000000000 type: snfs rlim: 4800000 alim: 4800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 4800000/4800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 3800081) Primes: RFBsize:335439, AFBsize:336417, largePrimes:8020664 encountered Relations: rels:7582836, finalFF:722525 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 78.95 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,165,5,0,0,0,0,0,0,0,0,4800000,4800000,28,28,48,48,2.5,2.5,100000 total time: 79.25 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

(19·10¹⁵⁹+71)/9 = 2(1)₁₅₈9_<160> = 13 · 21427248679_<11> · 352051289081_<12> · C137
C137 = P66 · P71
P66 = 250401041858585819131096746756630366154245800973610054933853193899_<66>
P71 = 85972441214000396829052981243585775513440893313292234278082838842690863_<71>

Number: n N=21527588851111722002830557879225910998694697479830930289731614802312922945498898793081333700260607997346333469572376218484361244054644837 ( 137 digits) SNFS difficulty: 161 digits. Divisors found: Thu Jun 26 14:22:48 2008 prp66 factor: 250401041858585819131096746756630366154245800973610054933853193899 Thu Jun 26 14:22:48 2008 prp71 factor: 85972441214000396829052981243585775513440893313292234278082838842690863 Thu Jun 26 14:22:48 2008 elapsed time 01:04:02 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 32.37 hours. Scaled time: 59.20 units (timescale=1.829). Factorization parameters were as follows: name: KA_2_1_158_9 n: 21527588851111722002830557879225910998694697479830930289731614802312922945498898793081333700260607997346333469572376218484361244054644837 skew: 2.06 deg: 5 c5: 19 c0: 710 m: 100000000000000000000000000000000 type: snfs rlim: 4200000 alim: 4200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 4200000/4200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2100097) Primes: RFBsize:296314, AFBsize:296187, largePrimes:7325398 encountered Relations: rels:6841474, finalFF:613001 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 32.20 hours. Total relation processing time: 0.17 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,4200000,4200000,28,28,48,48,2.5,2.5,100000 total time: 32.37 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

(7·10¹⁷⁰+17)/3 = 2(3)₁₆₉9_<171> = 239 · C168
C168 = P31 · P48 · P90
P31 = 2734097213579852352604376181511_<31>
P48 = 587102801544801723967976976231640540307396605327_<48>
P90 = 608206110816364789917478064076131806984451756354900504967234326972616286107690838688949133_<90>

Number: n N=357079511576955902498941916492360411034102781813871575217201017566042447728954311622582640108988805296696748643381230960452338753179831491 ( 138 digits) SNFS difficulty: 170 digits. Divisors found: Thu Jun 26 19:55:29 2008 prp48 factor: 587102801544801723967976976231640540307396605327 Thu Jun 26 19:55:29 2008 prp90 factor: 608206110816364789917478064076131806984451756354900504967234326972616286107690838688949133 Thu Jun 26 19:55:29 2008 elapsed time 02:50:04 (Msieve 1.36) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 109.62 hours. Scaled time: 143.49 units (timescale=1.309). Factorization parameters were as follows: name: KA_2_3_169_9 n: 357079511576955902498941916492360411034102781813871575217201017566042447728954311622582640108988805296696748643381230960452338753179831491 skew: 1.19 deg: 5 c5: 7 c0: 17 m: 10000000000000000000000000000000000 type: snfs rlim: 6200000 alim: 6200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 6200000/6200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 4200113) Primes: RFBsize:425648, AFBsize:426207, largePrimes:8293957 encountered Relations: rels:7938547, finalFF:885064 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 109.19 hours. Total relation processing time: 0.42 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,48,48,2.5,2.5,100000 total time: 109.62 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Jun 26, 2008 (2nd)

By Sinkiti Sibata / GGNFS
(22·10¹⁴⁰-31)/9 = 2(4)₁₃₉1_<141> = 17 · 1447 · 8237 · 86711 · 93229 · 881417 · C117
C117 = P35 · P82
P35 = 63355190713391485500322124879334139_<35>
P82 = 2672420577333034720731187670756586117081501976010031863655603623277223815204027931_<82>

Number: 24441_140 N=169311715343326193553763454607944049710794497657459785323473749818757455099325376029901018323588244645974454037836409 ( 117 digits) SNFS difficulty: 141 digits. Divisors found: r1=63355190713391485500322124879334139 (pp35) r2=2672420577333034720731187670756586117081501976010031863655603623277223815204027931 (pp82) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 13.15 hours. Scaled time: 8.89 units (timescale=0.676). Factorization parameters were as follows: name: 24441_140 n: 169311715343326193553763454607944049710794497657459785323473749818757455099325376029901018323588244645974454037836409 m: 10000000000000000000000000000 c5: 22 c0: -31 skew: 1.07 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [650000, 1850001) Primes: RFBsize:100021, AFBsize:99815, largePrimes:2696036 encountered Relations: rels:2660778, finalFF:252054 Max relations in full relation-set: 28 Initial matrix: 199902 x 252054 with sparse part having weight 23135386. Pruned matrix : 183699 x 184762 with weight 14732105. Total sieving time: 12.01 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.92 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,141,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 13.15 hours. --------- CPU info (if available) ----------

(22·10¹⁵³-31)/9 = 2(4)₁₅₂1_<154> = 4450992226721_<13> · 3130978137030994435259_<22> · C120
C120 = P55 · P65
P55 = 4672251179457423783044554303760906137448973750934054087_<55>
P65 = 37541975175578769737137485685757194683231428146965223756007180237_<65>

Number: 24441_153 N=175405537793259231219488124213779154690238530622835181016940877487171118032255677027504477326241747103099776251715478619 ( 120 digits) SNFS difficulty: 154 digits. Divisors found: r1=4672251179457423783044554303760906137448973750934054087 (pp55) r2=37541975175578769737137485685757194683231428146965223756007180237 (pp65) Version: GGNFS-0.77.1-20060513-k8 Total time: 37.78 hours. Scaled time: 74.38 units (timescale=1.969). Factorization parameters were as follows: name: 24441_153 n: 175405537793259231219488124213779154690238530622835181016940877487171118032255677027504477326241747103099776251715478619 m: 2000000000000000000000000000000 c5: 1375 c0: -62 skew: 0.54 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2800001) Primes: RFBsize:216816, AFBsize:216848, largePrimes:5787943 encountered Relations: rels:5857389, finalFF:638086 Max relations in full relation-set: 28 Initial matrix: 433730 x 638086 with sparse part having weight 53254032. Pruned matrix : 322563 x 324795 with weight 33104563. Total sieving time: 35.94 hours. Total relation processing time: 0.16 hours. Matrix solve time: 1.51 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,154,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 37.78 hours. --------- CPU info (if available) ----------

Jun 26, 2008

By Serge Batalov / pol51, Msieve, GMP-ECM
(22·10¹⁵⁰-31)/9 = 2(4)₁₄₉1_<151> = 78839 · 47567413 · 613925800595764424450450712559_<30> · C109
C109 = P41 · P68
P41 = 45972127484749710794015017878432605888239_<41>
P68 = 23095057306620505652516576474633038696841517536460420603268895763763_<68>

Number: 24441_150 N=1061728918767558176817203458627519930862711303791793816419560970916391073286967729158741586433757396924083357 ( 109 digits) Divisors found: r1=45972127484749710794015017878432605888239 (p41) r2=23095057306620505652516576474633038696841517536460420603268895763763 (p68) Version: Msieve v. 1.36; pol51 - gnfs,109 Total time: 9.60 hours. Scaled time: 28.33 units (timescale=2.951). Factorization parameters were as follows: name: 24441_150 n: 1061728918767558176817203458627519930862711303791793816419560970916391073286967729158741586433757396924083357 skew: 11015.45 # norm 1.37e+14 c5: 3600 c4: 1023682614 c3: -5433223933674 c2: -100960073103402731 c1: 129616438775426891628 c0: 1513442468498894463493856 # alpha -4.31 Y1: 108792954869 Y0: -783319249020200496039 # Murphy_E 1.21e-09 # M 527144102954660051708727624048815718732776484104453757771420413640585603452113943932347220759815262186792022 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1600000, 2700001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 429719 x 429967 Total sieving time: 5.50 hours. Total relation processing time: 0.00 hours. (see below) Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 5.60 hours. --------- CPU info (if available) ---------- Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init) Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618) Tue Jun 24 20:43:05 2008 Msieve v. 1.36 Tue Jun 24 20:43:05 2008 random seeds: 419df898 1074d5e8 Tue Jun 24 20:43:05 2008 factoring 1061728918767558176817203458627519930862711303791793816419560970916391073286967729158741586433757396924083357 (109 digits) Tue Jun 24 20:43:05 2008 no P-1/P+1/ECM available, skipping Tue Jun 24 20:43:05 2008 commencing number field sieve (109-digit input) Tue Jun 24 20:43:05 2008 R0: -783319249020200496039 Tue Jun 24 20:43:05 2008 R1: 108792954869 Tue Jun 24 20:43:05 2008 A0: 1513442468498894463493856 Tue Jun 24 20:43:05 2008 A1: 129616438775426891628 Tue Jun 24 20:43:05 2008 A2: -100960073103402731 Tue Jun 24 20:43:05 2008 A3: -5433223933674 Tue Jun 24 20:43:05 2008 A4: 1023682614 Tue Jun 24 20:43:05 2008 A5: 3600 Tue Jun 24 20:43:05 2008 size score = 5.545366e-11, Murphy alpha = -4.305145, combined = 2.328970e-10 Tue Jun 24 20:43:05 2008 generating factor base Tue Jun 24 20:43:07 2008 factor base complete: Tue Jun 24 20:43:07 2008 230209 rational roots (max prime = 3199997) Tue Jun 24 20:43:07 2008 229805 algebraic roots (max prime = 3199997) Tue Jun 24 20:43:07 2008 a range: [-4000000, 4000000] Tue Jun 24 20:43:07 2008 b range: [1, 300] ... Wed Jun 25 02:46:14 2008 sparse part has weight 29438035 (67.80/col) Wed Jun 25 02:46:28 2008 filtering completed in 3 passes Wed Jun 25 02:46:28 2008 matrix is 429767 x 429967 (131.2 MB) with weight 43306866 (100.72/col) Wed Jun 25 02:46:28 2008 sparse part has weight 29228734 (67.98/col) Wed Jun 25 02:46:33 2008 read 429967 cycles Wed Jun 25 02:46:34 2008 matrix is 429767 x 429967 (131.2 MB) with weight 43306866 (100.72/col) Wed Jun 25 02:46:34 2008 sparse part has weight 29228734 (67.98/col) Wed Jun 25 02:46:34 2008 saving the first 48 matrix rows for later Wed Jun 25 02:46:34 2008 matrix is 429719 x 429967 (126.5 MB) with weight 33748060 (78.49/col) Wed Jun 25 02:46:34 2008 sparse part has weight 28857124 (67.11/col) Wed Jun 25 02:46:34 2008 matrix includes 64 packed rows Wed Jun 25 02:46:34 2008 using block size 43690 for processor cache size 1024 kB Wed Jun 25 02:46:37 2008 commencing Lanczos iteration Wed Jun 25 02:46:37 2008 memory use: 116.5 MB Wed Jun 25 03:22:14 2008 lanczos halted after 6796 iterations (dim = 429715) Wed Jun 25 03:22:15 2008 recovered 41 nontrivial dependencies Wed Jun 25 03:22:15 2008 elapsed time 00:36:53 Wed Jun 25 03:22:15 2008 Wed Jun 25 03:22:15 2008 Wed Jun 25 03:22:15 2008 Msieve v. 1.36 Wed Jun 25 03:22:15 2008 random seeds: 17402b89 00ef29ea Wed Jun 25 03:22:15 2008 factoring 1061728918767558176817203458627519930862711303791793816419560970916391073286967729158741586433757396924083357 (109 digits) Wed Jun 25 03:22:16 2008 no P-1/P+1/ECM available, skipping Wed Jun 25 03:22:16 2008 commencing number field sieve (109-digit input) Wed Jun 25 03:22:16 2008 R0: -783319249020200496039 Wed Jun 25 03:22:16 2008 R1: 108792954869 Wed Jun 25 03:22:16 2008 A0: 1513442468498894463493856 Wed Jun 25 03:22:16 2008 A1: 129616438775426891628 Wed Jun 25 03:22:16 2008 A2: -100960073103402731 Wed Jun 25 03:22:16 2008 A3: -5433223933674 Wed Jun 25 03:22:16 2008 A4: 1023682614 Wed Jun 25 03:22:16 2008 A5: 3600 Wed Jun 25 03:22:16 2008 size score = 5.545366e-11, Murphy alpha = -4.305145, combined = 2.328970e-10 Wed Jun 25 03:22:16 2008 Wed Jun 25 03:22:16 2008 commencing square root phase Wed Jun 25 03:22:16 2008 reading relations for dependency 1 Wed Jun 25 03:22:16 2008 read 215006 cycles Wed Jun 25 03:22:17 2008 cycles contain 966311 unique relations Wed Jun 25 03:22:26 2008 read 966311 relations Wed Jun 25 03:22:31 2008 multiplying 1374744 relations Wed Jun 25 03:25:41 2008 multiply complete, coefficients have about 57.91 million bits Wed Jun 25 03:25:44 2008 initial square root is modulo 205847419 Wed Jun 25 03:32:07 2008 prp41 factor: 45972127484749710794015017878432605888239 Wed Jun 25 03:32:07 2008 prp68 factor: 23095057306620505652516576474633038696841517536460420603268895763763 Wed Jun 25 03:32:07 2008 elapsed time 00:09:52

(16·10¹⁸⁴-43)/9 = 1(7)₁₈₃3_<185> = 7 · 3598093 · 13132245417019_<14> · 107537092713773_<15> · 104005733668072867117900455439_<30> · C121
C121 = P43 · P78
P43 = 9530320599055730642353200206233150010763811_<43>
P78 = 504248918081124804358394041346970391553990768685952091678182150911229308328301_<78>
(22·10¹⁸⁴-31)/9 = 2(4)₁₈₃1_<185> = 3 · 7019 · 6705079 · 202293075931_<12> · 425042380540337999804473_<24> · 2233556149517112120304444591_<28> · C111
C111 = P45 · P67
P45 = 114423653990361075653055464062935164466831611_<45>
P67 = 7878686770508480786149343903599253200453322043489051808630270100369_<67>

Number: 24441_184 N=901508128927097743805796506111739621599509328568185510262339660197159877020209849161252647032352169836391964459 ( 111 digits) Divisors found: r1=114423653990361075653055464062935164466831611 (prp45) r2=7878686770508480786149343903599253200453322043489051808630270100369 (prp67) Version: Total time: 10.00 hours. Scaled time: 29.45 units (timescale=2.945). Factorization parameters were as follows: name: 24441_184 n: 901508128927097743805796506111739621599509328568185510262339660197159877020209849161252647032352169836391964459 skew: 46520.21 # norm 8.13e+15 c5: 18900 c4: -3935161950 c3: -315632321754924 c2: 6956788420149104008 c1: 165764613453978096609019 c0: -2648291551878358192286209268 # alpha -6.76 Y1: 308911050547 Y0: -2166227912833797164915 # Murphy_E 8.47e-10 # M 495691579157807496339000308739825919751575707403851431472491711303878872482938118133184764017988135434894218932 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1600000, 3100001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 429325 x 429573 Total sieving time: 8.90 hours. Total relation processing time: 0.00 hours. Matrix solve time: 00:38:19 hours. Time per square root: 00:31:06 hours. (2nd dep.) Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 10.00 hours. --------- CPU info (if available) ---------- Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init) Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618)

Jun 25, 2008 (4th)

By Robert Backstrom / Msieve, GGNFS
(22·10¹⁰⁸-31)/9 = 2(4)₁₀₇1_<109> = 17 · 181 · 104959 · 482753 · 21544099 · C87
C87 = P42 · P46
P42 = 138995389975794491309068904263146176694797_<42>
P46 = 5235754528978806667489969821427816016907360493_<46>

Wed Jun 25 05:45:44 2008 Wed Jun 25 05:45:44 2008 Wed Jun 25 05:45:44 2008 Msieve v. 1.36 Wed Jun 25 05:45:44 2008 random seeds: 2c2f2650 d595796d Wed Jun 25 05:45:44 2008 factoring 727745742572941432727590326080685974558243874913479827895808647003715217085608116454921 (87 digits) Wed Jun 25 05:45:44 2008 searching for 15-digit factors Wed Jun 25 05:45:45 2008 commencing quadratic sieve (87-digit input) Wed Jun 25 05:45:45 2008 using multiplier of 1 Wed Jun 25 05:45:45 2008 using 64kb Opteron sieve core Wed Jun 25 05:45:45 2008 sieve interval: 11 blocks of size 65536 Wed Jun 25 05:45:45 2008 processing polynomials in batches of 10 Wed Jun 25 05:45:45 2008 using a sieve bound of 1499123 (56987 primes) Wed Jun 25 05:45:45 2008 using large prime bound of 119929840 (26 bits) Wed Jun 25 05:45:45 2008 using double large prime bound of 348392707234640 (42-49 bits) Wed Jun 25 05:45:45 2008 using trial factoring cutoff of 49 bits Wed Jun 25 05:45:45 2008 polynomial 'A' values have 11 factors Wed Jun 25 06:18:28 2008 57110 relations (15937 full + 41173 combined from 597887 partial), need 57083 Wed Jun 25 06:18:29 2008 begin with 613823 relations Wed Jun 25 06:18:29 2008 reduce to 136931 relations in 10 passes Wed Jun 25 06:18:29 2008 attempting to read 136931 relations Wed Jun 25 06:18:31 2008 recovered 136931 relations Wed Jun 25 06:18:31 2008 recovered 114809 polynomials Wed Jun 25 06:18:31 2008 attempting to build 57110 cycles Wed Jun 25 06:18:31 2008 found 57110 cycles in 5 passes Wed Jun 25 06:18:31 2008 distribution of cycle lengths: Wed Jun 25 06:18:31 2008 length 1 : 15937 Wed Jun 25 06:18:31 2008 length 2 : 11207 Wed Jun 25 06:18:31 2008 length 3 : 9996 Wed Jun 25 06:18:31 2008 length 4 : 7557 Wed Jun 25 06:18:31 2008 length 5 : 5191 Wed Jun 25 06:18:31 2008 length 6 : 3117 Wed Jun 25 06:18:31 2008 length 7 : 1859 Wed Jun 25 06:18:31 2008 length 9+: 2246 Wed Jun 25 06:18:31 2008 largest cycle: 18 relations Wed Jun 25 06:18:31 2008 matrix is 56987 x 57110 (13.0 MB) with weight 3192278 (55.90/col) Wed Jun 25 06:18:31 2008 sparse part has weight 3192278 (55.90/col) Wed Jun 25 06:18:32 2008 filtering completed in 3 passes Wed Jun 25 06:18:32 2008 matrix is 52584 x 52648 (12.2 MB) with weight 2979847 (56.60/col) Wed Jun 25 06:18:32 2008 sparse part has weight 2979847 (56.60/col) Wed Jun 25 06:18:32 2008 saving the first 48 matrix rows for later Wed Jun 25 06:18:32 2008 matrix is 52536 x 52648 (7.8 MB) with weight 2338595 (44.42/col) Wed Jun 25 06:18:32 2008 sparse part has weight 1724452 (32.75/col) Wed Jun 25 06:18:32 2008 matrix includes 64 packed rows Wed Jun 25 06:18:32 2008 using block size 21059 for processor cache size 1024 kB Wed Jun 25 06:18:32 2008 commencing Lanczos iteration Wed Jun 25 06:18:32 2008 memory use: 7.7 MB Wed Jun 25 06:18:48 2008 lanczos halted after 832 iterations (dim = 52534) Wed Jun 25 06:18:48 2008 recovered 15 nontrivial dependencies Wed Jun 25 06:18:48 2008 prp42 factor: 138995389975794491309068904263146176694797 Wed Jun 25 06:18:48 2008 prp46 factor: 5235754528978806667489969821427816016907360493 Wed Jun 25 06:18:48 2008 elapsed time 00:33:04

(11·10¹⁶⁸+61)/9 = 1(2)₁₆₇9_<169> = 284576113 · C160
C160 = P45 · P116
P45 = 411666912515401882965759279521788799204135831_<45>
P116 = 10432917434026609382438829606769439297165342068877860732100883252228761348457631305397697008539566408107238406463843_<116>

Number: n N=4294886908593843300622432151296627704737193533254220188966535719820666122536511777508965491500062137057238610263195991513954729651614231663295725113169362258533 ( 160 digits) SNFS difficulty: 169 digits. Divisors found: Wed Jun 25 12:13:26 2008 prp45 factor: 411666912515401882965759279521788799204135831 Wed Jun 25 12:13:26 2008 prp116 factor: 10432917434026609382438829606769439297165342068877860732100883252228761348457631305397697008539566408107238406463843 Wed Jun 25 12:13:26 2008 elapsed time 02:24:39 (Msieve 1.34) Version: GGNFS-0.77.1-20050930-k8 Total time: 101.65 hours. Scaled time: 63.02 units (timescale=0.620). Factorization parameters were as follows: name: KA_1_2_167_9 n: 4294886908593843300622432151296627704737193533254220188966535719820666122536511777508965491500062137057238610263195991513954729651614231663295725113169362258533 type: snfs deg: 5 c5: 11000 c0: 61 skew: 0.35 m: 1000000000000000000000000000000000 rlim: 5800000 alim: 5800000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 5800000/5800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 5300093) Primes: RFBsize:399993, AFBsize:401226, largePrimes:5866471 encountered Relations: rels:6006996, finalFF:811405 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 101.36 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,169,5,0,0,0,0,0,0,0,0,5800000,5800000,27,27,48,48,2.5,2.5,100000 total time: 101.65 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).

Jun 25, 2008 (3rd)

By suberi / GMP-ECM
2·10¹⁹⁰+3 = 2(0)₁₈₉3_<191> = 76949 · 1032007 · C180
C180 = P33 · C148
P33 = 209094547936744449194474908906729_<33>
C148 = [1204485741923092584911687923487690778909963227537014315607526677383436191113446013891831878203679688385334440434720800302150846416269081049293062249_<148>]
2·10¹⁹¹+3 = 2(0)₁₉₀3_<192> = 2221 · 283112539 · 5806007837521_<13> · C167
C167 = P40 · C128
P40 = 2980061483271130133454822323000539259581_<40>
C128 = [18383131354982444551956076518958438866176346336034655261991448351404481492241607264551622466419738184569706208252244605090183537_<128>]

Jun 25, 2008 (2nd)

By Serge Batalov / Msieve, Pol51
(22·10¹⁰⁶-31)/9 = 2(4)₁₀₅1_<107> = 3² · 19 · 229 · 2557 · C99
C99 = P46 · P53
P46 = 9631591007156665672864019700139260889641266659_<46>
P53 = 25346606237218165683573730083344826363369886203189673_<53>

Number: vs N=244128144696331536415917888750242967148917292732461485370154311413947192044016455404328933748012507 ( 99 digits) SNFS difficulty: 107 digits. Divisors found: r1=9631591007156665672864019700139260889641266659 r2=25346606237218165683573730083344826363369886203189673 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.950). Factorization parameters were as follows: #res:5730 n: 244128144696331536415917888750242967148917292732461485370154311413947192044016455404328933748012507 name: 24441_106 Y0: -1000000000000000000000 Y1: 1 c5: 220 c0: -31 skew: 0.68 type: snfsFactor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [300000, 350001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 67178 x 67407 Total sieving time: 0.00 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,107,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 0.00 hours. --------- CPU info (if available) ---------- Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init) Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618) Msieve v. 1.36 Tue Jun 24 17:07:38 2008 random seeds: 6635feda 25f502d1 factoring 244128144696331536415917888750242967148917292732461485370154311413947192044016455404328933748012507 (99 digits) no P-1/P+1/ECM available, skipping commencing number field sieve (99-digit input) R0: -1000000000000000000000 R1: 1 A0: -31 A1: 0 A2: 0 A3: 0 A4: 0 A5: 220 size score = 1.115181e-07, Murphy alpha = -0.098283, combined = 1.152321e-07 commencing square root phase reading relations for dependency 1 read 33759 cycles cycles contain 150066 unique relations read 150066 relations multiplying 248786 relations multiply complete, coefficients have about 6.50 million bits initial square root is modulo 29586071 reading relations for dependency 2 read 33549 cycles cycles contain 149442 unique relations read 149442 relations multiplying 247648 relations multiply complete, coefficients have about 6.47 million bits initial square root is modulo 27412771 reading relations for dependency 3 read 33871 cycles cycles contain 150712 unique relations read 150712 relations multiplying 250366 relations multiply complete, coefficients have about 6.54 million bits initial square root is modulo 33020791 prp46 factor: 9631591007156665672864019700139260889641266659 prp53 factor: 25346606237218165683573730083344826363369886203189673 elapsed time 00:02:09 # 25 minutes. total! :-)

(22·10¹¹⁶-31)/9 = 2(4)₁₁₅1_<117> = 106816327 · 2341301839_<10> · C99
C99 = P44 · P56
P44 = 74779328381478672337559932601827975176268631_<44>
P56 = 13070841991426997088803843630742662043950302826857829687_<56>

Number: s99 N=977428785499340052582306526584012835139359060523885018765669359761522729518706248747753495558648497 ( 99 digits) SNFS difficulty: 117 digits. Divisors found: r1=74779328381478672337559932601827975176268631 r2=13070841991426997088803843630742662043950302826857829687 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.943). Factorization parameters were as follows: #res: 4974 name: 24441_116 n: 977428785499340052582306526584012835139359060523885018765669359761522729518706248747753495558648497 Y1: 1 Y0: -100000000000000000000000 c5: 220 c0: -31 skew: 0.68 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [300000, 400001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 99420 x 99635 Total sieving time: 0.00 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,117,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 0.00 hours. --------- CPU info (if available) ---------- Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init) Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618) Calibrating delay using timer specific routine.. 5600.56 BogoMIPS (lpj=11201124) ___________screen log_________ Msieve v. 1.36 Tue Jun 24 17:41:00 2008 random seeds: a8b54151 bdb568c5 factoring 977428785499340052582306526584012835139359060523885018765669359761522729518706248747753495558648497 (99 digits) no P-1/P+1/ECM available, skipping commencing number field sieve (99-digit input) R0: -100000000000000000000000 R1: 1 A0: -31 A1: 0 A2: 0 A3: 0 A4: 0 A5: 220 size score = 2.402585e-08, Murphy alpha = -0.098283, combined = 2.482600e-08 commencing linear algebra read 99882 cycles cycles contain 356766 unique relations read 356766 relations using 32 quadratic characters above 33550338 building initial matrix memory use: 48.3 MB read 99882 cycles matrix is 99716 x 99882 (30.2 MB) with weight 9788440 (98.00/col) sparse part has weight 6817281 (68.25/col) filtering completed in 2 passes matrix is 99468 x 99635 (30.2 MB) with weight 9773494 (98.09/col) sparse part has weight 6809835 (68.35/col) read 99635 cycles matrix is 99468 x 99635 (30.2 MB) with weight 9773494 (98.09/col) sparse part has weight 6809835 (68.35/col) saving the first 48 matrix rows for later matrix is 99420 x 99635 (28.8 MB) with weight 7580439 (76.08/col) sparse part has weight 6566360 (65.90/col) matrix includes 64 packed rows using block size 39854 for processor cache size 1024 kB commencing Lanczos iteration memory use: 25.9 MB linear algebra completed 96425 out of 99635 dimensions (96.8%) lanczos halted after 1573 iterations (dim = 99418) recovered 50 nontrivial dependencies elapsed time 00:03:35 =>nice -n 19 "/depts/BioInf/Batalov/MERSE/ggbin/msieve" -s s99.dat -l ggnfs.log -i s99.ini -v -nf s99.fb -t 1 -nc3 Msieve v. 1.36 Tue Jun 24 17:44:35 2008 random seeds: ac726169 0a8b790a factoring 977428785499340052582306526584012835139359060523885018765669359761522729518706248747753495558648497 (99 digits) no P-1/P+1/ECM available, skipping commencing number field sieve (99-digit input) R0: -100000000000000000000000 R1: 1 A0: -31 A1: 0 A2: 0 A3: 0 A4: 0 A5: 220 size score = 2.402585e-08, Murphy alpha = -0.098283, combined = 2.482600e-08 commencing square root phase reading relations for dependency 1 read 49629 cycles cycles contain 223442 unique relations read 223442 relations multiplying 346538 relations multiply complete, coefficients have about 9.09 million bits initial square root is modulo 168731 prp44 factor: 74779328381478672337559932601827975176268631 prp56 factor: 13070841991426997088803843630742662043950302826857829687 elapsed time 00:01:08 -> Computing time scale for this machine... sumName = s117-s99.txt -> Factorization summary written to s117-s99.txt. Start: 2008-06-24 17:10 Finish: 2008-06-24 17:47

(22·10¹³⁷-31)/9 = 2(4)₁₃₆1_<138> = 107 · 6260299 · C129
C129 = P40 · P89
P40 = 4230643473881898745530247026033528758893_<40>
P89 = 86257107301040353258760835519646764214155993239698998324248576055986190717546106427894309_<89>

Tue Jun 24 17:18:34 2008 Msieve v. 1.36 Tue Jun 24 17:18:34 2008 random seeds: 61323b09 a250f5eb Tue Jun 24 17:18:34 2008 factoring 364923068079077051345646208213109615163068484659184173606608115958004538540567489875997792910118943908918763856606819776147839937 (129 digits) Tue Jun 24 17:18:35 2008 no P-1/P+1/ECM available, skipping Tue Jun 24 17:18:35 2008 commencing number field sieve (129-digit input) Tue Jun 24 17:18:35 2008 R0: -1000000000000000000000000000 Tue Jun 24 17:18:35 2008 R1: 1 Tue Jun 24 17:18:35 2008 A0: -31 Tue Jun 24 17:18:35 2008 A1: 0 Tue Jun 24 17:18:35 2008 A2: 0 Tue Jun 24 17:18:35 2008 A3: 0 Tue Jun 24 17:18:35 2008 A4: 0 Tue Jun 24 17:18:35 2008 A5: 2200 Tue Jun 24 17:18:35 2008 size score = 7.036318e-10, Murphy alpha = -0.077176, combined = 7.219677e-10 Tue Jun 24 17:18:35 2008 generating factor base Tue Jun 24 17:18:36 2008 factor base complete: Tue Jun 24 17:18:36 2008 78498 rational roots (max prime = 999983) Tue Jun 24 17:18:36 2008 64300 algebraic roots (max prime = 799999) Tue Jun 24 17:18:36 2008 a range: [-2000000, 2000000] Tue Jun 24 17:18:36 2008 b range: [1, 200] Tue Jun 24 17:18:36 2008 number of hash buckets: 16 Tue Jun 24 17:18:36 2008 sieve block size: 65536 Tue Jun 24 17:18:36 2008 Tue Jun 24 17:18:36 2008 maximum RFB prime: 999983 Tue Jun 24 17:18:36 2008 RFB entries: 78498 Tue Jun 24 17:18:36 2008 medium RFB entries: 6542 Tue Jun 24 17:18:36 2008 resieved RFB entries: 6374 Tue Jun 24 17:18:36 2008 small RFB prime powers: 28 Tue Jun 24 17:18:36 2008 projective RFB roots: 0 Tue Jun 24 17:18:36 2008 RFB trial factoring cutoff: 52 or 78 bits Tue Jun 24 17:18:36 2008 single large prime RFB range: 20 - 25 bits Tue Jun 24 17:18:36 2008 double large prime RFB range: 40 - 48 bits Tue Jun 24 17:18:36 2008 triple large prime RFB range: 63 - 73 bits ... Tue Jun 24 19:41:53 2008 restarting with 1854989 relations Tue Jun 24 19:41:53 2008 Tue Jun 24 19:41:53 2008 commencing relation filtering Tue Jun 24 19:41:53 2008 commencing duplicate removal, pass 1 Tue Jun 24 19:42:07 2008 found 320701 hash collisions in 1854989 relations Tue Jun 24 19:42:07 2008 commencing duplicate removal, pass 2 Tue Jun 24 19:42:08 2008 found 368524 duplicates and 1486465 unique relations Tue Jun 24 19:42:08 2008 memory use: 39.7 MB Tue Jun 24 19:42:08 2008 ignoring smallest 86756 rational and 87067 algebraic ideals Tue Jun 24 19:42:08 2008 filtering rational ideals above 1114112 Tue Jun 24 19:42:08 2008 filtering algebraic ideals above 1114112 Tue Jun 24 19:42:08 2008 need 260734 more relations than ideals Tue Jun 24 19:42:08 2008 commencing singleton removal, pass 1 Tue Jun 24 19:42:20 2008 relations with 0 large ideals: 43587 Tue Jun 24 19:42:20 2008 relations with 1 large ideals: 319974 Tue Jun 24 19:42:20 2008 relations with 2 large ideals: 715856 Tue Jun 24 19:42:20 2008 relations with 3 large ideals: 331819 Tue Jun 24 19:42:20 2008 relations with 4 large ideals: 56954 Tue Jun 24 19:42:20 2008 relations with 5 large ideals: 3204 Tue Jun 24 19:42:20 2008 relations with 6 large ideals: 15071 Tue Jun 24 19:42:20 2008 relations with 7+ large ideals: 0 Tue Jun 24 19:42:20 2008 1486465 relations and about 1477266 large ideals Tue Jun 24 19:42:20 2008 commencing singleton removal, pass 2 Tue Jun 24 19:42:33 2008 found 825689 singletons Tue Jun 24 19:42:33 2008 current dataset: 660776 relations and about 478158 large ideals Tue Jun 24 19:42:33 2008 commencing singleton removal, pass 3 Tue Jun 24 19:42:38 2008 found 117444 singletons Tue Jun 24 19:42:38 2008 current dataset: 543332 relations and about 353249 large ideals Tue Jun 24 19:42:38 2008 commencing singleton removal, final pass Tue Jun 24 19:42:43 2008 memory use: 15.3 MB Tue Jun 24 19:42:43 2008 commencing in-memory singleton removal Tue Jun 24 19:42:43 2008 begin with 543332 relations and 357367 unique ideals Tue Jun 24 19:42:44 2008 reduce to 500693 relations and 314037 ideals in 9 passes Tue Jun 24 19:42:44 2008 max relations containing the same ideal: 21 Tue Jun 24 19:42:44 2008 filtering rational ideals above 445644 Tue Jun 24 19:42:44 2008 filtering algebraic ideals above 445644 Tue Jun 24 19:42:44 2008 need 74845 more relations than ideals Tue Jun 24 19:42:44 2008 commencing singleton removal, final pass Tue Jun 24 19:42:49 2008 keeping 412739 ideals with weight <= 20, new excess is 75080 Tue Jun 24 19:42:49 2008 memory use: 16.5 MB Tue Jun 24 19:42:49 2008 commencing in-memory singleton removal Tue Jun 24 19:42:49 2008 begin with 500711 relations and 412739 unique ideals Tue Jun 24 19:42:49 2008 reduce to 500015 relations and 412037 ideals in 6 passes Tue Jun 24 19:42:49 2008 max relations containing the same ideal: 20 Tue Jun 24 19:42:50 2008 relations with 0 large ideals: 1946 Tue Jun 24 19:42:50 2008 relations with 1 large ideals: 11438 Tue Jun 24 19:42:50 2008 relations with 2 large ideals: 68326 Tue Jun 24 19:42:50 2008 relations with 3 large ideals: 149117 Tue Jun 24 19:42:50 2008 relations with 4 large ideals: 153528 Tue Jun 24 19:42:50 2008 relations with 5 large ideals: 82207 Tue Jun 24 19:42:50 2008 relations with 6 large ideals: 29396 Tue Jun 24 19:42:50 2008 relations with 7+ large ideals: 4057 Tue Jun 24 19:42:50 2008 commencing 2-way merge Tue Jun 24 19:42:50 2008 reduce to 317885 relation sets and 229906 unique ideals Tue Jun 24 19:42:50 2008 commencing full merge Tue Jun 24 19:42:55 2008 memory use: 25.6 MB Tue Jun 24 19:42:55 2008 found 159297 cycles, need 148106 Tue Jun 24 19:42:55 2008 weight of 148106 cycles is about 10444887 (70.52/cycle) Tue Jun 24 19:42:55 2008 distribution of cycle lengths: Tue Jun 24 19:42:55 2008 1 relations: 9928 Tue Jun 24 19:42:55 2008 2 relations: 14156 Tue Jun 24 19:42:55 2008 3 relations: 16705 Tue Jun 24 19:42:55 2008 4 relations: 16718 Tue Jun 24 19:42:55 2008 5 relations: 16065 Tue Jun 24 19:42:55 2008 6 relations: 14160 Tue Jun 24 19:42:55 2008 7 relations: 12125 Tue Jun 24 19:42:55 2008 8 relations: 10328 Tue Jun 24 19:42:55 2008 9 relations: 8802 Tue Jun 24 19:42:55 2008 10+ relations: 29119 Tue Jun 24 19:42:55 2008 heaviest cycle: 18 relations Tue Jun 24 19:42:55 2008 commencing cycle optimization Tue Jun 24 19:42:56 2008 start with 917995 relations Tue Jun 24 19:42:58 2008 pruned 13768 relations Tue Jun 24 19:42:58 2008 memory use: 28.1 MB Tue Jun 24 19:42:58 2008 distribution of cycle lengths: Tue Jun 24 19:42:58 2008 1 relations: 9928 Tue Jun 24 19:42:58 2008 2 relations: 14233 Tue Jun 24 19:42:58 2008 3 relations: 16970 Tue Jun 24 19:42:58 2008 4 relations: 16921 Tue Jun 24 19:42:58 2008 5 relations: 16400 Tue Jun 24 19:42:58 2008 6 relations: 14355 Tue Jun 24 19:42:58 2008 7 relations: 12496 Tue Jun 24 19:42:58 2008 8 relations: 10360 Tue Jun 24 19:42:58 2008 9 relations: 8865 Tue Jun 24 19:42:58 2008 10+ relations: 27578 Tue Jun 24 19:42:58 2008 heaviest cycle: 18 relations Tue Jun 24 19:42:58 2008 elapsed time 00:01:07 Tue Jun 24 19:42:58 2008 Tue Jun 24 19:42:58 2008 Tue Jun 24 19:42:58 2008 Msieve v. 1.36 Tue Jun 24 19:42:58 2008 random seeds: 2b1162a1 26955b9f Tue Jun 24 19:42:58 2008 factoring 364923068079077051345646208213109615163068484659184173606608115958004538540567489875997792910118943908918763856606819776147839937 (129 digits) Tue Jun 24 19:42:59 2008 no P-1/P+1/ECM available, skipping Tue Jun 24 19:42:59 2008 commencing number field sieve (129-digit input) Tue Jun 24 19:42:59 2008 R0: -1000000000000000000000000000 Tue Jun 24 19:42:59 2008 R1: 1 Tue Jun 24 19:42:59 2008 A0: -31 Tue Jun 24 19:42:59 2008 A1: 0 Tue Jun 24 19:42:59 2008 A2: 0 Tue Jun 24 19:42:59 2008 A3: 0 Tue Jun 24 19:42:59 2008 A4: 0 Tue Jun 24 19:42:59 2008 A5: 2200 Tue Jun 24 19:42:59 2008 size score = 7.036318e-10, Murphy alpha = -0.077176, combined = 7.219677e-10 Tue Jun 24 19:42:59 2008 Tue Jun 24 19:42:59 2008 commencing linear algebra Tue Jun 24 19:42:59 2008 read 148106 cycles Tue Jun 24 19:43:00 2008 cycles contain 434300 unique relations Tue Jun 24 19:43:03 2008 read 434300 relations Tue Jun 24 19:43:04 2008 using 32 quadratic characters above 33549864 Tue Jun 24 19:43:08 2008 building initial matrix Tue Jun 24 19:43:13 2008 memory use: 59.8 MB Tue Jun 24 19:43:14 2008 read 148106 cycles Tue Jun 24 19:43:14 2008 matrix is 147922 x 148106 (44.4 MB) with weight 14140130 (95.47/col) Tue Jun 24 19:43:14 2008 sparse part has weight 10001765 (67.53/col) Tue Jun 24 19:43:16 2008 filtering completed in 2 passes Tue Jun 24 19:43:16 2008 matrix is 147661 x 147845 (44.3 MB) with weight 14122072 (95.52/col) Tue Jun 24 19:43:16 2008 sparse part has weight 9991367 (67.58/col) Tue Jun 24 19:43:17 2008 read 147845 cycles Tue Jun 24 19:43:17 2008 matrix is 147661 x 147845 (44.3 MB) with weight 14122072 (95.52/col) Tue Jun 24 19:43:17 2008 sparse part has weight 9991367 (67.58/col) Tue Jun 24 19:43:17 2008 saving the first 48 matrix rows for later Tue Jun 24 19:43:17 2008 matrix is 147613 x 147845 (41.9 MB) with weight 10871070 (73.53/col) Tue Jun 24 19:43:17 2008 sparse part has weight 9508778 (64.32/col) Tue Jun 24 19:43:17 2008 matrix includes 64 packed rows Tue Jun 24 19:43:17 2008 using block size 43690 for processor cache size 1024 kB Tue Jun 24 19:43:19 2008 commencing Lanczos iteration Tue Jun 24 19:43:19 2008 memory use: 38.1 MB ... linear algebra completed 145627 out of 147845 dimensions (98.5%) lanczos halted after 2337 iterations (dim = 147613) recovered 51 nontrivial dependencies elapsed time 00:04:39 =>nice -n 19 "/depts/BioInf/Batalov/MERSE/ggbin/msieve" -s vs3.dat -l ggnfs.log -i vs3.ini -v -nf vs3.fb -t 1 -nc3 Msieve v. 1.36 Tue Jun 24 19:47:37 2008 random seeds: df5fa5c3 612405f0 factoring 364923068079077051345646208213109615163068484659184173606608115958004538540567489875997792910118943908918763856606819776147839937 (129 digits) no P-1/P+1/ECM available, skipping commencing number field sieve (129-digit input) R0: -1000000000000000000000000000 R1: 1 A0: -31 A1: 0 A2: 0 A3: 0 A4: 0 A5: 2200 size score = 7.036318e-10, Murphy alpha = -0.077176, combined = 7.219677e-10 commencing square root phase reading relations for dependency 1 read 74221 cycles cycles contain 270946 unique relations read 270946 relations multiplying 452950 relations multiply complete, coefficients have about 13.57 million bits initial square root is modulo 62672501 prp40 factor: 4230643473881898745530247026033528758893 prp89 factor: 86257107301040353258760835519646764214155993239698998324248576055986190717546106427894309 elapsed time 00:01:57 -> Computing time scale for this machine... sumName = s138-vs3.txt -> Factorization summary written to s138-vs3.txt. N=364923068079077051345646208213109615163068484659184173606608115958004538540567489875997792910118943908918763856606819776147839937 ( 129 digits) SNFS difficulty: 138 digits. Divisors found: r1=4230643473881898745530247026033528758893 r2=86257107301040353258760835519646764214155993239698998324248576055986190717546106427894309 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.944). Factorization parameters were as follows: #res:2795 name: 24441_137 n: 364923068079077051345646208213109615163068484659184173606608115958004538540567489875997792910118943908918763856606819776147839937 Y1: 1 Y0: -1000000000000000000000000000 c5: 2200 c0: -31 skew: 0.43 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved rational special-q in [500000, 1325001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 147613 x 147845 Total sieving time: 0.00 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,138,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 0.00 hours. --------- CPU info (if available) ---------- Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init) Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618)

(22·10¹⁹⁴-31)/9 = 2(4)₁₉₃1_<195> = 278595861831598911140273_<24> · 11894864327951802442292729804333_<32> · 35018293618452818567197231650421_<32> · C109
C109 = P49 · P60
P49 = 5372482836426580900512209972203814089751370013919_<49>
P60 = 392081183737090877140072638124636771184362766568147368455751_<60>

Number: 24441_194 N=2106449430113337418439686498093665737072417104177983028241236957255256900579714385299982462974479850405598169 ( 109 digits) Divisors found: r1=5372482836426580900512209972203814089751370013919 r2=392081183737090877140072638124636771184362766568147368455751 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.944). Factorization parameters were as follows: name: 24441_194 n: 2106449430113337418439686498093665737072417104177983028241236957255256900579714385299982462974479850405598169 skew: 40436.56 # norm 9.50e+14 c5: 6300 c4: -6074415 c3: 15044965730376 c2: -513817562282863186 c1: -38591011017509739247904 c0: -189964629514345907912503176 # alpha -5.99 Y1: 85707496171 Y0: -803234042785158511595 # Murphy_E 1.13e-09 # M 1924700740393856439702834402358433334952951283649528228384901939772757800330389208057432806240169632309889192 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1600000, 2800001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: 7534340 relations Max relations in full relation-set: Initial matrix: Pruned matrix : 384322 x 384563 Total sieving time: 7.98 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.33 hours. Time per square root: 0.10 hours. x 4 times Prototype def-par.txt line would be: gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 0.00 hours. --------- CPU info (if available) ---------- Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init) Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618)

Jun 25, 2008

By Sinkiti Sibata / Msieve, GGNFS
(22·10¹¹⁷-31)/9 = 2(4)₁₁₆1_<118> = 29 · 461 · 349093 · 406887201344489491693_<21> · C88
C88 = P34 · P54
P34 = 4410818249195386441095460907024479_<34>
P54 = 291841410464168265137439674268152491306019075364735359_<54>

Wed Jun 25 06:06:08 2008 Msieve v. 1.36 Wed Jun 25 06:06:08 2008 random seeds: 170cc727 b201353d Wed Jun 25 06:06:08 2008 factoring 1287259419146274799029762849499144221452245222008169345367185110030166353130963969852961 (88 digits) Wed Jun 25 06:06:09 2008 no P-1/P+1/ECM available, skipping Wed Jun 25 06:06:09 2008 commencing quadratic sieve (88-digit input) Wed Jun 25 06:06:09 2008 using multiplier of 1 Wed Jun 25 06:06:09 2008 using 64kb Pentium 4 sieve core Wed Jun 25 06:06:09 2008 sieve interval: 12 blocks of size 65536 Wed Jun 25 06:06:09 2008 processing polynomials in batches of 9 Wed Jun 25 06:06:09 2008 using a sieve bound of 1508383 (57210 primes) Wed Jun 25 06:06:09 2008 using large prime bound of 120670640 (26 bits) Wed Jun 25 06:06:09 2008 using double large prime bound of 352275850752880 (42-49 bits) Wed Jun 25 06:06:09 2008 using trial factoring cutoff of 49 bits Wed Jun 25 06:06:09 2008 polynomial 'A' values have 11 factors Wed Jun 25 07:24:25 2008 57416 relations (15610 full + 41806 combined from 604346 partial), need 57306 Wed Jun 25 07:24:27 2008 begin with 619956 relations Wed Jun 25 07:24:28 2008 reduce to 138236 relations in 10 passes Wed Jun 25 07:24:28 2008 attempting to read 138236 relations Wed Jun 25 07:24:31 2008 recovered 138236 relations Wed Jun 25 07:24:31 2008 recovered 115495 polynomials Wed Jun 25 07:24:32 2008 attempting to build 57416 cycles Wed Jun 25 07:24:32 2008 found 57416 cycles in 5 passes Wed Jun 25 07:24:32 2008 distribution of cycle lengths: Wed Jun 25 07:24:32 2008 length 1 : 15610 Wed Jun 25 07:24:32 2008 length 2 : 11329 Wed Jun 25 07:24:32 2008 length 3 : 10241 Wed Jun 25 07:24:32 2008 length 4 : 7591 Wed Jun 25 07:24:32 2008 length 5 : 5209 Wed Jun 25 07:24:32 2008 length 6 : 3257 Wed Jun 25 07:24:32 2008 length 7 : 1922 Wed Jun 25 07:24:32 2008 length 9+: 2257 Wed Jun 25 07:24:32 2008 largest cycle: 19 relations Wed Jun 25 07:24:32 2008 matrix is 57210 x 57416 (13.2 MB) with weight 3220877 (56.10/col) Wed Jun 25 07:24:32 2008 sparse part has weight 3220877 (56.10/col) Wed Jun 25 07:24:33 2008 filtering completed in 3 passes Wed Jun 25 07:24:33 2008 matrix is 52838 x 52902 (12.2 MB) with weight 2996218 (56.64/col) Wed Jun 25 07:24:33 2008 sparse part has weight 2996218 (56.64/col) Wed Jun 25 07:24:33 2008 saving the first 48 matrix rows for later Wed Jun 25 07:24:33 2008 matrix is 52790 x 52902 (7.7 MB) with weight 2328421 (44.01/col) Wed Jun 25 07:24:33 2008 sparse part has weight 1694223 (32.03/col) Wed Jun 25 07:24:33 2008 matrix includes 64 packed rows Wed Jun 25 07:24:33 2008 using block size 21160 for processor cache size 512 kB Wed Jun 25 07:24:34 2008 commencing Lanczos iteration Wed Jun 25 07:24:34 2008 memory use: 7.7 MB Wed Jun 25 07:25:04 2008 lanczos halted after 837 iterations (dim = 52788) Wed Jun 25 07:25:04 2008 recovered 16 nontrivial dependencies Wed Jun 25 07:25:05 2008 prp34 factor: 4410818249195386441095460907024479 Wed Jun 25 07:25:05 2008 prp54 factor: 291841410464168265137439674268152491306019075364735359 Wed Jun 25 07:25:05 2008 elapsed time 01:18:57

(22·10¹¹⁸-31)/9 = 2(4)₁₁₇1_<119> = 3 · 14983 · 622449689 · C105
C105 = P46 · P60
P46 = 4537615633666849151611716577755232938567642751_<46>
P60 = 192543196468245533005352464734298731237544060158976608782531_<60>

Number: 24441_118 N=873687018450498585860962414011205494434864693142153285668563056838354780242500796832845469760044657582781 ( 105 digits) SNFS difficulty: 119 digits. Divisors found: r1=4537615633666849151611716577755232938567642751 (pp46) r2=192543196468245533005352464734298731237544060158976608782531 (pp60) Version: GGNFS-0.77.1-20060513-k8 Total time: 3.79 hours. Scaled time: 7.58 units (timescale=2.001). Factorization parameters were as follows: name: 24441_118 n: 873687018450498585860962414011205494434864693142153285668563056838354780242500796832845469760044657582781 m: 200000000000000000000000 c5: 1375 c0: -62 skew: 0.54 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 650001) Primes: RFBsize:49098, AFBsize:63870, largePrimes:2479128 encountered Relations: rels:3033113, finalFF:650178 Max relations in full relation-set: 28 Initial matrix: 113034 x 650178 with sparse part having weight 58691005. Pruned matrix : 72863 x 73492 with weight 7919281. Total sieving time: 3.65 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.04 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,119,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 3.79 hours. --------- CPU info (if available) ----------

(22·10¹³³-31)/9 = 2(4)₁₃₂1_<134> = 3² · 7 · 139 · 1889 · 72848313288111029_<17> · 12107233034358661681_<20> · C91
C91 = P34 · P57
P34 = 5639657496580140043807608755154479_<34>
P57 = 297081584751261613839479981912844720413453322599248782527_<57>

Wed Jun 25 07:41:23 2008 Msieve v. 1.36 Wed Jun 25 07:41:23 2008 random seeds: c50e3e98 41efd23e Wed Jun 25 07:41:23 2008 factoring 1675438386538360779538911366534090700731296549280307459985836895534653957674705576560988433 (91 digits) Wed Jun 25 07:41:25 2008 no P-1/P+1/ECM available, skipping Wed Jun 25 07:41:25 2008 commencing quadratic sieve (91-digit input) Wed Jun 25 07:41:25 2008 using multiplier of 3 Wed Jun 25 07:41:25 2008 using 64kb Pentium 4 sieve core Wed Jun 25 07:41:25 2008 sieve interval: 18 blocks of size 65536 Wed Jun 25 07:41:25 2008 processing polynomials in batches of 6 Wed Jun 25 07:41:25 2008 using a sieve bound of 1648001 (62353 primes) Wed Jun 25 07:41:25 2008 using large prime bound of 145024088 (27 bits) Wed Jun 25 07:41:25 2008 using double large prime bound of 490447101569216 (42-49 bits) Wed Jun 25 07:41:25 2008 using trial factoring cutoff of 49 bits Wed Jun 25 07:41:25 2008 polynomial 'A' values have 12 factors Wed Jun 25 10:35:54 2008 62959 relations (16185 full + 46774 combined from 698397 partial), need 62449 Wed Jun 25 10:35:57 2008 begin with 714582 relations Wed Jun 25 10:35:58 2008 reduce to 156061 relations in 11 passes Wed Jun 25 10:35:58 2008 attempting to read 156061 relations Wed Jun 25 10:36:02 2008 recovered 156061 relations Wed Jun 25 10:36:02 2008 recovered 138295 polynomials Wed Jun 25 10:36:02 2008 attempting to build 62959 cycles Wed Jun 25 10:36:02 2008 found 62959 cycles in 5 passes Wed Jun 25 10:36:02 2008 distribution of cycle lengths: Wed Jun 25 10:36:02 2008 length 1 : 16185 Wed Jun 25 10:36:02 2008 length 2 : 11807 Wed Jun 25 10:36:02 2008 length 3 : 11185 Wed Jun 25 10:36:02 2008 length 4 : 8494 Wed Jun 25 10:36:02 2008 length 5 : 6109 Wed Jun 25 10:36:02 2008 length 6 : 3932 Wed Jun 25 10:36:02 2008 length 7 : 2309 Wed Jun 25 10:36:02 2008 length 9+: 2938 Wed Jun 25 10:36:02 2008 largest cycle: 21 relations Wed Jun 25 10:36:03 2008 matrix is 62353 x 62959 (15.9 MB) with weight 3905559 (62.03/col) Wed Jun 25 10:36:03 2008 sparse part has weight 3905559 (62.03/col) Wed Jun 25 10:36:04 2008 filtering completed in 3 passes Wed Jun 25 10:36:04 2008 matrix is 58686 x 58749 (14.8 MB) with weight 3639529 (61.95/col) Wed Jun 25 10:36:04 2008 sparse part has weight 3639529 (61.95/col) Wed Jun 25 10:36:04 2008 saving the first 48 matrix rows for later Wed Jun 25 10:36:04 2008 matrix is 58638 x 58749 (9.6 MB) with weight 2901339 (49.39/col) Wed Jun 25 10:36:04 2008 sparse part has weight 2164287 (36.84/col) Wed Jun 25 10:36:04 2008 matrix includes 64 packed rows Wed Jun 25 10:36:04 2008 using block size 21845 for processor cache size 512 kB Wed Jun 25 10:36:05 2008 commencing Lanczos iteration Wed Jun 25 10:36:05 2008 memory use: 9.2 MB Wed Jun 25 10:36:43 2008 lanczos halted after 929 iterations (dim = 58636) Wed Jun 25 10:36:43 2008 recovered 18 nontrivial dependencies Wed Jun 25 10:36:44 2008 prp34 factor: 5639657496580140043807608755154479 Wed Jun 25 10:36:44 2008 prp57 factor: 297081584751261613839479981912844720413453322599248782527 Wed Jun 25 10:36:44 2008 elapsed time 02:55:21

(22·10¹²³-31)/9 = 2(4)₁₂₂1_<124> = 23 · 433 · 1117 · 68729 · 501031 · C106
C106 = P30 · P37 · P41
P30 = 112756411670894054808299206741_<30>
P37 = 1273632833538519302423429506126087703_<37>
P41 = 44434587248671470710438581903003136233111_<41>

Number: 24441_123 N=6381262987518437582596006673142664010499591113432826140506374373786489676493680985755553880923201431516453 ( 106 digits) SNFS difficulty: 124 digits. Divisors found: r1=112756411670894054808299206741 (pp30) r2=1273632833538519302423429506126087703 (pp37) r3=44434587248671470710438581903003136233111 (pp41) Version: GGNFS-0.77.1-20060513-k8 Total time: 2.80 hours. Scaled time: 5.54 units (timescale=1.980). Factorization parameters were as follows: name: 24441_123 n: 6381262987518437582596006673142664010499591113432826140506374373786489676493680985755553880923201431516453 m: 2000000000000000000000000 c5: 1375 c0: -62 skew: 0.54 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 650001) Primes: RFBsize:49098, AFBsize:63870, largePrimes:2087371 encountered Relations: rels:2089010, finalFF:148808 Max relations in full relation-set: 28 Initial matrix: 113034 x 148808 with sparse part having weight 13134472. Pruned matrix : 103383 x 104012 with weight 7096421. Total sieving time: 2.64 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.06 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,124,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.80 hours. --------- CPU info (if available) ----------

(22·10¹²⁶-31)/9 = 2(4)₁₂₅1_<127> = 251 · 947197 · 7866056173_<10> · 147800376943_<12> · C97
C97 = P48 · P50
P48 = 125539892302209994144376261639415159617845478621_<48>
P50 = 70445263698076214469967576860456601215668550017537_<50>

Number: 24441_126 N=8843690817857271302023221252006081640529860641541495178285378366218188996613539373465225708576477 ( 97 digits) SNFS difficulty: 127 digits. Divisors found: r1=125539892302209994144376261639415159617845478621 (pp48) r2=70445263698076214469967576860456601215668550017537 (pp50) Version: GGNFS-0.77.1-20060513-k8 Total time: 4.06 hours. Scaled time: 8.12 units (timescale=1.999). Factorization parameters were as follows: name: 24441_126 n: 8843690817857271302023221252006081640529860641541495178285378366218188996613539373465225708576477 m: 10000000000000000000000000 c5: 220 c0: -31 skew: 0.68 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 750001) Primes: RFBsize:49098, AFBsize:64395, largePrimes:2456079 encountered Relations: rels:2883954, finalFF:504666 Max relations in full relation-set: 28 Initial matrix: 113560 x 504666 with sparse part having weight 50686424. Pruned matrix : 82776 x 83407 with weight 10580662. Total sieving time: 3.89 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.05 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,127,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 4.06 hours. --------- CPU info (if available) ----------

(22·10¹³⁶-31)/9 = 2(4)₁₃₅1_<137> = 3 · 102913 · 15234311306269949_<17> · 1562581549839689958881_<22> · C94
C94 = P41 · P53
P41 = 70140031482922619884047309665806073419879_<41>
P53 = 47419525476324695463991738004843827169691997828599769_<53>

Wed Jun 25 10:55:40 2008 Msieve v. 1.36 Wed Jun 25 10:55:40 2008 random seeds: df7de77d 5750ec7f Wed Jun 25 10:55:40 2008 factoring 3326007009814665382594988238225932795513919969611140665785160095361635024439266642871779407951 (94 digits) Wed Jun 25 10:55:41 2008 no P-1/P+1/ECM available, skipping Wed Jun 25 10:55:42 2008 commencing quadratic sieve (94-digit input) Wed Jun 25 10:55:42 2008 using multiplier of 31 Wed Jun 25 10:55:42 2008 using 64kb Pentium 4 sieve core Wed Jun 25 10:55:42 2008 sieve interval: 18 blocks of size 65536 Wed Jun 25 10:55:42 2008 processing polynomials in batches of 6 Wed Jun 25 10:55:42 2008 using a sieve bound of 2021197 (75294 primes) Wed Jun 25 10:55:42 2008 using large prime bound of 270840398 (28 bits) Wed Jun 25 10:55:42 2008 using double large prime bound of 1509677378791104 (42-51 bits) Wed Jun 25 10:55:42 2008 using trial factoring cutoff of 51 bits Wed Jun 25 10:55:42 2008 polynomial 'A' values have 12 factors Wed Jun 25 15:40:24 2008 75402 relations (19171 full + 56231 combined from 1058328 partial), need 75390 Wed Jun 25 15:40:28 2008 begin with 1077499 relations Wed Jun 25 15:40:29 2008 reduce to 192564 relations in 10 passes Wed Jun 25 15:40:29 2008 attempting to read 192564 relations Wed Jun 25 15:40:35 2008 recovered 192564 relations Wed Jun 25 15:40:35 2008 recovered 174670 polynomials Wed Jun 25 15:40:35 2008 attempting to build 75402 cycles Wed Jun 25 15:40:35 2008 found 75402 cycles in 5 passes Wed Jun 25 15:40:35 2008 distribution of cycle lengths: Wed Jun 25 15:40:35 2008 length 1 : 19171 Wed Jun 25 15:40:35 2008 length 2 : 13461 Wed Jun 25 15:40:35 2008 length 3 : 13067 Wed Jun 25 15:40:35 2008 length 4 : 10176 Wed Jun 25 15:40:35 2008 length 5 : 7411 Wed Jun 25 15:40:35 2008 length 6 : 4990 Wed Jun 25 15:40:35 2008 length 7 : 3086 Wed Jun 25 15:40:35 2008 length 9+: 4040 Wed Jun 25 15:40:35 2008 largest cycle: 22 relations Wed Jun 25 15:40:36 2008 matrix is 75294 x 75402 (20.0 MB) with weight 4929129 (65.37/col) Wed Jun 25 15:40:36 2008 sparse part has weight 4929129 (65.37/col) Wed Jun 25 15:40:38 2008 filtering completed in 4 passes Wed Jun 25 15:40:38 2008 matrix is 71405 x 71469 (19.1 MB) with weight 4713847 (65.96/col) Wed Jun 25 15:40:38 2008 sparse part has weight 4713847 (65.96/col) Wed Jun 25 15:40:38 2008 saving the first 48 matrix rows for later Wed Jun 25 15:40:38 2008 matrix is 71357 x 71469 (12.9 MB) with weight 3798547 (53.15/col) Wed Jun 25 15:40:38 2008 sparse part has weight 2962125 (41.45/col) Wed Jun 25 15:40:38 2008 matrix includes 64 packed rows Wed Jun 25 15:40:38 2008 using block size 21845 for processor cache size 512 kB Wed Jun 25 15:40:39 2008 commencing Lanczos iteration Wed Jun 25 15:40:39 2008 memory use: 11.9 MB Wed Jun 25 15:41:38 2008 lanczos halted after 1130 iterations (dim = 71357) Wed Jun 25 15:41:38 2008 recovered 18 nontrivial dependencies Wed Jun 25 15:41:40 2008 prp41 factor: 70140031482922619884047309665806073419879 Wed Jun 25 15:41:40 2008 prp53 factor: 47419525476324695463991738004843827169691997828599769 Wed Jun 25 15:41:40 2008 elapsed time 04:46:00

(22·10¹³⁰-31)/9 = 2(4)₁₂₉1_<131> = 3 · 5791 · 117231343 · C119
C119 = P50 · P69
P50 = 85995374291128139645665669095946376417031817673599_<50>
P69 = 139568213783908770745527523180712684153776037520035004684966931153181_<69>

Number: 24441_130 N=12002220783491424354719810893455669531170424853954026778227280515249519161486614070059907571911548826570017617728568419 ( 119 digits) SNFS difficulty: 131 digits. Divisors found: r1=85995374291128139645665669095946376417031817673599 (pp50) r2=139568213783908770745527523180712684153776037520035004684966931153181 (pp69) Version: GGNFS-0.77.1-20060513-k8 Total time: 4.42 hours. Scaled time: 8.76 units (timescale=1.982). Factorization parameters were as follows: name: 24441_130 n: 12002220783491424354719810893455669531170424853954026778227280515249519161486614070059907571911548826570017617728568419 m: 100000000000000000000000000 c5: 22 c0: -31 skew: 1.07 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [400000, 950001) Primes: RFBsize:63951, AFBsize:63540, largePrimes:1452971 encountered Relations: rels:1426412, finalFF:147328 Max relations in full relation-set: 28 Initial matrix: 127557 x 147328 with sparse part having weight 11031003. Pruned matrix : 122110 x 122811 with weight 7660398. Total sieving time: 4.23 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.09 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 4.42 hours. --------- CPU info (if available) ----------

(22·10¹³⁸-31)/9 = 2(4)₁₃₇1_<139> = 137977193 · 18449653031753849_<17> · C114
C114 = P46 · P69
P46 = 3825837938755335201721050723402917950510257463_<46>
P69 = 250990967874013770505290290531406928058853824186456271102008457235151_<69>

Number: 24441_138 N=960250767177323400882844976192636287552667446686675098746530710972955996716839535226165913888973758453802143681913 ( 114 digits) SNFS difficulty: 139 digits. Divisors found: r1=3825837938755335201721050723402917950510257463 (pp46) r2=250990967874013770505290290531406928058853824186456271102008457235151 (pp69) Version: GGNFS-0.77.1-20060513-k8 Total time: 13.38 hours. Scaled time: 26.78 units (timescale=2.002). Factorization parameters were as follows: name: 24441_138 n: 960250767177323400882844976192636287552667446686675098746530710972955996716839535226165913888973758453802143681913 m: 2000000000000000000000000000 c5: 1375 c0: -62 skew: 0.54 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 2125001) Primes: RFBsize:78498, AFBsize:63870, largePrimes:1660537 encountered Relations: rels:1687384, finalFF:168711 Max relations in full relation-set: 28 Initial matrix: 142434 x 168711 with sparse part having weight 18605604. Pruned matrix : 135990 x 136766 with weight 13766077. Total sieving time: 13.07 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.17 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,139,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 13.38 hours. --------- CPU info (if available) ----------

Jun 24, 2008 (5th)

By matsui / GGNFS
6·10¹⁷⁶+7 = 6(0)₁₇₅7_<177> = 149 · C175
C175 = P45 · P131
P45 = 230266112072425854835615673997286041414191311_<45>
P131 = 17487790979496472353574388242068301111731661211926813193993672549877478287762758543465832179237070194085811306528123110099573405413_<131>

N=4026845637583892617449664429530201342281879194630872483221476510067114093959731543624161073825503355704697986577181208053691275167785234899328859060402684563758389261744966443 ( 175 digits) SNFS difficulty: 176 digits. Divisors found: r1=230266112072425854835615673997286041414191311 (pp45) r2=17487790979496472353574388242068301111731661211926813193993672549877478287762758543465832179237070194085811306528123110099573405413 (pp131) Version: GGNFS-0.77.1-20060513-prescott Total time: 252.84 hours. Scaled time: 347.40 units (timescale=1.374). Factorization parameters were as follows: n: 4026845637583892617449664429530201342281879194630872483221476510067114093959731543624161073825503355704697986577181208053691275167785234899328859060402684563758389261744966443 m: 100000000000000000000000000000000000 c5: 60 c0: 7 skew: 0.65 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 14200001) Primes: RFBsize:501962, AFBsize:502341, largePrimes:6688647 encountered Relations: rels:7170745, finalFF:1136864 Max relations in full relation-set: 28 Initial matrix: 1004370 x 1136864 with sparse part having weight 89462948. Pruned matrix : 897008 x 902093 with weight 70418949. Total sieving time: 237.69 hours. Total relation processing time: 0.25 hours. Matrix solve time: 14.56 hours. Time per square root: 0.34 hours. Prototype def-par.txt line would be: snfs,176,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 252.84 hours.

Jun 24, 2008 (4th)

By suberi / GMP-ECM, Msieve
(64·10²⁰⁵+53)/9 = 7(1)₂₀₄7_<206> = 7 · 11 · 239 · 39217 · 303337 · 818638853244139_<15> · 32171339726493257_<17> · C161
C161 = P43 · P118
P43 = 6792360722740653194989864506125393681527657_<43>
P118 = 1815795106708801594507912771850228677646491129523164275329155811015085729329124219820438570716764628453647583068010181_<118>
2·10¹⁸⁷+3 = 2(0)₁₈₆3_<188> = 2650288267127376709_<19> · 21691476478039441219_<20> · C150
C150 = P31 · P33 · P87
P31 = 4899431565604784118723228083483_<31>
P33 = 389595763391679786994327160166767_<33>
P87 = 182258522814260407226204545556975019230375927589496525253684233311399812906067616297913_<87>
2·10¹⁸⁴+3 = 2(0)₁₈₃3_<185> = 241 · 4253 · 41715550696982867_<17> · 45046753479013599736939609_<26> · C137
C137 = P35 · P44 · P59
P35 = 16450357456538149478222257267964459_<35>
P44 = 56831071349735800699564104034197250430260949_<44>
P59 = 11106952378085416134328784349105056515147150726616078638907_<59>

Tue Jun 24 18:53:10 2008 Tue Jun 24 18:53:10 2008 Tue Jun 24 18:53:10 2008 Msieve v. 1.36 Tue Jun 24 18:53:10 2008 random seeds: 93ee3b85 0329cb0a Tue Jun 24 18:53:10 2008 factoring 182713336872251556937124341395782902015287266671894633925232526091403812179727966275170606313 (93 digits) Tue Jun 24 18:53:11 2008 no P-1/P+1/ECM available, skipping Tue Jun 24 18:53:11 2008 commencing quadratic sieve (93-digit input) Tue Jun 24 18:53:11 2008 using multiplier of 10 Tue Jun 24 18:53:11 2008 using 64kb Opteron sieve core Tue Jun 24 18:53:11 2008 sieve interval: 18 blocks of size 65536 Tue Jun 24 18:53:11 2008 processing polynomials in batches of 6 Tue Jun 24 18:53:11 2008 using a sieve bound of 1884611 (70588 primes) Tue Jun 24 18:53:11 2008 using large prime bound of 220499487 (27 bits) Tue Jun 24 18:53:11 2008 using double large prime bound of 1042638218764623 (42-50 bits) Tue Jun 24 18:53:11 2008 using trial factoring cutoff of 50 bits Tue Jun 24 18:53:11 2008 polynomial 'A' values have 12 factors Tue Jun 24 21:54:01 2008 70947 relations (18129 full + 52818 combined from 924198 partial), need 70684 Tue Jun 24 21:54:01 2008 begin with 942327 relations Tue Jun 24 21:54:02 2008 reduce to 180003 relations in 11 passes Tue Jun 24 21:54:02 2008 attempting to read 180003 relations Tue Jun 24 21:54:04 2008 recovered 180003 relations Tue Jun 24 21:54:04 2008 recovered 162383 polynomials Tue Jun 24 21:54:04 2008 attempting to build 70947 cycles Tue Jun 24 21:54:04 2008 found 70947 cycles in 6 passes Tue Jun 24 21:54:05 2008 distribution of cycle lengths: Tue Jun 24 21:54:05 2008 length 1 : 18129 Tue Jun 24 21:54:05 2008 length 2 : 12833 Tue Jun 24 21:54:05 2008 length 3 : 12206 Tue Jun 24 21:54:05 2008 length 4 : 9619 Tue Jun 24 21:54:05 2008 length 5 : 6914 Tue Jun 24 21:54:05 2008 length 6 : 4575 Tue Jun 24 21:54:05 2008 length 7 : 2879 Tue Jun 24 21:54:05 2008 length 9+: 3792 Tue Jun 24 21:54:05 2008 largest cycle: 20 relations Tue Jun 24 21:54:05 2008 matrix is 70588 x 70947 (18.9 MB) with weight 4387637 (61.84/col) Tue Jun 24 21:54:05 2008 sparse part has weight 4387637 (61.84/col) Tue Jun 24 21:54:06 2008 filtering completed in 4 passes Tue Jun 24 21:54:06 2008 matrix is 66689 x 66753 (17.8 MB) with weight 4139213 (62.01/col) Tue Jun 24 21:54:06 2008 sparse part has weight 4139213 (62.01/col) Tue Jun 24 21:54:07 2008 saving the first 48 matrix rows for later Tue Jun 24 21:54:07 2008 matrix is 66641 x 66753 (10.8 MB) with weight 3149445 (47.18/col) Tue Jun 24 21:54:07 2008 sparse part has weight 2163279 (32.41/col) Tue Jun 24 21:54:07 2008 matrix includes 64 packed rows Tue Jun 24 21:54:07 2008 using block size 21845 for processor cache size 512 kB Tue Jun 24 21:54:07 2008 commencing Lanczos iteration Tue Jun 24 21:54:07 2008 memory use: 10.0 MB Tue Jun 24 21:54:45 2008 lanczos halted after 1055 iterations (dim = 66638) Tue Jun 24 21:54:45 2008 recovered 16 nontrivial dependencies Tue Jun 24 21:54:46 2008 prp35 factor: 16450357456538149478222257267964459 Tue Jun 24 21:54:46 2008 prp59 factor: 11106952378085416134328784349105056515147150726616078638907 Tue Jun 24 21:54:46 2008 elapsed time 03:01:36

Jun 24, 2008 (3rd)

By Sinkiti Sibata / GGNFS
(7·10¹⁷⁹+17)/3 = 2(3)₁₇₈9_<180> = 22109 · 90469 · 1256323 · 35493226964893_<14> · 193576298168347_<15> · 952212640912740996809_<21> · C116
C116 = P49 · P68
P49 = 1083418340932707176216084357421154856286028373779_<49>
P68 = 13100226135502534549666209653747467840650514145509640203419928010693_<68>

Number: 23339_179 N=14193025265569445974228728704378542441338653383710387152481587867346291078132553015148374680826377638347769312818847 ( 116 digits) Divisors found: r1=1083418340932707176216084357421154856286028373779 (pp49) r2=13100226135502534549666209653747467840650514145509640203419928010693 (pp68) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 68.57 hours. Scaled time: 46.28 units (timescale=0.675). Factorization parameters were as follows: name: 23339_179 n: 14193025265569445974228728704378542441338653383710387152481587867346291078132553015148374680826377638347769312818847 skew: 53352.58 # norm 4.55e+15 c5: 22800 c4: -1212675256 c3: -208058952557963 c2: 6664111048874094952 c1: 245754196746015982431972 c0: 1432227789190934188360900848 # alpha -5.51 Y1: 2378383133929 Y0: -14415469381987635808679 # Murphy_E 5.17e-10 # M 814671274571655966892064727200267112760459559660949635982948791244348566256512818571951807542954013572351015531657 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2250000, 3570001) Primes: RFBsize:315948, AFBsize:315628, largePrimes:7558239 encountered Relations: rels:7641850, finalFF:796002 Max relations in full relation-set: 28 Initial matrix: 631652 x 796002 with sparse part having weight 57923912. Pruned matrix : 485483 x 488705 with weight 31317677. Polynomial selection time: 3.01 hours. Total sieving time: 54.29 hours. Total relation processing time: 0.54 hours. Matrix solve time: 10.31 hours. Time per square root: 0.42 hours. Prototype def-par.txt line would be: gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 68.57 hours. --------- CPU info (if available) ----------

7·10¹⁸²+3 = 7(0)₁₈₁3_<183> = 19 · 37 · C180
C180 = P76 · P105
P76 = 5796213552807101290302139288236547086048674920761890437988566399723613188147_<76>
P105 = 171790180884158531835765998721853676674416631560705620499042258287282118632167531441001689658431400392783_<105>

Number: 70003_182 N=995732574679943100995732574679943100995732574679943100995732574679943100995732574679943100995732574679943100995732574679943100995732574679943100995732574679943100995732574679943101 ( 180 digits) SNFS difficulty: 182 digits. Divisors found: r1=5796213552807101290302139288236547086048674920761890437988566399723613188147 (pp76) r2=171790180884158531835765998721853676674416631560705620499042258287282118632167531441001689658431400392783 (pp105) Version: GGNFS-0.77.1-20060513-k8 Total time: 549.90 hours. Scaled time: 1098.71 units (timescale=1.998). Factorization parameters were as follows: name: 70003_182 n: 995732574679943100995732574679943100995732574679943100995732574679943100995732574679943100995732574679943100995732574679943100995732574679943100995732574679943100995732574679943101 m: 1000000000000000000000000000000000000 c5: 700 c0: 3 skew: 0.34 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 9800001) Primes: RFBsize:501962, AFBsize:501711, largePrimes:6541906 encountered Relations: rels:7006429, finalFF:1144045 Max relations in full relation-set: 28 Initial matrix: 1003740 x 1144045 with sparse part having weight 73023928. Pruned matrix : 886255 x 891337 with weight 55995755. Total sieving time: 538.86 hours. Total relation processing time: 0.43 hours. Matrix solve time: 10.28 hours. Time per square root: 0.33 hours. Prototype def-par.txt line would be: snfs,182,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 549.90 hours. --------- CPU info (if available) ----------

Jun 24, 2008 (2nd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve
(19·10¹⁶²+71)/9 = 2(1)₁₆₁9_<163> = 73 · C161
C161 = P32 · P59 · P70
P32 = 43940526090123600470562056510603_<32>
P59 = 73998714678262655889943985399989215015429575850397477288273_<59>
P70 = 8894034356803247423111327983734140548254674728357494938725391032087637_<70>

Number: n N=658147110707748824755832441227848690652084205220911259328710039673874479237845455658772436193296458069020869661212196684848380901 ( 129 digits) SNFS difficulty: 163 digits. Divisors found: Tue Jun 24 03:33:39 2008 prp59 factor: 73998714678262655889943985399989215015429575850397477288273 Tue Jun 24 03:33:39 2008 prp70 factor: 8894034356803247423111327983734140548254674728357494938725391032087637 Tue Jun 24 03:33:39 2008 elapsed time 01:05:25 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 43.80 hours. Scaled time: 80.10 units (timescale=1.829). Factorization parameters were as follows: name: KA_2_1_161_9 n: 658147110707748824755832441227848690652084205220911259328710039673874479237845455658772436193296458069020869661212196684848380901 skew: 0.52 deg: 5 c5: 1900 c0: 71 m: 100000000000000000000000000000000 type: snfs rlim: 4500000 alim: 4500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 3000299) Primes: RFBsize:315948, AFBsize:316312, largePrimes:7290029 encountered Relations: rels:6865799, finalFF:650394 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 43.52 hours. Total relation processing time: 0.28 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,163,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,48,48,2.5,2.5,100000 total time: 43.80 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

Jun 24, 2008

The factor table of 244...441 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Jun 23, 2008 (3rd)

By Sinkiti Sibata / GGNFS
(7·10¹⁵⁹+17)/3 = 2(3)₁₅₈9_<160> = 103 · 36353 · 678599 · 9047282575964125799445511_<25> · C123
C123 = P45 · P78
P45 = 913307551148821962130752701805568948809731623_<45>
P78 = 111135008099498608276431343957760234609000836576351644580968422062061256514043_<78>

Number: 23339_159 N=101500442094257568219640318443861829710581176391361977483716297025113928351635619590108271896052359109780634699299360681789 ( 123 digits) SNFS difficulty: 160 digits. Divisors found: r1=913307551148821962130752701805568948809731623 (pp45) r2=111135008099498608276431343957760234609000836576351644580968422062061256514043 (pp78) Version: GGNFS-0.77.1-20060513-k8 Total time: 75.68 hours. Scaled time: 149.77 units (timescale=1.979). Factorization parameters were as follows: name: 23339_159 n: 101500442094257568219640318443861829710581176391361977483716297025113928351635619590108271896052359109780634699299360681789 m: 100000000000000000000000000000000 c5: 7 c0: 170 skew: 1.89 type: snfs Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2000000, 4500001) Primes: RFBsize:283146, AFBsize:283272, largePrimes:5891949 encountered Relations: rels:5985703, finalFF:688056 Max relations in full relation-set: 28 Initial matrix: 566483 x 688056 with sparse part having weight 56480525. Pruned matrix : 485332 x 488228 with weight 41065012. Total sieving time: 71.84 hours. Total relation processing time: 0.20 hours. Matrix solve time: 3.41 hours. Time per square root: 0.23 hours. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 75.68 hours. --------- CPU info (if available) ----------

Jun 23, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve
(4·10¹⁶⁹+23)/9 = (4)₁₆₈7_<169> = 7 · 17 · 57349 · C162
C162 = P48 · P115
P48 = 503852761342782171346683824703620971518120723133_<48>
P115 = 1292531178579433361975754521183369234349970232633887731714815503149502104258374903219488361379931169871046875018089_<115>

Number: n N=651245403448888201173742846862948449416442601615326305125501583104310676359217130736814653555598830812614734176523550767729598480019278166432893988531145135752837 ( 162 digits) SNFS difficulty: 170 digits. Divisors found: Mon Jun 23 18:23:51 2008 prp48 factor: 503852761342782171346683824703620971518120723133 Mon Jun 23 18:23:51 2008 prp115 factor: 1292531178579433361975754521183369234349970232633887731714815503149502104258374903219488361379931169871046875018089 Mon Jun 23 18:23:51 2008 elapsed time 01:31:12 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 68.29 hours. Scaled time: 124.91 units (timescale=1.829). Factorization parameters were as follows: name: KA_4_168_7 n: 651245403448888201173742846862948449416442601615326305125501583104310676359217130736814653555598830812614734176523550767729598480019278166432893988531145135752837 skew: 2.25 deg: 5 c5: 2 c0: 115 m: 10000000000000000000000000000000000 type: snfs rlim: 5750000 alim: 5750000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 5750000/5750000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 4116257) Primes: RFBsize:396826, AFBsize:396180, largePrimes:8129248 encountered Relations: rels:7699340, finalFF:795201 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 68.06 hours. Total relation processing time: 0.24 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,5750000,5750000,28,28,48,48,2.5,2.5,100000 total time: 68.29 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

(7·10¹⁶³+17)/3 = 2(3)₁₆₂9_<164> = 239 · C161
C161 = P52 · P110
P52 = 1538551780009680675999212973840188207025515314791083_<52>
P110 = 63455134257676194489120480630580987480409038207260499417697608713351090232023365272936682525567211829286754047_<110>

Number: n N=97629009762900976290097629009762900976290097629009762900976290097629009762900976290097629009762900976290097629009762900976290097629009762900976290097629009762901 ( 161 digits) SNFS difficulty: 163 digits. Divisors found: Mon Jun 23 20:47:10 2008 prp52 factor: 1538551780009680675999212973840188207025515314791083 Mon Jun 23 20:47:10 2008 prp110 factor: 63455134257676194489120480630580987480409038207260499417697608713351090232023365272936682525567211829286754047 Mon Jun 23 20:47:10 2008 elapsed time 02:10:56 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 61.47 hours. Scaled time: 108.18 units (timescale=1.760). Factorization parameters were as follows: name: KA_2_3_162_9 n: 97629009762900976290097629009762900976290097629009762900976290097629009762900976290097629009762900976290097629009762900976290097629009762900976290097629009762901 type: snfs skew: 0.30 deg: 5 c5: 7000 c0: 17 m: 100000000000000000000000000000000 rlim: 4600000 alim: 4600000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 4600000/4600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 3000001) Primes: RFBsize:322441, AFBsize:322486, largePrimes:7447109 encountered Relations: rels:6929923, finalFF:646339 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 61.20 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,163,5,0,0,0,0,0,0,0,0,4600000,4600000,28,28,48,48,2.3,2.3,100000 total time: 61.47 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Jun 23, 2008

By suberi / GMP-ECM
(64·10¹⁸⁴+53)/9 = 7(1)₁₈₃7_<185> = 19 · 239 · 379 · 3653118301152191_<16> · C164
C164 = P40 · P124
P40 = 6408857844198902795079491084505047743261_<40>
P124 = 1764827968268619245848314702240512687857444858790408730674667676478953242420913659802142902523798197322058590130173904669953_<124>

Jun 22, 2008 (5th)

By Wataru Sakai / GGNFS
(7·10¹⁷³-61)/9 = (7)₁₇₂1_<173> = 5647 · 4150793 · 4174507 · C156
C156 = P76 · P81
P76 = 4697092831087200551529024233831603689378002454075748867575435175236949613467_<76>
P81 = 169228042188601079552332909893272905914334638988209627060854725312063782925308629_<81>

Number: 77771_173 N=794879823783000459297146595802866396258287289283368570900870245484647858993845972343965939158115233217484416191400328069663743260194300173826749173229706743 ( 156 digits) SNFS difficulty: 173 digits. Divisors found: r1=4697092831087200551529024233831603689378002454075748867575435175236949613467 (pp76) r2=169228042188601079552332909893272905914334638988209627060854725312063782925308629 (pp81) Version: GGNFS-0.77.1-20060722-nocona Total time: 278.56 hours. Scaled time: 497.22 units (timescale=1.785). Factorization parameters were as follows: n: 794879823783000459297146595802866396258287289283368570900870245484647858993845972343965939158115233217484416191400328069663743260194300173826749173229706743 m: 10000000000000000000000000000000000 c5: 7000 c0: -61 skew: 0.39 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 13600001) Primes: RFBsize:501962, AFBsize:502027, largePrimes:6884572 encountered Relations: rels:7500187, finalFF:1264391 Max relations in full relation-set: 32 Initial matrix: 1004056 x 1264391 with sparse part having weight 98282831. Pruned matrix : 783753 x 788837 with weight 77243787. Total sieving time: 270.20 hours. Total relation processing time: 0.13 hours. Matrix solve time: 7.94 hours. Time per square root: 0.29 hours. Prototype def-par.txt line would be: snfs,173,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 278.56 hours. --------- CPU info (if available) ----------

Jun 22, 2008 (4th)

By matsui / GGNFS
10¹⁷¹+3 = 1(0)₁₇₀3_<172> = 11766503516695099357653883_<26> · C146
C146 = P49 · P98
P49 = 3324774752229019712326210320791873479173334110257_<49>
P98 = 25561735879742056874997330779164365467172026436929398740217995340496906772469307561544143733079913_<98>

N=84987014076113040368276240003085477274619465136310452297603910182168194570059311533447910927491502082842012464686661684313334515329656218133967641 ( 146 digits) SNFS difficulty: 171 digits. Divisors found: r1=3324774752229019712326210320791873479173334110257 (pp49) r2=25561735879742056874997330779164365467172026436929398740217995340496906772469307561544143733079913 (pp98) Version: GGNFS-0.77.1-20060513-prescott Total time: 141.52 hours. Scaled time: 192.33 units (timescale=1.359). Factorization parameters were as follows: n: 84987014076113040368276240003085477274619465136310452297603910182168194570059311533447910927491502082842012464686661684313334515329656218133967641 m: 10000000000000000000000000000000000 c5: 10 c0: 3 skew: 0.79 type: snfs Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3000000, 8500001) Primes: RFBsize:412849, AFBsize:412801, largePrimes:6211987 encountered Relations: rels:6507104, finalFF:950866 Max relations in full relation-set: 28 Initial matrix: 825716 x 950866 with sparse part having weight 68018418. Pruned matrix : 726189 x 730381 with weight 51238543. Total sieving time: 129.70 hours. Total relation processing time: 0.16 hours. Matrix solve time: 11.39 hours. Time per square root: 0.27 hours. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000 total time: 141.52 hours.

Jun 22, 2008 (3rd)

By Serge Batalov / pol51, Msieve 1.36
(7·10¹⁶⁷+17)/3 = 2(3)₁₆₆9_<168> = 19 · 172264217003920050943279_<24> · 157079089306604304108830836083629_<33> · C111
C111 = P38 · P74
P38 = 44403506544729569591382802255945107907_<38>
P74 = 10220978328444765863502623751657798456955829517191510572947586215944141713_<74>

Sat Jun 21 09:55:24 2008 Msieve v. 1.36 Sat Jun 21 09:55:24 2008 random seeds: 4fcf0dfc 252e6970 Sat Jun 21 09:55:24 2008 factoring 453847278100636257345202489577127970120979761678674473533642473400515264972284842096436647814028980618284824691 (111 digits) Sat Jun 21 09:55:25 2008 no P-1/P+1/ECM available, skipping Sat Jun 21 09:55:25 2008 commencing number field sieve (111-digit input) Sat Jun 21 09:55:25 2008 R0: -2648889719843403962270 Sat Jun 21 09:55:25 2008 R1: 284568061549 Sat Jun 21 09:55:25 2008 A0: 1173007414994245235539459029 Sat Jun 21 09:55:25 2008 A1: 99595796075874533170621 Sat Jun 21 09:55:25 2008 A2: -978964025831487987 Sat Jun 21 09:55:25 2008 A3: -74405497406433 Sat Jun 21 09:55:25 2008 A4: 828092306 Sat Jun 21 09:55:25 2008 A5: 3480 Sat Jun 21 09:55:25 2008 size score = 1.835450e-11, Murphy alpha = -5.910601, combined = 1.316405e-10 Sat Jun 21 09:55:25 2008 Sat Jun 21 09:55:25 2008 commencing linear algebra Sat Jun 21 09:55:25 2008 read 468867 cycles Sat Jun 21 09:55:26 2008 cycles contain 1696762 unique relations Sat Jun 21 09:55:41 2008 read 1696762 relations Sat Jun 21 09:55:43 2008 using 32 quadratic characters above 134217410 Sat Jun 21 09:56:02 2008 building initial matrix Sat Jun 21 09:56:19 2008 memory use: 214.2 MB Sat Jun 21 09:56:22 2008 read 468867 cycles Sat Jun 21 09:56:22 2008 matrix is 468576 x 468867 (142.8 MB) with weight 47963556 (102.30/col) Sat Jun 21 09:56:22 2008 sparse part has weight 31802368 (67.83/col) Sat Jun 21 09:56:34 2008 filtering completed in 3 passes Sat Jun 21 09:56:34 2008 matrix is 465332 x 465532 (142.1 MB) with weight 47694935 (102.45/col) Sat Jun 21 09:56:34 2008 sparse part has weight 31664613 (68.02/col) Sat Jun 21 09:56:40 2008 read 465532 cycles Sat Jun 21 09:56:41 2008 matrix is 465332 x 465532 (142.1 MB) with weight 47694935 (102.45/col) Sat Jun 21 09:56:41 2008 sparse part has weight 31664613 (68.02/col) Sat Jun 21 09:56:41 2008 saving the first 48 matrix rows for later Sat Jun 21 09:56:41 2008 matrix is 465284 x 465532 (138.4 MB) with weight 37310151 (80.15/col) Sat Jun 21 09:56:41 2008 sparse part has weight 31614095 (67.91/col) Sat Jun 21 09:56:41 2008 matrix includes 64 packed rows Sat Jun 21 09:56:41 2008 using block size 43690 for processor cache size 1024 kB Sat Jun 21 09:56:44 2008 commencing Lanczos iteration Sat Jun 21 09:56:44 2008 memory use: 126.8 MB Sat Jun 21 10:39:05 2008 lanczos halted after 7359 iterations (dim = 465284) Sat Jun 21 10:39:06 2008 recovered 44 nontrivial dependencies Sat Jun 21 10:39:06 2008 elapsed time 00:43:42 Sat Jun 21 10:39:06 2008 Sat Jun 21 10:39:06 2008 Sat Jun 21 10:39:06 2008 Msieve v. 1.36 Sat Jun 21 10:39:06 2008 random seeds: b323b31d 6a581883 Sat Jun 21 10:39:06 2008 factoring 453847278100636257345202489577127970120979761678674473533642473400515264972284842096436647814028980618284824691 (111 digits) Sat Jun 21 10:39:07 2008 no P-1/P+1/ECM available, skipping Sat Jun 21 10:39:07 2008 commencing number field sieve (111-digit input) Sat Jun 21 10:39:07 2008 R0: -2648889719843403962270 Sat Jun 21 10:39:07 2008 R1: 284568061549 Sat Jun 21 10:39:07 2008 A0: 1173007414994245235539459029 Sat Jun 21 10:39:07 2008 A1: 99595796075874533170621 Sat Jun 21 10:39:07 2008 A2: -978964025831487987 Sat Jun 21 10:39:07 2008 A3: -74405497406433 Sat Jun 21 10:39:07 2008 A4: 828092306 Sat Jun 21 10:39:07 2008 A5: 3480 Sat Jun 21 10:39:07 2008 size score = 1.835450e-11, Murphy alpha = -5.910601, combined = 1.316405e-10 Sat Jun 21 10:39:07 2008 Sat Jun 21 10:39:07 2008 commencing square root phase Sat Jun 21 10:39:07 2008 reading relations for dependency 1 Sat Jun 21 10:39:07 2008 read 233173 cycles Sat Jun 21 10:39:08 2008 cycles contain 1034223 unique relations Sat Jun 21 10:39:17 2008 read 1034223 relations Sat Jun 21 10:39:23 2008 multiplying 1470374 relations Sat Jun 21 10:42:36 2008 multiply complete, coefficients have about 60.48 million bits Sat Jun 21 10:42:38 2008 initial square root is modulo 481325497 prp38 factor: 44403506544729569591382802255945107907 prp74 factor: 10220978328444765863502623751657798456955829517191510572947586215944141713 Sat Jun 21 10:49:18 2008 elapsed time 00:10:12

Jun 22, 2008 (2nd)

By Sinkiti Sibata / GGNFS
(7·10¹⁵⁴+17)/3 = 2(3)₁₅₃9_<155> = 30269 · 129967723442083_<15> · 1419277675450441_<16> · C121
C121 = P41 · P80
P41 = 53214050296629292416897411287835743443231_<41>
P80 = 78532516246414065130742159934751039833478176834632670589017775608994139603053867_<80>

Number: 23339_154 N=4179033269457535108462874239499699892492658734372965840608209926925321293346293445858237021220932202079153367369349524277 ( 121 digits) SNFS difficulty: 155 digits. Divisors found: r1=53214050296629292416897411287835743443231 (pp41) r2=78532516246414065130742159934751039833478176834632670589017775608994139603053867 (pp80) Version: GGNFS-0.77.1-20060513-k8 Total time: 49.94 hours. Scaled time: 99.43 units (timescale=1.991). Factorization parameters were as follows: name: 23339_154 n: 4179033269457535108462874239499699892492658734372965840608209926925321293346293445858237021220932202079153367369349524277 m: 10000000000000000000000000000000 c5: 7 c0: 170 skew: 1.89 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 3200001) Primes: RFBsize:216816, AFBsize:216831, largePrimes:5819124 encountered Relations: rels:5836380, finalFF:567100 Max relations in full relation-set: 28 Initial matrix: 433712 x 567100 with sparse part having weight 52312857. Pruned matrix : 372931 x 375163 with weight 34242270. Total sieving time: 47.37 hours. Total relation processing time: 0.18 hours. Matrix solve time: 2.21 hours. Time per square root: 0.18 hours. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 49.94 hours. --------- CPU info (if available) ----------

Jun 22, 2008

By Robert Backstrom / GMP-ECM, GGNFS, Msieve
(4·10¹⁸⁶-31)/9 = (4)₁₈₅1_<186> = 3 · 499 · C183
C183 = P42 · P141
P42 = 598138986459096730395341182841727820103903_<42>
P141 = 496356337189696433117694214004247077816195442584545699193391463991218138922878239760308283346772475928822571944307529233372143772747733213151_<141>
(7·10¹⁶²+17)/3 = 2(3)₁₆₁9_<163> = 43 · 1290083 · 245861039 · C147
C147 = P41 · P106
P41 = 43557628308424616166797635232339288714119_<41>
P106 = 3927685813921292174635198623350959368323057014448428705707920626668776971593108079668441340990588761661091_<106>

Number: n N=171080678795055855404521716225376616271445673441345458338745464113339205428455017351146799445290278089868761209155962498970919891782836131864643829 ( 147 digits) SNFS difficulty: 162 digits. Divisors found: Sun Jun 22 17:30:45 2008 prp41 factor: 43557628308424616166797635232339288714119 Sun Jun 22 17:30:45 2008 prp106 factor: 3927685813921292174635198623350959368323057014448428705707920626668776971593108079668441340990588761661091 Sun Jun 22 17:30:45 2008 elapsed time 01:24:32 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 43.24 hours. Scaled time: 79.08 units (timescale=1.829). Factorization parameters were as follows: name: KA_2_3_161_9 n: 171080678795055855404521716225376616271445673441345458338745464113339205428455017351146799445290278089868761209155962498970919891782836131864643829 skew: 0.48 deg: 5 c5: 700 c0: 17 m: 100000000000000000000000000000000 type: snfs rlim: 4500000 alim: 4500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2673527) Primes: RFBsize:315948, AFBsize:319141, largePrimes:7588284 encountered Relations: rels:7132335, finalFF:663363 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 43.01 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,162,5,0,0,0,0,0,0,0,0,4500000,4500000,28,28,48,48,2.5,2.5,100000 total time: 43.24 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

Jun 21, 2008 (4th)

By Robert Backstrom / GGNFS, Msieve
(7·10¹⁶¹+17)/3 = 2(3)₁₆₀9_<162> = 23 · 199 · C158
C158 = P75 · P84
P75 = 417946621514914850377965094249262197174211343113481758802230384518928472269_<75>
P84 = 121976187229760653869170760767223283184214542228118013644651384235208199727139732903_<84>

Number: n N=50979535357949166120457359260068458233194960308790328453863520501056004660986089869638045298958560920544752749253513946544315781807588667977569004442502366907 ( 158 digits) SNFS difficulty: 161 digits. Divisors found: Sat Jun 21 20:08:55 2008 prp75 factor: 417946621514914850377965094249262197174211343113481758802230384518928472269 Sat Jun 21 20:08:55 2008 prp84 factor: 121976187229760653869170760767223283184214542228118013644651384235208199727139732903 Sat Jun 21 20:08:55 2008 elapsed time 01:17:34 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 39.59 hours. Scaled time: 42.24 units (timescale=1.067). Factorization parameters were as follows: name: KA_2_3_160_9 n: 50979535357949166120457359260068458233194960308790328453863520501056004660986089869638045298958560920544752749253513946544315781807588667977569004442502366907 m: 100000000000000000000000000000000 deg: 5 c5: 70 c0: 17 skew: 0.75 type: snfs # These parameters should be manually set: rlim: 4000000 alim: 4000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 1900001) Primes: RFBsize:283146, AFBsize:283347, largePrimes:7532339 encountered Relations: rels:7183166, finalFF:710737 Max relations in full relation-set: 28 Initial matrix: 566560 x 710737 with sparse part having weight 43297736. Pruned matrix : 437204 x 440100 with weight 23469831. Total sieving time: 39.36 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,161,5,0,0,0,0,0,0,0,0,4000000,4000000,28,28,48,48,2.5,2.5,100000 total time: 39.59 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

Jun 21, 2008 (3rd)

By Serge Batalov / pol51, Msieve 1.36
(7·10¹⁸²+17)/3 = 2(3)₁₈₁9_<183> = 67 · 263 · 1900937 · 13440434009_<11> · 48375581147_<11> · 951589712077612133_<18> · 488665648860358418437252373_<27> · C107
C107 = P52 · P56
P52 = 1477088288774321744891374447367639204725377033864653_<52>
P56 = 15598075496263923715557038856491111313580736481605334217_<56>

Number: 23339_182 N=23039734642949158512389218312077989194926064666066772598653542994568986691659234818295104220330335207731701 ( 107 digits) Divisors found: r1=1477088288774321744891374447367639204725377033864653 r2=15598075496263923715557038856491111313580736481605334217 Version: Msieve v. 1.36 Total time: 4.03 hours. Factorization parameters were as follows: name: 23339_182 n: 23039734642949158512389218312077989194926064666066772598653542994568986691659234818295104220330335207731701 skew: 14986.36 # norm 3.69e+14 c5: 14580 c4: -403641738 c3: 23116709876478 c2: 73595465736422882 c1: -2826481295785857219317 c0: -1754227893603197984715460 # alpha -5.74 Y1: 36932884747 Y0: -275260764929799055773 # Murphy_E 1.48e-09 # M 10668570985258081896153286729973393070486963170843217333059578589374620638201361193672818543994648530861085 type: gnfs rlim: 2500000 alim: 2500000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 150000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1250000, 2550001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 280216 x 280442 Total sieving time: 4.03 hours. Total relation processing time: 0.23 hours. Matrix solve time: 00:16:07 Time per square root: 00:05:19 Prototype def-par.txt line would be: gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 0.03 hours. --------- CPU info (if available) ---------- Memory: 33030820k/34078720k available (1920k kernel code, 522988k reserved, 885k data, 196k init) Calibrating delay using timer specific routine.. 5609.80 BogoMIPS (lpj=11219618) _________________log____________ Msieve v. 1.36 ... Fri Jun 20 21:20:34 2008 restarting with 813821 relations Fri Jun 20 22:00:18 2008 restarting with 1447052 relations Fri Jun 20 22:41:11 2008 restarting with 2082702 relations Fri Jun 20 23:23:05 2008 restarting with 2928687 relations Sat Jun 21 00:06:00 2008 restarting with 4146072 relations Sat Jun 21 00:50:01 2008 restarting with 5343099 relations ... Msieve v. 1.36 Sat Jun 21 00:53:44 2008 random seeds: 30e59766 2c15b3e7 factoring 23039734642949158512389218312077989194926064666066772598653542994568986691659234818295104220330335207731701 (107 digits) commencing number field sieve (107-digit input) R0: -275260764929799055773 R1: 36932884747 A0: -1754227893603197984715460 A1: -2826481295785857219317 A2: 73595465736422882 A3: 23116709876478 A4: -403641738 A5: 14580 size score = 5.079226e-11, Murphy alpha = -5.726172, combined = 3.425672e-10 commencing linear algebra read 280900 cycles cycles contain 903261 unique relations read 903261 relations using 32 quadratic characters above 67108650 building initial matrix memory use: 118.1 MB read 280900 cycles matrix is 280722 x 280900 (84.8 MB) with weight 28464436 (101.33/col) sparse part has weight 18846930 (67.09/col) filtering completed in 2 passes matrix is 280264 x 280442 (84.7 MB) with weight 28429949 (101.38/col) sparse part has weight 18829626 (67.14/col) read 280442 cycles matrix is 280264 x 280442 (84.7 MB) with weight 28429949 (101.38/col) sparse part has weight 18829626 (67.14/col) saving the first 48 matrix rows for later matrix is 280216 x 280442 (81.6 MB) with weight 22142180 (78.95/col) sparse part has weight 18586804 (66.28/col) matrix includes 64 packed rows using block size 43690 for processor cache size 1024 kB commencing Lanczos iteration memory use: 74.7 MB linear algebra completed 279198 out of 280442 dimensions (99.6%) lanczos halted after 4434 iterations (dim = 280213) recovered 40 nontrivial dependencies elapsed time 00:16:07 Msieve v. 1.36 Sat Jun 21 01:09:51 2008 commencing square root phase reading relations for dependency 1 read 139967 cycles cycles contain 565071 unique relations read 565071 relations multiplying 874324 relations multiply complete, coefficients have about 36.33 million bits initial square root is modulo 164987 prp52 factor: 1477088288774321744891374447367639204725377033864653 prp56 factor: 15598075496263923715557038856491111313580736481605334217 elapsed time 00:05:19 -> Computing time scale for this machine... sumName = g107-23339_182.txt -> Factorization summary written to g107-23339_182.txt.

Jun 21, 2008 (2nd)

By suberi / GMP-ECM
(64·10¹⁹⁸+53)/9 = 7(1)₁₉₇7_<199> = 13 · 17 · 239 · 659 · 17164139387516599_<17> · C176
C176 = P37 · P140
P37 = 1053947316666084614295602974773924601_<37>
P140 = 11293301951476245566388760055470099805134724921150625162401162556882527928893529688436385162911773878376001344332111171233605201210655091323_<140>

Jun 21, 2008

By Sinkiti Sibata / GGNFS
(7·10¹⁵⁰+17)/3 = 2(3)₁₄₉9_<151> = 9927675833_<10> · 27850032279480012968457853_<26> · C115
C115 = P46 · P70
P46 = 2162964817432196944368364287263298935912589503_<46>
P70 = 3901701488783183216290172472354578578481164704106467605063761861590737_<70>

Number: 23339_150 N=8439243048360848899390133873267331807205480475339932256875802759406740186112702376997344956850716178544540468233711 ( 115 digits) SNFS difficulty: 150 digits. Divisors found: r1=2162964817432196944368364287263298935912589503 (pp46) r2=3901701488783183216290172472354578578481164704106467605063761861590737 (pp70) Version: GGNFS-0.77.1-20060513-k8 Total time: 26.01 hours. Scaled time: 52.10 units (timescale=2.003). Factorization parameters were as follows: name: 23339_150 n: 8439243048360848899390133873267331807205480475339932256875802759406740186112702376997344956850716178544540468233711 m: 1000000000000000000000000000000 c5: 7 c0: 17 skew: 1.19 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2100001) Primes: RFBsize:176302, AFBsize:176653, largePrimes:6113908 encountered Relations: rels:6522242, finalFF:919725 Max relations in full relation-set: 28 Initial matrix: 353020 x 919725 with sparse part having weight 85181103. Pruned matrix : 219865 x 221694 with weight 38860597. Total sieving time: 24.89 hours. Total relation processing time: 0.16 hours. Matrix solve time: 0.84 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,150,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 26.01 hours. --------- CPU info (if available) ----------

Jun 20, 2008 (4th)

By Wataru Sakai / GGNFS
(19·10¹⁷⁹+17)/9 = 2(1)₁₇₈3_<180> = 3 · 7 · C179
C179 = P52 · P58 · P70
P52 = 1849590095332545517981729396507306427776395737285843_<52>
P58 = 1590976674832112443983760714051680873712445958345760173293_<58>
P70 = 3416272406688343554143889986701948138927926610009907327005065997766947_<70>

Number: 21113_179 N=10052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910053 ( 179 digits) SNFS difficulty: 181 digits. Divisors found: r1=1849590095332545517981729396507306427776395737285843 (pp52) r2=1590976674832112443983760714051680873712445958345760173293 (pp58) r3=3416272406688343554143889986701948138927926610009907327005065997766947 (pp70) Version: GGNFS-0.77.1-20060722-nocona Total time: 552.22 hours. Scaled time: 1112.17 units (timescale=2.014). Factorization parameters were as follows: n: 10052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910052910053 m: 1000000000000000000000000000000000000 c5: 19 c0: 170 skew: 1.55 type: snfsFactor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 10800001) Primes: RFBsize:501962, AFBsize:503851, largePrimes:6702609 encountered Relations: rels:7184475, finalFF:1158871 Max relations in full relation-set: 32 Initial matrix: 1005878 x 1158871 with sparse part having weight 84778609. Pruned matrix : 880411 x 885504 with weight 65680688. Total sieving time: 545.72 hours. Total relation processing time: 0.11 hours. Matrix solve time: 6.15 hours. Time per square root: 0.24 hours. Prototype def-par.txt line would be: snfs,181,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 552.22 hours. --------- CPU info (if available) ----------

(7·10¹⁷⁴+11)/9 = (7)₁₇₃9_<174> = 251261 · 504617 · C163
C163 = P75 · P89
P75 = 151293655346678656951755233333841852499976949563535402282411057817628895559_<75>
P89 = 40545984826172869298143920767413765609952888879712288603313656316625649848981920183195313_<89>

Number: 77779_174 N=6134350253982660622277335689861201645599590140587053606604573046120563089433155514660435665006240828163050381504272365473039274996529904470390521720915719775314967 ( 163 digits) SNFS difficulty: 175 digits. Divisors found: r1=151293655346678656951755233333841852499976949563535402282411057817628895559 (pp75) r2=40545984826172869298143920767413765609952888879712288603313656316625649848981920183195313 (pp89) Version: GGNFS-0.77.1-20060722-nocona Total time: 291.50 hours. Scaled time: 585.04 units (timescale=2.007). Factorization parameters were as follows: n: 6134350253982660622277335689861201645599590140587053606604573046120563089433155514660435665006240828163050381504272365473039274996529904470390521720915719775314967 m: 100000000000000000000000000000000000 c5: 7 c0: 110 skew: 1.73 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 14300001) Primes: RFBsize:501962, AFBsize:502982, largePrimes:6844410 encountered Relations: rels:7419841, finalFF:1221660 Max relations in full relation-set: 32 Initial matrix: 1005009 x 1221660 with sparse part having weight 100226513. Pruned matrix : 824853 x 829942 with weight 78137577. Total sieving time: 283.78 hours. Total relation processing time: 0.12 hours. Matrix solve time: 7.36 hours. Time per square root: 0.25 hours. Prototype def-par.txt line would be: snfs,175,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 291.50 hours.

Jun 20, 2008 (3rd)

By suberi / GMP-ECM
4·10¹⁷¹-3 = 3(9)₁₇₀7_<172> = 7 · 992551249 · 11060804449_<11> · 19009303771_<11> · C142
C142 = P37 · P106
P37 = 1249207319055289192086424463607428111_<37>
P106 = 2191904185664257747583477319317672323649397459016399392947765286350833997120102120957046738111957790744991_<106>
4·10¹⁸²-3 = 3(9)₁₈₁7_<183> = 3313 · 11483 · 176053 · C170
C170 = P35 · P136
P35 = 39387975579353615896504296945339241_<35>
P136 = 1516268457802174096132783680473005131671559431263031934817627015235299434290293219117245850021882172515022423742506186276722478373533891_<136>

Jun 20, 2008 (2nd)

By Sinkiti Sibata / Msieve, GGNFS
(17·10¹⁸¹+1)/9 = 1(8)₁₈₀9_<182> = 19 · 44839 · 48731 · 1008779 · 12003314779_<11> · 5830558817883227437007237_<25> · 758822763085731218605641418771_<30> · C100
C100 = P45 · P56
P45 = 242103400334044748484073044835249209568097447_<45>
P56 = 35078653987811118622758840608304843178836958530915817471_<56>

Thu Jun 19 06:38:30 2008 Msieve v. 1.36 Thu Jun 19 06:38:30 2008 random seeds: 57997b87 8224c00e Thu Jun 19 06:38:30 2008 factoring 8492661409590470524891423727868139850632579649757129010224121294326903739481230882899276916193096537 (100 digits) Thu Jun 19 06:38:31 2008 no P-1/P+1/ECM available, skipping Thu Jun 19 06:38:31 2008 commencing quadratic sieve (100-digit input) Thu Jun 19 06:38:32 2008 using multiplier of 17 Thu Jun 19 06:38:32 2008 using 64kb Pentium 4 sieve core Thu Jun 19 06:38:32 2008 sieve interval: 18 blocks of size 65536 Thu Jun 19 06:38:32 2008 processing polynomials in batches of 6 Thu Jun 19 06:38:32 2008 using a sieve bound of 2751379 (100000 primes) Thu Jun 19 06:38:32 2008 using large prime bound of 412706850 (28 bits) Thu Jun 19 06:38:32 2008 using double large prime bound of 3222218636339400 (43-52 bits) Thu Jun 19 06:38:32 2008 using trial factoring cutoff of 52 bits Thu Jun 19 06:38:32 2008 polynomial 'A' values have 13 factors Fri Jun 20 04:01:17 2008 100109 relations (23520 full + 76589 combined from 1507622 partial), need 100096 Fri Jun 20 04:01:23 2008 begin with 1531142 relations Fri Jun 20 04:01:25 2008 reduce to 264987 relations in 10 passes Fri Jun 20 04:01:25 2008 attempting to read 264987 relations Fri Jun 20 04:01:34 2008 recovered 264987 relations Fri Jun 20 04:01:34 2008 recovered 256717 polynomials Fri Jun 20 04:01:35 2008 attempting to build 100109 cycles Fri Jun 20 04:01:35 2008 found 100109 cycles in 6 passes Fri Jun 20 04:01:35 2008 distribution of cycle lengths: Fri Jun 20 04:01:35 2008 length 1 : 23520 Fri Jun 20 04:01:35 2008 length 2 : 17176 Fri Jun 20 04:01:35 2008 length 3 : 16902 Fri Jun 20 04:01:35 2008 length 4 : 13567 Fri Jun 20 04:01:35 2008 length 5 : 10292 Fri Jun 20 04:01:35 2008 length 6 : 7180 Fri Jun 20 04:01:35 2008 length 7 : 4698 Fri Jun 20 04:01:35 2008 length 9+: 6774 Fri Jun 20 04:01:35 2008 largest cycle: 20 relations Fri Jun 20 04:01:36 2008 matrix is 100000 x 100109 (28.3 MB) with weight 7027440 (70.20/col) Fri Jun 20 04:01:36 2008 sparse part has weight 7027440 (70.20/col) Fri Jun 20 04:01:38 2008 filtering completed in 3 passes Fri Jun 20 04:01:38 2008 matrix is 96171 x 96234 (27.4 MB) with weight 6799375 (70.65/col) Fri Jun 20 04:01:38 2008 sparse part has weight 6799375 (70.65/col) Fri Jun 20 04:01:39 2008 saving the first 48 matrix rows for later Fri Jun 20 04:01:39 2008 matrix is 96123 x 96234 (17.6 MB) with weight 5431041 (56.44/col) Fri Jun 20 04:01:39 2008 sparse part has weight 4041126 (41.99/col) Fri Jun 20 04:01:39 2008 matrix includes 64 packed rows Fri Jun 20 04:01:39 2008 using block size 21845 for processor cache size 512 kB Fri Jun 20 04:01:40 2008 commencing Lanczos iteration Fri Jun 20 04:01:40 2008 memory use: 16.6 MB Fri Jun 20 04:03:29 2008 lanczos halted after 1521 iterations (dim = 96123) Fri Jun 20 04:03:29 2008 recovered 18 nontrivial dependencies Fri Jun 20 04:03:33 2008 prp45 factor: 242103400334044748484073044835249209568097447 Fri Jun 20 04:03:33 2008 prp56 factor: 35078653987811118622758840608304843178836958530915817471 Fri Jun 20 04:03:33 2008 elapsed time 21:25:03

(7·10¹⁴⁶+17)/3 = 2(3)₁₄₅9_<147> = 41873810519116707626863_<23> · C124
C124 = P59 · P66
P59 = 21804397652798991947920303404221539210667198756143728491239_<59>
P66 = 255558427991811864344755703271114165099174644030525182217947392227_<66>

Number: 23339_146 N=5572297587457662816333162127727176214809046786511556224921466488809034721917819970726236103796689823938279599964261266199253 ( 124 digits) SNFS difficulty: 146 digits. Divisors found: r1=21804397652798991947920303404221539210667198756143728491239 (pp59) r2=255558427991811864344755703271114165099174644030525182217947392227 (pp66) Version: GGNFS-0.77.1-20060513-k8 Total time: 19.48 hours. Scaled time: 39.02 units (timescale=2.003). Factorization parameters were as follows: name: 23339_146 n: 5572297587457662816333162127727176214809046786511556224921466488809034721917819970726236103796689823938279599964261266199253 m: 100000000000000000000000000000 c5: 70 c0: 17 skew: 0.75 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [750000, 2850001) Primes: RFBsize:114155, AFBsize:114392, largePrimes:2827827 encountered Relations: rels:2801739, finalFF:256860 Max relations in full relation-set: 28 Initial matrix: 228614 x 256860 with sparse part having weight 27064766. Pruned matrix : 220197 x 221404 with weight 21616388. Total sieving time: 18.70 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.57 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 19.48 hours. --------- CPU info (if available) ----------

(19·10¹⁵³+71)/9 = 2(1)₁₅₂9_<154> = 13 · 17 · 1931 · 17681 · 79167967819_<11> · C133
C133 = P55 · P79
P55 = 2330871598302278901853376041628293375034044869755858891_<55>
P79 = 1516218784411238460729939570299747737958774664936753931542252342962491493263081_<79>

Number: 21119_153 N=3534111301396561829241944371109709550951878020320586502879799576712460981422857149193925613075150874769889794783911449876155375903171 ( 133 digits) SNFS difficulty: 154 digits. Divisors found: r1=2330871598302278901853376041628293375034044869755858891 (pp55) r2=1516218784411238460729939570299747737958774664936753931542252342962491493263081 (pp79) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 55.24 hours. Scaled time: 37.23 units (timescale=0.674). Factorization parameters were as follows: name: 21119_153 n: 3534111301396561829241944371109709550951878020320586502879799576712460981422857149193925613075150874769889794783911449876155375903171 m: 1000000000000000000000000000000 c5: 19000 c0: 71 skew: 0.33 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2700001) Primes: RFBsize:176302, AFBsize:176259, largePrimes:5780933 encountered Relations: rels:5751272, finalFF:468492 Max relations in full relation-set: 28 Initial matrix: 352628 x 468492 with sparse part having weight 49607110. Pruned matrix : 312585 x 314412 with weight 31405699. Total sieving time: 50.22 hours. Total relation processing time: 0.31 hours. Matrix solve time: 4.53 hours. Time per square root: 0.18 hours. Prototype def-par.txt line would be: snfs,154,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 55.24 hours. --------- CPU info (if available) ----------

Jun 20, 2008

By Robert Backstrom / GGNFS, Msieve, GMP-ECM
(19·10¹⁷³+17)/9 = 2(1)₁₇₂3_<174> = 3 · 7 · C173
C173 = P38 · P57 · P79
P38 = 11908775400215661195548462282129043797_<38>
P57 = 826889165198643841886538166294656560201100292366830050189_<57>
P79 = 1020886335567388225849072357898453571339187176611699612014911899812973186198741_<79>

Number: n N=844159849780020235129746469497252431004627125959824403139627884770709057725585735018317388737365147113252112148503478738967403158612049 ( 135 digits) SNFS difficulty: 174 digits. Divisors found: Fri Jun 20 02:44:06 2008 prp57 factor: 826889165198643841886538166294656560201100292366830050189 Fri Jun 20 02:44:06 2008 prp79 factor: 1020886335567388225849072357898453571339187176611699612014911899812973186198741 Fri Jun 20 02:44:06 2008 elapsed time 02:59:28 (Msieve 1.34) Version: GGNFS-0.77.1-20050930-k8 Total time: 96.48 hours. Scaled time: 80.94 units (timescale=0.839). Factorization parameters were as follows: name: KA_2_1_172_3 n: 844159849780020235129746469497252431004627125959824403139627884770709057725585735018317388737365147113252112148503478738967403158612049 type: snfs deg: 5 c5: 19000 c0: 17 skew: 0.25 m: 10000000000000000000000000000000000 rlim: 4500000 alim: 4500000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 11300747) Primes: RFBsize:315948, AFBsize:315306, largePrimes:6194474 encountered Relations: rels:6248801, finalFF:651129 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 96.15 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,174,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.5,2.5,100000 total time: 96.48 hours. --------- CPU info (if available) ----------

8·10¹⁶⁹+9 = 8(0)₁₆₈9_<170> = 2083 · 21187 · C163
C163 = P33 · P130
P33 = 347913094655913140947256232930961_<33>
P130 = 5210272953749998271101503426402444733270293388626467088714412188109283843702487962421130258535164821785639637952029491481694049489_<130>
(11·10¹⁶⁷+61)/9 = 1(2)₁₆₆9_<168> = 3⁴ · 449 · 33087070891123_<14> · C150
C150 = P72 · P78
P72 = 748005811625541632642916647689589194648693239663159298286037563308548193_<72>
P78 = 135786164695082180429353840411133841148804527719360141316474387898066866066119_<78>

Number: n N=101568840330264413237388822930979889101910651497072026084643242058579491153939325114881169376679390422211703898084569112611049921791675345871035972967 ( 150 digits) SNFS difficulty: 168 digits. Divisors found: Fri Jun 20 20:10:57 2008 prp72 factor: 748005811625541632642916647689589194648693239663159298286037563308548193 Fri Jun 20 20:10:57 2008 prp78 factor: 135786164695082180429353840411133841148804527719360141316474387898066866066119 Fri Jun 20 20:10:57 2008 elapsed time 02:27:34 (Msieve 1.36) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 113.07 hours. Scaled time: 148.57 units (timescale=1.314). Factorization parameters were as follows: name: KA_1_2_166_9 n: 101568840330264413237388822930979889101910651497072026084643242058579491153939325114881169376679390422211703898084569112611049921791675345871035972967 skew: 0.56 deg: 5 c5: 1100 c0: 61 m: 1000000000000000000000000000000000 type: snfs rlim: 3800000 alim: 3800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3800000/3800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 5000001) Primes: RFBsize:269987, AFBsize:269319, largePrimes:7804913 encountered Relations: rels:7226972, finalFF:542557 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 112.54 hours. Total relation processing time: 0.53 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,168,5,0,0,0,0,0,0,0,0,3800000,3800000,28,28,48,48,2.5,2.5,100000 total time: 113.07 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Jun 19, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve
(19·10¹⁵⁴+71)/9 = 2(1)₁₅₃9_<155> = 7 · 73 · 4483 · 33487 · 83735683584829_<14> · C130
C130 = P46 · P85
P46 = 1791677943138389668968679508662606052300273107_<46>
P85 = 1834318275709524259788133515195304765934811811430526130176162937982551937357179892483_<85>

Number: n N=3286507595284397990244440725109649136011496454300802589054816534378305641090379440018700033067620390985386802795054882189796354681 ( 130 digits) SNFS difficulty: 156 digits. Divisors found: Fri Jun 20 00:19:02 2008 prp46 factor: 1791677943138389668968679508662606052300273107 Fri Jun 20 00:19:02 2008 prp85 factor: 1834318275709524259788133515195304765934811811430526130176162937982551937357179892483 Fri Jun 20 00:19:02 2008 elapsed time 00:29:43 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 23.65 hours. Scaled time: 43.12 units (timescale=1.823). Factorization parameters were as follows: name: KA_2_1_153_9 n: 3286507595284397990244440725109649136011496454300802589054816534378305641090379440018700033067620390985386802795054882189796354681 skew: 2.06 deg: 5 c5: 19 c0: 710 m: 10000000000000000000000000000000 type: snfs rlim: 1500000 alim: 1500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 1800311) Primes: RFBsize:114155, AFBsize:114373, largePrimes:7133643 encountered Relations: rels:6460420, finalFF:245971 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 23.49 hours. Total relation processing time: 0.16 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,100000 total time: 23.65 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

Jun 19, 2008 (2nd)

By Sinkiti Sibata / GGNFS, Msieve
(7·10¹⁵⁸+17)/3 = 2(3)₁₅₇9_<159> = 242357443 · 28030229173069_<14> · 1454061345137057_<16> · 16465999087301435553750282083_<29> · C94
C94 = P44 · P50
P44 = 19146295587768898703757081073237370039739239_<44>
P50 = 74926974982117317392890572430494126577076446433113_<50>

Wed Jun 18 20:51:43 2008 Msieve v. 1.36 Wed Jun 18 20:51:43 2008 random seeds: 1a54057b b92e04e7 Wed Jun 18 20:51:43 2008 factoring 1434574010504983451855968360270997415967569984416379180128533164708864833002769858886175021007 (94 digits) Wed Jun 18 20:51:45 2008 no P-1/P+1/ECM available, skipping Wed Jun 18 20:51:45 2008 commencing quadratic sieve (94-digit input) Wed Jun 18 20:51:45 2008 using multiplier of 3 Wed Jun 18 20:51:45 2008 using 64kb Pentium 4 sieve core Wed Jun 18 20:51:45 2008 sieve interval: 18 blocks of size 65536 Wed Jun 18 20:51:45 2008 processing polynomials in batches of 6 Wed Jun 18 20:51:45 2008 using a sieve bound of 1987303 (74118 primes) Wed Jun 18 20:51:45 2008 using large prime bound of 256362087 (27 bits) Wed Jun 18 20:51:45 2008 using double large prime bound of 1367529713306016 (42-51 bits) Wed Jun 18 20:51:45 2008 using trial factoring cutoff of 51 bits Wed Jun 18 20:51:45 2008 polynomial 'A' values have 12 factors Thu Jun 19 01:10:48 2008 74480 relations (18948 full + 55532 combined from 1022585 partial), need 74214 Thu Jun 19 01:10:52 2008 begin with 1041533 relations Thu Jun 19 01:10:53 2008 reduce to 189783 relations in 11 passes Thu Jun 19 01:10:53 2008 attempting to read 189783 relations Thu Jun 19 01:10:59 2008 recovered 189783 relations Thu Jun 19 01:10:59 2008 recovered 170542 polynomials Thu Jun 19 01:10:59 2008 attempting to build 74480 cycles Thu Jun 19 01:10:59 2008 found 74480 cycles in 5 passes Thu Jun 19 01:10:59 2008 distribution of cycle lengths: Thu Jun 19 01:10:59 2008 length 1 : 18948 Thu Jun 19 01:10:59 2008 length 2 : 13347 Thu Jun 19 01:10:59 2008 length 3 : 12736 Thu Jun 19 01:10:59 2008 length 4 : 10257 Thu Jun 19 01:10:59 2008 length 5 : 7348 Thu Jun 19 01:10:59 2008 length 6 : 4791 Thu Jun 19 01:10:59 2008 length 7 : 3039 Thu Jun 19 01:10:59 2008 length 9+: 4014 Thu Jun 19 01:10:59 2008 largest cycle: 21 relations Thu Jun 19 01:10:59 2008 matrix is 74118 x 74480 (18.5 MB) with weight 4549876 (61.09/col) Thu Jun 19 01:10:59 2008 sparse part has weight 4549876 (61.09/col) Thu Jun 19 01:11:01 2008 filtering completed in 3 passes Thu Jun 19 01:11:01 2008 matrix is 70109 x 70173 (17.5 MB) with weight 4299746 (61.27/col) Thu Jun 19 01:11:01 2008 sparse part has weight 4299746 (61.27/col) Thu Jun 19 01:11:01 2008 saving the first 48 matrix rows for later Thu Jun 19 01:11:01 2008 matrix is 70061 x 70173 (10.1 MB) with weight 3250963 (46.33/col) Thu Jun 19 01:11:01 2008 sparse part has weight 2225728 (31.72/col) Thu Jun 19 01:11:01 2008 matrix includes 64 packed rows Thu Jun 19 01:11:01 2008 using block size 21845 for processor cache size 512 kB Thu Jun 19 01:11:02 2008 commencing Lanczos iteration Thu Jun 19 01:11:02 2008 memory use: 10.4 MB Thu Jun 19 01:11:52 2008 lanczos halted after 1110 iterations (dim = 70060) Thu Jun 19 01:11:52 2008 recovered 17 nontrivial dependencies Thu Jun 19 01:11:53 2008 prp44 factor: 19146295587768898703757081073237370039739239 Thu Jun 19 01:11:53 2008 prp50 factor: 74926974982117317392890572430494126577076446433113 Thu Jun 19 01:11:53 2008 elapsed time 04:20:10

(7·10¹⁴³+17)/3 = 2(3)₁₄₂9_<144> = 1867 · 4339 · C137
C137 = P39 · P98
P39 = 535765703863921912750851250492181849899_<39>
P98 = 53761070475339461599109698874173573872281314889937566690752801724933075409845431841588828412544097_<98>

Number: 23339_143 N=28803337763698157643877095499400293933947116002027590388062843451513839654040641262698825840165587919945978105595422803989295198372496203 ( 137 digits) SNFS difficulty: 143 digits. Divisors found: r1=535765703863921912750851250492181849899 (pp39) r2=53761070475339461599109698874173573872281314889937566690752801724933075409845431841588828412544097 (pp98) Version: GGNFS-0.77.1-20060513-k8 Total time: 18.67 hours. Scaled time: 37.52 units (timescale=2.010). Factorization parameters were as follows: name: 23339_143 n: 28803337763698157643877095499400293933947116002027590388062843451513839654040641262698825840165587919945978105595422803989295198372496203 m: 10000000000000000000000000000 c5: 7000 c0: 17 skew: 0.3 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [650000, 2750001) Primes: RFBsize:100021, AFBsize:100228, largePrimes:2937213 encountered Relations: rels:2987873, finalFF:275507 Max relations in full relation-set: 28 Initial matrix: 200316 x 275507 with sparse part having weight 32504675. Pruned matrix : 181772 x 182837 with weight 20348065. Total sieving time: 18.00 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.46 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,143,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 18.67 hours. --------- CPU info (if available) ----------

(7·10¹⁴⁴+17)/3 = 2(3)₁₄₃9_<145> = 6112388617_<10> · C135
C135 = P45 · P90
P45 = 626946312457987940199614144659177704270837173_<45>
P90 = 608885279634814638970724327573961019652307778580222127000169140138289548248184830103481879_<90>

Number: 23339_144 N=381738380776997859744121916215088281147051506809213294713740439081334892377529819179907247270716742343762095474325325171538145565088067 ( 135 digits) SNFS difficulty: 145 digits. Divisors found: r1=626946312457987940199614144659177704270837173 (pp45) r2=608885279634814638970724327573961019652307778580222127000169140138289548248184830103481879 (pp90) Version: GGNFS-0.77.1-20060513-k8 Total time: 29.13 hours. Scaled time: 58.34 units (timescale=2.003). Factorization parameters were as follows: name: 23339_144 n: 381738380776997859744121916215088281147051506809213294713740439081334892377529819179907247270716742343762095474325325171538145565088067 m: 100000000000000000000000000000 c5: 7 c0: 170 skew: 1.89 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [650000, 4150001) Primes: RFBsize:100021, AFBsize:100013, largePrimes:3149571 encountered Relations: rels:3284509, finalFF:230295 Max relations in full relation-set: 28 Initial matrix: 200099 x 230295 with sparse part having weight 31044379. Pruned matrix : 193206 x 194270 with weight 25166348. Total sieving time: 28.35 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.53 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 29.13 hours. --------- CPU info (if available) ----------

Jun 19, 2008

By Robert Backstrom / GGNFS, Msieve, GMP-ECM
(7·10¹⁶⁰+17)/3 = 2(3)₁₅₉9_<161> = 3701 · 35593 · 69389 · 459841 · 93435119 · 17324364797_<11> · 3387727253081_<13> · 102689731400639_<15> · C97
C97 = P44 · P54
P44 = 38407669121855954038639728065299289990791621_<44>
P54 = 256669293719185842934861313379909281435703545898255851_<54>

Number: n N=9858069306906950463503372591344284125766706149980496147484008217952622305609424926370754685024471 ( 97 digits) Divisors found: Thu Jun 19 03:19:13 2008 prp44 factor: 38407669121855954038639728065299289990791621 Thu Jun 19 03:19:13 2008 prp54 factor: 256669293719185842934861313379909281435703545898255851 Thu Jun 19 03:19:13 2008 elapsed time 00:16:07 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 6.39 hours. Scaled time: 9.30 units (timescale=1.454). Factorization parameters were as follows: name: KA_2_3_159_9 n: 9858069306906950463503372591344284125766706149980496147484008217952622305609424926370754685024471 m: 15110236062892358326859 deg: 4 c4: 189106680 c3: -174424676846 c2: -1805591920498891697 c1: 846965004993150148 c0: 1950101995051999511698950 skew: 1635.250 type: gnfs # adj. I(F,S) = 54.947 # E(F1,F2) = 2.502940e-05 # GGNFS version 0.77.1-20051202-athlon polyselect. # Options were: # lcd=1, enumLCD=24, maxS1=60.00000000, seed=1213786088. # 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 special-q in [100000, 1060357) Primes: RFBsize:92938, AFBsize:93239, largePrimes:1777853 encountered Relations: rels:1790024, finalFF:200325 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 6.30 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,96,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000 total time: 6.39 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

(7·10¹⁵⁶+17)/3 = 2(3)₁₅₅9_<157> = 31 · 239 · 128262209 · 54153681173_<11> · C134
C134 = P39 · P95
P39 = 527845703954308242079195374698855965483_<39>
P95 = 85898088634340166008079398675596416314617721039017551057834275703819076412196974341860416371741_<95>
(19·10¹⁵⁸+71)/9 = 2(1)₁₅₇9_<159> = 3 · 5111043929_<10> · 8586699613_<10> · C139
C139 = P61 · P79
P61 = 1552232375168401888226285240732768948412176616299065734638659_<61>
P79 = 1032992611981958171657311747096309357508297728486040740667074691813325998649211_<79>

Number: n N=1603444575628166296323850859232332205498429149271953164507338103129857597627597826527727616013810322286400015061749747416092265207180448049 ( 139 digits) SNFS difficulty: 159 digits. Divisors found: Thu Jun 19 18:40:36 2008 prp61 factor: 1552232375168401888226285240732768948412176616299065734638659 Thu Jun 19 18:40:36 2008 prp79 factor: 1032992611981958171657311747096309357508297728486040740667074691813325998649211 Thu Jun 19 18:40:36 2008 elapsed time 01:19:33 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 48.30 hours. Scaled time: 84.96 units (timescale=1.759). Factorization parameters were as follows: name: KA_2_1_157_9 n: 1603444575628166296323850859232332205498429149271953164507338103129857597627597826527727616013810322286400015061749747416092265207180448049 type: snfs skew: 0.33 deg: 5 c5: 19000 c0: 71 m: 10000000000000000000000000000000 rlim: 2800000 alim: 2800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2500213) Primes: RFBsize:203362, AFBsize:203478, largePrimes:7041615 encountered Relations: rels:6395775, finalFF:429719 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 48.07 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,159,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.3,2.3,100000 total time: 48.30 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(7·10¹⁵²+17)/3 = 2(3)₁₅₁9_<153> = 23029 · 840704633 · 1326812001547_<13> · C127
C127 = P45 · P83
P45 = 610101261968507830368749150447308985874102137_<45>
P83 = 14888363041956731209585176317112178230936915291439811404040951408011091747600139293_<83>

Number: n N=9083409080543093805913755278938747676141202257994375217606729563473712226337971583897960187761658473791899659290793982508969141 ( 127 digits) SNFS difficulty: 152 digits. Divisors found: Thu Jun 19 19:24:26 2008 prp45 factor: 610101261968507830368749150447308985874102137 Thu Jun 19 19:24:26 2008 prp83 factor: 14888363041956731209585176317112178230936915291439811404040951408011091747600139293 Thu Jun 19 19:24:26 2008 elapsed time 00:51:02 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 18.07 hours. Scaled time: 33.05 units (timescale=1.829). Factorization parameters were as follows: name: KA_2_3_151_9 n: 9083409080543093805913755278938747676141202257994375217606729563473712226337971583897960187761658473791899659290793982508969141 skew: 0.48 deg: 5 c5: 700 c0: 17 m: 1000000000000000000000000000000 type: snfs rlim: 1500000 alim: 1500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 1500157) Primes: RFBsize:114155, AFBsize:114427, largePrimes:6826015 encountered Relations: rels:6086022, finalFF:228605 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 17.92 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,100000 total time: 18.07 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

Jun 18, 2008 (4th)

By suberi / GMP-ECM
(16·10²⁴⁴-61)/9 = 1(7)₂₄₃1_<245> = 13 · 11093 · 1330706156723_<13> · 3353370740535258743_<19> · C209
C209 = P35 · C175
P35 = 23927338568455349437657020835689181_<35>
C175 = [1154587832011312664684319787690887343855960034230279419823600016435051159772210847611408481790922675000344963443900485817612482088891032224245876772595417312934546709619016891_<175>]
(16·10²⁵⁰-61)/9 = 1(7)₂₄₉1_<251> = 13 · 1117 · 3001 · 68960274559011859_<17> · 105187359738922024391561_<24> · C203
C203 = P35 · P169
P35 = 47127519770374767542490387021015569_<35>
P169 = 1193377463091214465280930122329596329399002506548645441537440214904924329099256353065394411257513274567225314616795075715769044965685150587906045369454735928523088581121_<169>

Jun 18, 2008 (3rd)

By Sinkiti Sibata / GGNFS, Msieve
(7·10¹¹⁷+17)/3 = 2(3)₁₁₆9_<118> = 23 · 2333 · 594170435227_<12> · C101
C101 = P40 · P62
P40 = 7055000601307972440354361852306418014519_<40>
P62 = 10373519245946236498753585760743609141393461815640085096926917_<62>

Number: 23339_117 N=73185184517830523349631685351219188493971228777679019193467213732990802157068577513278831575587907923 ( 101 digits) SNFS difficulty: 117 digits. Divisors found: r1=7055000601307972440354361852306418014519 (pp40) r2=10373519245946236498753585760743609141393461815640085096926917 (pp62) Version: GGNFS-0.77.1-20060513-k8 Total time: 2.27 hours. Scaled time: 4.53 units (timescale=1.996). Factorization parameters were as follows: name: 23339_117 n: 73185184517830523349631685351219188493971228777679019193467213732990802157068577513278831575587907923 m: 100000000000000000000000 c5: 700 c0: 17 skew: 0.48 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 550001) Primes: RFBsize:49098, AFBsize:64083, largePrimes:2285266 encountered Relations: rels:2533749, finalFF:360298 Max relations in full relation-set: 28 Initial matrix: 113248 x 360298 with sparse part having weight 33638715. Pruned matrix : 75040 x 75670 with weight 6289789. Total sieving time: 2.15 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.03 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,117,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.27 hours. --------- CPU info (if available) ----------

(7·10¹²³+17)/3 = 2(3)₁₂₂9_<124> = 541 · 8875041087261656332723028987_<28> · C93
C93 = P41 · P53
P41 = 39640352959941520079217079058662355588447_<41>
P53 = 12259468301921439444803232407524450529599277231054411_<53>

Wed Jun 18 10:30:39 2008 Msieve v. 1.36 Wed Jun 18 10:30:39 2008 random seeds: 071b2352 82b713c7 Wed Jun 18 10:30:39 2008 factoring 485969650589380773048129474294923494937486054697957352921123969457889678948105771180179989717 (93 digits) Wed Jun 18 10:30:40 2008 no P-1/P+1/ECM available, skipping Wed Jun 18 10:30:40 2008 commencing quadratic sieve (93-digit input) Wed Jun 18 10:30:40 2008 using multiplier of 13 Wed Jun 18 10:30:40 2008 using 64kb Pentium 4 sieve core Wed Jun 18 10:30:40 2008 sieve interval: 18 blocks of size 65536 Wed Jun 18 10:30:40 2008 processing polynomials in batches of 6 Wed Jun 18 10:30:40 2008 using a sieve bound of 1922351 (71765 primes) Wed Jun 18 10:30:40 2008 using large prime bound of 232604471 (27 bits) Wed Jun 18 10:30:40 2008 using double large prime bound of 1147922137951622 (42-51 bits) Wed Jun 18 10:30:40 2008 using trial factoring cutoff of 51 bits Wed Jun 18 10:30:40 2008 polynomial 'A' values have 12 factors Wed Jun 18 10:30:45 2008 restarting with 18575 full and 956051 partial relations Wed Jun 18 10:30:45 2008 72209 relations (18575 full + 53634 combined from 956051 partial), need 71861 Wed Jun 18 10:30:48 2008 begin with 974626 relations Wed Jun 18 10:30:49 2008 reduce to 182680 relations in 11 passes Wed Jun 18 10:30:49 2008 attempting to read 182680 relations Wed Jun 18 10:30:55 2008 recovered 182680 relations Wed Jun 18 10:30:55 2008 recovered 161924 polynomials Wed Jun 18 10:30:55 2008 attempting to build 72209 cycles Wed Jun 18 10:30:55 2008 found 72209 cycles in 6 passes Wed Jun 18 10:30:55 2008 distribution of cycle lengths: Wed Jun 18 10:30:55 2008 length 1 : 18575 Wed Jun 18 10:30:55 2008 length 2 : 13202 Wed Jun 18 10:30:55 2008 length 3 : 12365 Wed Jun 18 10:30:55 2008 length 4 : 9549 Wed Jun 18 10:30:55 2008 length 5 : 7117 Wed Jun 18 10:30:55 2008 length 6 : 4605 Wed Jun 18 10:30:55 2008 length 7 : 2941 Wed Jun 18 10:30:55 2008 length 9+: 3855 Wed Jun 18 10:30:55 2008 largest cycle: 19 relations Wed Jun 18 10:30:56 2008 matrix is 71765 x 72209 (18.3 MB) with weight 4519177 (62.58/col) Wed Jun 18 10:30:56 2008 sparse part has weight 4519177 (62.58/col) Wed Jun 18 10:30:57 2008 filtering completed in 3 passes Wed Jun 18 10:30:57 2008 matrix is 67627 x 67691 (17.2 MB) with weight 4244832 (62.71/col) Wed Jun 18 10:30:57 2008 sparse part has weight 4244832 (62.71/col) Wed Jun 18 10:30:58 2008 saving the first 48 matrix rows for later Wed Jun 18 10:30:58 2008 matrix is 67579 x 67691 (10.6 MB) with weight 3302713 (48.79/col) Wed Jun 18 10:30:58 2008 sparse part has weight 2369433 (35.00/col) Wed Jun 18 10:30:58 2008 matrix includes 64 packed rows Wed Jun 18 10:30:58 2008 using block size 21845 for processor cache size 512 kB Wed Jun 18 10:30:58 2008 commencing Lanczos iteration Wed Jun 18 10:30:58 2008 memory use: 10.4 MB Wed Jun 18 10:31:46 2008 lanczos halted after 1070 iterations (dim = 67575) Wed Jun 18 10:31:47 2008 recovered 15 nontrivial dependencies Wed Jun 18 10:31:48 2008 prp41 factor: 39640352959941520079217079058662355588447 Wed Jun 18 10:31:48 2008 prp53 factor: 12259468301921439444803232407524450529599277231054411 Wed Jun 18 10:31:48 2008 elapsed time 00:01:09

(7·10¹¹⁸+17)/3 = 2(3)₁₁₇9_<119> = 19227743 · C112
C112 = P49 · P63
P49 = 3093087719815041604894591181802808992385054200749_<49>
P63 = 392334265399879349992246101266524172412020862047021909878065977_<63>

Number: 23339_118 N=1213524298371022190869377302023088894694157984810455045781157639424103667982941800986903836468655386819624816773 ( 112 digits) SNFS difficulty: 118 digits. Divisors found: r1=3093087719815041604894591181802808992385054200749 (pp49) r2=392334265399879349992246101266524172412020862047021909878065977 (pp63) Version: GGNFS-0.77.1-20060513-k8 Total time: 2.32 hours. Scaled time: 4.58 units (timescale=1.973). Factorization parameters were as follows: name: 23339_118 n: 1213524298371022190869377302023088894694157984810455045781157639424103667982941800986903836468655386819624816773 m: 100000000000000000000000 c5: 7000 c0: 17 skew: 0.3 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 550001) Primes: RFBsize:49098, AFBsize:64188, largePrimes:2227594 encountered Relations: rels:2431241, finalFF:324093 Max relations in full relation-set: 28 Initial matrix: 113353 x 324093 with sparse part having weight 30217094. Pruned matrix : 77229 x 77859 with weight 5970872. Total sieving time: 2.20 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.03 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,118,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.32 hours. --------- CPU info (if available) ----------

(7·10¹²⁶+17)/3 = 2(3)₁₂₅9_<127> = 31 · 3613 · 86753 · 731135486302163043392089_<24> · C93
C93 = P41 · P52
P41 = 68030424514091868787676449965273815693041_<41>
P52 = 4827936880554905413919785453314420134437806840877729_<52>

Wed Jun 18 10:40:16 2008 Msieve v. 1.36 Wed Jun 18 10:40:16 2008 random seeds: b05deab3 ec6c7f99 Wed Jun 18 10:40:16 2008 factoring 328446595511390663902274889915254013499180885468671028135877513010323355822376511174877183889 (93 digits) Wed Jun 18 10:40:17 2008 no P-1/P+1/ECM available, skipping Wed Jun 18 10:40:17 2008 commencing quadratic sieve (93-digit input) Wed Jun 18 10:40:17 2008 using multiplier of 19 Wed Jun 18 10:40:17 2008 using 64kb Pentium 4 sieve core Wed Jun 18 10:40:17 2008 sieve interval: 18 blocks of size 65536 Wed Jun 18 10:40:17 2008 processing polynomials in batches of 6 Wed Jun 18 10:40:17 2008 using a sieve bound of 1919377 (71765 primes) Wed Jun 18 10:40:17 2008 using large prime bound of 232244617 (27 bits) Wed Jun 18 10:40:17 2008 using double large prime bound of 1144727446588341 (42-51 bits) Wed Jun 18 10:40:17 2008 using trial factoring cutoff of 51 bits Wed Jun 18 10:40:17 2008 polynomial 'A' values have 12 factors Wed Jun 18 14:37:22 2008 72231 relations (18362 full + 53869 combined from 958546 partial), need 71861 Wed Jun 18 14:37:26 2008 begin with 976908 relations Wed Jun 18 14:37:27 2008 reduce to 183295 relations in 10 passes Wed Jun 18 14:37:27 2008 attempting to read 183295 relations Wed Jun 18 14:37:32 2008 recovered 183295 relations Wed Jun 18 14:37:32 2008 recovered 163365 polynomials Wed Jun 18 14:37:33 2008 attempting to build 72231 cycles Wed Jun 18 14:37:33 2008 found 72231 cycles in 5 passes Wed Jun 18 14:37:33 2008 distribution of cycle lengths: Wed Jun 18 14:37:33 2008 length 1 : 18362 Wed Jun 18 14:37:33 2008 length 2 : 13186 Wed Jun 18 14:37:33 2008 length 3 : 12410 Wed Jun 18 14:37:33 2008 length 4 : 9670 Wed Jun 18 14:37:33 2008 length 5 : 7135 Wed Jun 18 14:37:33 2008 length 6 : 4786 Wed Jun 18 14:37:33 2008 length 7 : 2899 Wed Jun 18 14:37:33 2008 length 9+: 3783 Wed Jun 18 14:37:33 2008 largest cycle: 19 relations Wed Jun 18 14:37:33 2008 matrix is 71765 x 72231 (18.7 MB) with weight 4625287 (64.03/col) Wed Jun 18 14:37:33 2008 sparse part has weight 4625287 (64.03/col) Wed Jun 18 14:37:35 2008 filtering completed in 3 passes Wed Jun 18 14:37:35 2008 matrix is 67539 x 67603 (17.6 MB) with weight 4340466 (64.21/col) Wed Jun 18 14:37:35 2008 sparse part has weight 4340466 (64.21/col) Wed Jun 18 14:37:35 2008 saving the first 48 matrix rows for later Wed Jun 18 14:37:35 2008 matrix is 67491 x 67603 (11.0 MB) with weight 3412442 (50.48/col) Wed Jun 18 14:37:35 2008 sparse part has weight 2475447 (36.62/col) Wed Jun 18 14:37:35 2008 matrix includes 64 packed rows Wed Jun 18 14:37:35 2008 using block size 21845 for processor cache size 512 kB Wed Jun 18 14:37:36 2008 commencing Lanczos iteration Wed Jun 18 14:37:36 2008 memory use: 10.6 MB Wed Jun 18 14:38:25 2008 lanczos halted after 1069 iterations (dim = 67490) Wed Jun 18 14:38:25 2008 recovered 18 nontrivial dependencies Wed Jun 18 14:38:26 2008 prp41 factor: 68030424514091868787676449965273815693041 Wed Jun 18 14:38:26 2008 prp52 factor: 4827936880554905413919785453314420134437806840877729 Wed Jun 18 14:38:26 2008 elapsed time 03:58:10

(7·10¹¹⁹+17)/3 = 2(3)₁₁₈9_<120> = 47 · 1667 · 1598728711_<10> · 526853357803_<12> · C94
C94 = P43 · P52
P43 = 2487899235307330769877021031219003735293763_<43>
P52 = 1421169944438458969216053661423570617164050231393409_<52>

Wed Jun 18 14:47:16 2008 Msieve v. 1.36 Wed Jun 18 14:47:16 2008 random seeds: 31d20917 2261db0f Wed Jun 18 14:47:16 2008 factoring 3535727618010203827241863252367638975873802814867733018263403913509911611397412713507437008067 (94 digits) Wed Jun 18 14:47:17 2008 no P-1/P+1/ECM available, skipping Wed Jun 18 14:47:17 2008 commencing quadratic sieve (94-digit input) Wed Jun 18 14:47:18 2008 using multiplier of 3 Wed Jun 18 14:47:18 2008 using 64kb Pentium 4 sieve core Wed Jun 18 14:47:18 2008 sieve interval: 18 blocks of size 65536 Wed Jun 18 14:47:18 2008 processing polynomials in batches of 6 Wed Jun 18 14:47:18 2008 using a sieve bound of 2023201 (75294 primes) Wed Jun 18 14:47:18 2008 using large prime bound of 271108934 (28 bits) Wed Jun 18 14:47:18 2008 using double large prime bound of 1512372783942046 (42-51 bits) Wed Jun 18 14:47:18 2008 using trial factoring cutoff of 51 bits Wed Jun 18 14:47:18 2008 polynomial 'A' values have 12 factors Wed Jun 18 20:40:18 2008 75496 relations (18487 full + 57009 combined from 1076904 partial), need 75390 Wed Jun 18 20:40:22 2008 begin with 1095391 relations Wed Jun 18 20:40:23 2008 reduce to 196684 relations in 12 passes Wed Jun 18 20:40:23 2008 attempting to read 196684 relations Wed Jun 18 20:40:29 2008 recovered 196684 relations Wed Jun 18 20:40:29 2008 recovered 181534 polynomials Wed Jun 18 20:40:29 2008 attempting to build 75496 cycles Wed Jun 18 20:40:30 2008 found 75496 cycles in 6 passes Wed Jun 18 20:40:30 2008 distribution of cycle lengths: Wed Jun 18 20:40:30 2008 length 1 : 18487 Wed Jun 18 20:40:30 2008 length 2 : 13231 Wed Jun 18 20:40:30 2008 length 3 : 12825 Wed Jun 18 20:40:30 2008 length 4 : 10112 Wed Jun 18 20:40:30 2008 length 5 : 7521 Wed Jun 18 20:40:30 2008 length 6 : 5337 Wed Jun 18 20:40:30 2008 length 7 : 3381 Wed Jun 18 20:40:30 2008 length 9+: 4602 Wed Jun 18 20:40:30 2008 largest cycle: 21 relations Wed Jun 18 20:40:30 2008 matrix is 75294 x 75496 (19.6 MB) with weight 4844871 (64.17/col) Wed Jun 18 20:40:30 2008 sparse part has weight 4844871 (64.17/col) Wed Jun 18 20:40:31 2008 filtering completed in 3 passes Wed Jun 18 20:40:31 2008 matrix is 71867 x 71931 (18.8 MB) with weight 4647852 (64.62/col) Wed Jun 18 20:40:31 2008 sparse part has weight 4647852 (64.62/col) Wed Jun 18 20:40:32 2008 saving the first 48 matrix rows for later Wed Jun 18 20:40:32 2008 matrix is 71819 x 71931 (11.7 MB) with weight 3646166 (50.69/col) Wed Jun 18 20:40:32 2008 sparse part has weight 2648356 (36.82/col) Wed Jun 18 20:40:32 2008 matrix includes 64 packed rows Wed Jun 18 20:40:32 2008 using block size 21845 for processor cache size 512 kB Wed Jun 18 20:40:33 2008 commencing Lanczos iteration Wed Jun 18 20:40:33 2008 memory use: 11.5 MB Wed Jun 18 20:41:29 2008 lanczos halted after 1137 iterations (dim = 71817) Wed Jun 18 20:41:29 2008 recovered 17 nontrivial dependencies Wed Jun 18 20:41:31 2008 prp43 factor: 2487899235307330769877021031219003735293763 Wed Jun 18 20:41:31 2008 prp52 factor: 1421169944438458969216053661423570617164050231393409 Wed Jun 18 20:41:31 2008 elapsed time 05:54:15

(7·10¹⁴²+17)/3 = 2(3)₁₄₁9_<143> = 239 · 359 · 3864886943178480283_<19> · C119
C119 = P46 · P73
P46 = 8736112065016231832182289058545466897704748911_<46>
P73 = 8054330474086409141498305541361295838218114061746685318944976380558270903_<73>

Number: 23339_142 N=70363533630294185294165706482946113409918647922182584068184418398232967632488922819202335829444250304263960981932236633 ( 119 digits) SNFS difficulty: 142 digits. Divisors found: r1=8736112065016231832182289058545466897704748911 (pp46) r2=8054330474086409141498305541361295838218114061746685318944976380558270903 (pp73) Version: GGNFS-0.77.1-20060513-k8 Total time: 18.48 hours. Scaled time: 37.14 units (timescale=2.010). Factorization parameters were as follows: name: 23339_142 n: 70363533630294185294165706482946113409918647922182584068184418398232967632488922819202335829444250304263960981932236633 m: 10000000000000000000000000000 c5: 700 c0: 17 skew: 0.48 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [650000, 2750001) Primes: RFBsize:100021, AFBsize:100193, largePrimes:2963927 encountered Relations: rels:3028488, finalFF:283712 Max relations in full relation-set: 28 Initial matrix: 200281 x 283712 with sparse part having weight 33966330. Pruned matrix : 180243 x 181308 with weight 20552126. Total sieving time: 17.84 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.44 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,142,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 18.48 hours. --------- CPU info (if available) ----------

Jun 18, 2008 (2nd)

By Jo Yeong Uk / GGNFS
(19·10¹⁷⁵+71)/9 = 2(1)₁₇₄9_<176> = C176
C176 = P80 · P96
P80 = 60850084350740294278005008684441134760052865768236487179773355418574426998451693_<80>
P96 = 346936431335518371490342055169677665804525006321550138544617865907161312009720281338190068074283_<96>

Number: 21119_175 N=21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111119 ( 176 digits) SNFS difficulty: 176 digits. Divisors found: r1=60850084350740294278005008684441134760052865768236487179773355418574426998451693 (pp80) r2=346936431335518371490342055169677665804525006321550138544617865907161312009720281338190068074283 (pp96) Version: GGNFS-0.77.1-20050930-nocona Total time: 155.75 hours. Scaled time: 367.09 units (timescale=2.357). Factorization parameters were as follows: n: 21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111119 m: 100000000000000000000000000000000000 c5: 19 c0: 71 skew: 1.3 type: snfs Factor base limits: 8400000/8400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved algebraic special-q in [4200000, 7100001) Primes: RFBsize:564877, AFBsize:565827, largePrimes:10879977 encountered Relations: rels:10992982, finalFF:1297142 Max relations in full relation-set: 28 Initial matrix: 1130769 x 1297142 with sparse part having weight 89502042. Pruned matrix : 985530 x 991247 with weight 62042272. Total sieving time: 147.48 hours. Total relation processing time: 0.17 hours. Matrix solve time: 7.98 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,176,5,0,0,0,0,0,0,0,0,8400000,8400000,28,28,50,50,2.6,2.6,100000 total time: 155.75 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: 8047200k/8912896k available (2440k kernel code, 339088k reserved, 1234k data, 192k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805) Calibrating delay using timer specific routine.. 5344.81 BogoMIPS (lpj=2672409) Calibrating delay using timer specific routine.. 5344.41 BogoMIPS (lpj=2672208) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672385)

Jun 18, 2008

By Robert Backstrom / GMP-ECM, GGNFS, Msieve
(7·10¹⁰²+17)/3 = 2(3)₁₀₁9_<103> = C103
C103 = P34 · P69
P34 = 6419956900481202228469077758003149_<34>
P69 = 363449999665642674884178819352787543464290520450591658241900375546311_<69>
(7·10¹⁵³+17)/3 = 2(3)₁₅₂9_<154> = 560459 · 230304748630662063984749951147_<30> · 262935549327310361422795083043_<30> · C89
C89 = P40 · P50
P40 = 1895549872520483456073059398581094704841_<40>
P50 = 36269830185861666534847203262383843474869227650761_<50>

Wed Jun 18 08:10:17 2008 Wed Jun 18 08:10:17 2008 Wed Jun 18 08:10:17 2008 Msieve v. 1.36 Wed Jun 18 08:10:17 2008 random seeds: 6aa74100 9e706eaf Wed Jun 18 08:10:17 2008 factoring 68751271985149664776156554199563981434395577319158661478300292012981830544670599124034001 (89 digits) Wed Jun 18 08:10:18 2008 searching for 15-digit factors Wed Jun 18 08:10:19 2008 commencing quadratic sieve (89-digit input) Wed Jun 18 08:10:19 2008 using multiplier of 5 Wed Jun 18 08:10:19 2008 using 64kb Opteron sieve core Wed Jun 18 08:10:19 2008 sieve interval: 17 blocks of size 65536 Wed Jun 18 08:10:19 2008 processing polynomials in batches of 6 Wed Jun 18 08:10:19 2008 using a sieve bound of 1564307 (59333 primes) Wed Jun 18 08:10:19 2008 using large prime bound of 125144560 (26 bits) Wed Jun 18 08:10:19 2008 using double large prime bound of 376132987801280 (42-49 bits) Wed Jun 18 08:10:19 2008 using trial factoring cutoff of 49 bits Wed Jun 18 08:10:19 2008 polynomial 'A' values have 11 factors Wed Jun 18 08:50:40 2008 59748 relations (16594 full + 43154 combined from 626616 partial), need 59429 Wed Jun 18 08:50:41 2008 begin with 643209 relations Wed Jun 18 08:50:41 2008 reduce to 143702 relations in 11 passes Wed Jun 18 08:50:41 2008 attempting to read 143702 relations Wed Jun 18 08:50:42 2008 recovered 143702 relations Wed Jun 18 08:50:42 2008 recovered 117032 polynomials Wed Jun 18 08:50:43 2008 attempting to build 59748 cycles Wed Jun 18 08:50:43 2008 found 59748 cycles in 5 passes Wed Jun 18 08:50:43 2008 distribution of cycle lengths: Wed Jun 18 08:50:43 2008 length 1 : 16594 Wed Jun 18 08:50:43 2008 length 2 : 11669 Wed Jun 18 08:50:43 2008 length 3 : 10367 Wed Jun 18 08:50:43 2008 length 4 : 7898 Wed Jun 18 08:50:43 2008 length 5 : 5487 Wed Jun 18 08:50:43 2008 length 6 : 3538 Wed Jun 18 08:50:43 2008 length 7 : 1911 Wed Jun 18 08:50:43 2008 length 9+: 2284 Wed Jun 18 08:50:43 2008 largest cycle: 18 relations Wed Jun 18 08:50:43 2008 matrix is 59333 x 59748 (14.6 MB) with weight 3578395 (59.89/col) Wed Jun 18 08:50:43 2008 sparse part has weight 3578395 (59.89/col) Wed Jun 18 08:50:44 2008 filtering completed in 3 passes Wed Jun 18 08:50:44 2008 matrix is 54872 x 54936 (13.5 MB) with weight 3307764 (60.21/col) Wed Jun 18 08:50:44 2008 sparse part has weight 3307764 (60.21/col) Wed Jun 18 08:50:44 2008 saving the first 48 matrix rows for later Wed Jun 18 08:50:44 2008 matrix is 54824 x 54936 (10.0 MB) with weight 2755556 (50.16/col) Wed Jun 18 08:50:44 2008 sparse part has weight 2295339 (41.78/col) Wed Jun 18 08:50:44 2008 matrix includes 64 packed rows Wed Jun 18 08:50:44 2008 using block size 21974 for processor cache size 1024 kB Wed Jun 18 08:50:44 2008 commencing Lanczos iteration Wed Jun 18 08:50:44 2008 memory use: 9.0 MB Wed Jun 18 08:51:06 2008 lanczos halted after 868 iterations (dim = 54822) Wed Jun 18 08:51:06 2008 recovered 16 nontrivial dependencies Wed Jun 18 08:51:07 2008 prp40 factor: 1895549872520483456073059398581094704841 Wed Jun 18 08:51:07 2008 prp50 factor: 36269830185861666534847203262383843474869227650761 Wed Jun 18 08:51:07 2008 elapsed time 00:40:50

(7·10¹⁰⁴+17)/3 = 2(3)₁₀₃9_<105> = 1549 · 431213149 · C93
C93 = P38 · P55
P38 = 84021039913865811864528095862181648183_<38>
P55 = 4157625043236494780959904525049407778407073398238277733_<55>

Number: n N=349327979704661599779941625272810754908557163679461621704641746110472048389941659397248809139 ( 93 digits) SNFS difficulty: 105 digits. Divisors found: r1=84021039913865811864528095862181648183 (pp38) r2=4157625043236494780959904525049407778407073398238277733 (pp55) Version: GGNFS-0.77.1-20051202-athlon Total time: 0.70 hours. Scaled time: 1.27 units (timescale=1.829). Factorization parameters were as follows: name: KA_2_3_103_9 n: 349327979704661599779941625272810754908557163679461621704641746110472048389941659397248809139 skew: 1.89 deg: 5 c5: 7 c0: 170 m: 1000000000000000000000 type: snfs rlim: 600000 alim: 600000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 160001) Primes: RFBsize:49098, AFBsize:49011, largePrimes:4196488 encountered Relations: rels:3702660, finalFF:250006 Max relations in full relation-set: 48 Initial matrix: 98174 x 250005 with sparse part having weight 17311302. Pruned matrix : 56789 x 57343 with weight 2371582. Total sieving time: 0.63 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.01 hours. Total square root time: 0.01 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,105,5,0,0,0,0,0,0,0,0,600000,600000,28,28,48,48,2.5,2.5,50000 total time: 0.70 hours. --------- CPU info (if available) ----------

(19·10¹⁵⁷+71)/9 = 2(1)₁₅₆9_<158> = 149 · 331 · 447977019071_<12> · C141
C141 = P68 · P74
P68 = 77929169194250521052812225269081813650033303291080915556048887978241_<68>
P74 = 12261427866582958791184193364468933936256879057608293595733557701239457191_<74>

Number: n N=955522886778041600093440240348014365106179622949600182179310014977255835521154610734965233983597443817269068745577149968079675757884258981031 ( 141 digits) SNFS difficulty: 158 digits. Divisors found: Wed Jun 18 10:38:00 2008 prp68 factor: 77929169194250521052812225269081813650033303291080915556048887978241 Wed Jun 18 10:38:00 2008 prp74 factor: 12261427866582958791184193364468933936256879057608293595733557701239457191 Wed Jun 18 10:38:00 2008 elapsed time 01:11:42 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 35.86 hours. Scaled time: 51.68 units (timescale=1.441). Factorization parameters were as follows: name: KA_2_1_156_9 n: 955522886778041600093440240348014365106179622949600182179310014977255835521154610734965233983597443817269068745577149968079675757884258981031 skew: 0.52 deg: 5 c5: 1900 c0: 71 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 1800167) Primes: RFBsize:216816, AFBsize:217002, largePrimes:7060869 encountered Relations: rels:6477932, finalFF:461756 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 35.65 hours. Total relation processing time: 0.21 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 35.86 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

(7·10¹¹¹+17)/3 = 2(3)₁₁₀9_<112> = 31 · 283 · C108
C108 = P42 · P67
P42 = 141365583583934397402332467178657836374287_<42>
P67 = 1881416574075439492986128061851660298139048768985554696504455656689_<67>

Number: n N=265967551958661043352710969261750066491887989665260838177742315437516622971997416315209544435578859379155743 ( 108 digits) SNFS difficulty: 111 digits. Divisors found: r1=141365583583934397402332467178657836374287 (pp42) r2=1881416574075439492986128061851660298139048768985554696504455656689 (pp67) Version: GGNFS-0.77.1-20051202-athlon Total time: 0.71 hours. Scaled time: 1.30 units (timescale=1.818). Factorization parameters were as follows: name: KA_2_3_110_9 n: 265967551958661043352710969261750066491887989665260838177742315437516622971997416315209544435578859379155743 skew: 0.75 deg: 5 c5: 70 c0: 17 m: 10000000000000000000000 type: snfs rlim: 600000 alim: 600000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 160001) Primes: RFBsize:49098, AFBsize:49186, largePrimes:3947445 encountered Relations: rels:3357682, finalFF:166084 Max relations in full relation-set: 48 Initial matrix: 98351 x 166084 with sparse part having weight 12282582. Pruned matrix : 73535 x 74090 with weight 3129235. Total sieving time: 0.63 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.02 hours. Total square root time: 0.02 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,111,5,0,0,0,0,0,0,0,0,600000,600000,28,28,48,48,2.5,2.5,50000 total time: 0.71 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

(7·10¹¹³+17)/3 = 2(3)₁₁₂9_<114> = 19 · 29 · 10193 · 73999 · C102
C102 = P40 · P62
P40 = 8339601674524220895513383477312681123489_<40>
P62 = 67321224002953796493692732850668437799328402691094933774632243_<62>

Number: n N=561432192426053654517340771240223116430397943672531177239167575604615218442742295215856972269044055827 ( 102 digits) SNFS difficulty: 113 digits. Divisors found: r1=8339601674524220895513383477312681123489 (pp40) r2=67321224002953796493692732850668437799328402691094933774632243 (pp62) Version: GGNFS-0.77.1-20051202-athlon Total time: 1.10 hours. Scaled time: 1.58 units (timescale=1.443). Factorization parameters were as follows: name: KA_2_3_112_9 n: 561432192426053654517340771240223116430397943672531177239167575604615218442742295215856972269044055827 skew: 0.30 deg: 5 c5: 7000 c0: 17 m: 10000000000000000000000 type: snfs rlim: 600000 alim: 600000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 180001) Primes: RFBsize:49098, AFBsize:49326, largePrimes:3980336 encountered Relations: rels:3357490, finalFF:133469 Max relations in full relation-set: 28 Initial matrix: 98491 x 133469 with sparse part having weight 9073890. Pruned matrix : 84080 x 84636 with weight 3936525. Total sieving time: 0.94 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.05 hours. Total square root time: 0.03 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,113,5,0,0,0,0,0,0,0,0,600000,600000,28,28,48,48,2.5,2.5,50000 total time: 1.10 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

(19·10¹⁶¹+71)/9 = 2(1)₁₆₀9_<162> = 3⁵ · C159
C159 = P30 · P57 · P74
P30 = 286786067147872235350150512053_<30>
P57 = 112622410320040502526431761387219772249611150037774127671_<57>
P74 = 26898121553328486879024622069541410307556323510188262663095503894721747591_<74>

Number: n N=3029331282417286052913425605800649802144685572686579710389061333460545261055441205830769603801466446700995622384536686522670690561 ( 130 digits) SNFS difficulty: 162 digits. Divisors found: Wed Jun 18 21:16:51 2008 prp57 factor: 112622410320040502526431761387219772249611150037774127671 Wed Jun 18 21:16:51 2008 prp74 factor: 26898121553328486879024622069541410307556323510188262663095503894721747591 Wed Jun 18 21:16:51 2008 elapsed time 01:28:47 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 47.58 hours. Scaled time: 87.02 units (timescale=1.829). Factorization parameters were as follows: name: KA_2_1_160_9 n: 3029331282417286052913425605800649802144685572686579710389061333460545261055441205830769603801466446700995622384536686522670690561 skew: 0.82 deg: 5 c5: 190 c0: 71 m: 100000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 3300203) Primes: RFBsize:216816, AFBsize:216642, largePrimes:7501597 encountered Relations: rels:6884203, finalFF:446447 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 47.36 hours. Total relation processing time: 0.22 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 47.58 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

Jun 17, 2008 (4th)

By matsui / GGNFS
2·10¹⁷⁴-7 = 1(9)₁₇₃3_<175> = 45162104857_<11> · C164
C164 = P50 · P115
P50 = 15567016412456914292718994439665667659340737216997_<50>
P115 = 2844791473480904522073711775181098198268760967308959673803332033658988249807406032658488263343289877533029503274317_<115>

N=44284915557694729347765040994665790317727838758514044960205208090042409601502511298241282501081457510774761806182217110651884955832318902850555861105887073645966049 ( 164 digits) SNFS difficulty: 175 digits. Divisors found: r1=15567016412456914292718994439665667659340737216997 (pp50) r2=2844791473480904522073711775181098198268760967308959673803332033658988249807406032658488263343289877533029503274317 (pp115) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 243.25 hours. Scaled time: 308.92 units (timescale=1.270). Factorization parameters were as follows: n: 44284915557694729347765040994665790317727838758514044960205208090042409601502511298241282501081457510774761806182217110651884955832318902850555861105887073645966049 m: 100000000000000000000000000000000000 c5: 1 c0: -35 skew: 2.04 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 11600001) Primes: RFBsize:501962, AFBsize:501746, largePrimes:6521482 encountered Relations: rels:6972572, finalFF:1128905 Max relations in full relation-set: 28 Initial matrix: 1003772 x 1128905 with sparse part having weight 73472770. Pruned matrix : 897602 x 902684 with weight 56663657. Total sieving time: 203.55 hours. Total relation processing time: 0.14 hours. Matrix solve time: 39.17 hours. Time per square root: 0.39 hours. Prototype def-par.txt line would be: snfs,175,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 243.25 hours.

Jun 17, 2008 (3rd)

By suberi / GMP-ECM
(16·10²⁴⁷-61)/9 = 1(7)₂₄₆1_<248> = 11 · 1519462863204010887343118174303851_<34> · C214
C214 = P40 · P174
P40 = 2446972297993506364536910147344312252817_<40>
P174 = 434675983297164654943064917508776598208565289076376758993205934839973130416427780890879508995035601216645271796689898925197909151263983145235974828216649664885501680694980083_<174>

Jun 17, 2008 (2nd)

By Sinkiti Sibata / GGNFS
(19·10¹⁵²+71)/9 = 2(1)₁₅₁9_<153> = 3² · 5495167 · C145
C145 = P49 · P96
P49 = 4901819949628641796466086337480125061060531270983_<49>
P96 = 870823883755497713499331899758122000845092549202887776729665908427056553088983618255881653274831_<96>

Number: 21119_152 N=4268621886005792021144542126464362252040163679003165895314335328381610626839328108400852990174236765408001271564047120580100681827647844634528873 ( 145 digits) SNFS difficulty: 153 digits. Divisors found: r1=4901819949628641796466086337480125061060531270983 (pp49) r2=870823883755497713499331899758122000845092549202887776729665908427056553088983618255881653274831 (pp96) Version: GGNFS-0.77.1-20060513-k8 Total time: 35.70 hours. Scaled time: 71.08 units (timescale=1.991). Factorization parameters were as follows: name: 21119_152 n: 4268621886005792021144542126464362252040163679003165895314335328381610626839328108400852990174236765408001271564047120580100681827647844634528873 m: 1000000000000000000000000000000 c5: 1900 c0: 71 skew: 0.52 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2500001) Primes: RFBsize:176302, AFBsize:176824, largePrimes:5811367 encountered Relations: rels:5835518, finalFF:527410 Max relations in full relation-set: 28 Initial matrix: 353193 x 527410 with sparse part having weight 54511221. Pruned matrix : 293898 x 295727 with weight 31266050. Total sieving time: 33.99 hours. Total relation processing time: 0.16 hours. Matrix solve time: 1.40 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 35.70 hours. --------- CPU info (if available) ----------

Jun 17, 2008

The factor table of 233...339 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Jun 16, 2008 (3rd)

By Robert Backstrom / GMP-ECM
(19·10¹⁶⁷+71)/9 = 2(1)₁₆₆9_<168> = 3 · 2243 · 235493 · C159
C159 = P44 · P116
P44 = 10766075811599655430741404354340972913661347_<44>
P116 = 12374427833338457331814433209166661760078812457314883748540314012065840097373485608599199199387260515247162077378041_<116>

Jun 16, 2008 (2nd)

By suberi / GMP-ECM
(17·10¹⁸¹+1)/9 = 1(8)₁₈₀9_<182> = 19 · 44839 · 48731 · 1008779 · 12003314779_<11> · 5830558817883227437007237_<25> · C130
C130 = P30 · C100
P30 = 758822763085731218605641418771_<30>
C100 = [8492661409590470524891423727868139850632579649757129010224121294326903739481230882899276916193096537_<100>]
(17·10¹⁹⁰+1)/9 = 1(8)₁₈₉9_<191> = 13 · 649123 · 707912267722698978623_<21> · C163
C163 = P32 · C132
P32 = 24592951456281913764228758669239_<32>
C132 = [128571873140924523664948060149189103090155858942672937006248438418113765818485839629694932311203935787591124351688800743261858830663_<132>]

Jun 16, 2008

By Sinkiti Sibata / GGNFS
(19·10¹⁷⁸+71)/9 = 2(1)₁₇₇9_<179> = 7 · 73 · 107 · 173 · 35321990716170607082142191_<26> · 3823874316784361716576388467133_<31> · C116
C116 = P29 · P87
P29 = 27406547521000446067339104767_<29>
P87 = 602916541684842867507687365160027289170544020368979297591614953242064948580130894740539_<87>

Number: 21119_178 N=16523860850882892395144792212261432649907044400229056482377148949941650807074754921165115690888775495900605003049413 ( 116 digits) Divisors found: r1=27406547521000446067339104767 (pp29) r2=602916541684842867507687365160027289170544020368979297591614953242064948580130894740539 (pp87) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 73.94 hours. Scaled time: 49.98 units (timescale=0.676). Factorization parameters were as follows: name: 21119_178 n: 16523860850882892395144792212261432649907044400229056482377148949941650807074754921165115690888775495900605003049413 skew: 40127.03 # norm 7.16e+15 c5: 40080 c4: -7945983226 c3: -232895586882496 c2: 10778743211792435213 c1: 140457272524332146727036 c0: -2681001619694258614734421287 # alpha -5.71 Y1: 2400596004961 Y0: -13275163457864381099522 # Murphy_E 4.83e-10 # M 4699310249935613700118238101142154720824295796173609648981454158679885067087264384430956907404713390557562756410728 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2250000, 3630001) Primes: RFBsize:315948, AFBsize:315637, largePrimes:7499982 encountered Relations: rels:7511772, finalFF:737157 Max relations in full relation-set: 28 Initial matrix: 631664 x 737157 with sparse part having weight 56387280. Pruned matrix : 538707 x 541929 with weight 34822728. Polynomial selection time: 3.11 hours. Total sieving time: 56.46 hours. Total relation processing time: 0.53 hours. Matrix solve time: 13.40 hours. Time per square root: 0.44 hours. Prototype def-par.txt line would be: gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 73.94 hours. --------- CPU info (if available) ----------

(19·10¹⁵¹+71)/9 = 2(1)₁₅₀9_<152> = 389 · 46451 · 38559392769341_<14> · C131
C131 = P42 · P90
P42 = 123898729947282037215260261192283618233521_<42>
P90 = 244550965417535587962509097180011853513331875232412883300691306397524357045415864687563861_<90>

Number: 21119_151 N=30299554022614350384504348767263079177531164143037702442023852003276625984676290612901044365561203878923175331353497936833698384581 ( 131 digits) SNFS difficulty: 152 digits. Divisors found: r1=123898729947282037215260261192283618233521 (pp42) r2=244550965417535587962509097180011853513331875232412883300691306397524357045415864687563861 (pp90) Version: GGNFS-0.77.1-20060513-k8 Total time: 35.56 hours. Scaled time: 70.79 units (timescale=1.991). Factorization parameters were as follows: name: 21119_151 n: 30299554022614350384504348767263079177531164143037702442023852003276625984676290612901044365561203878923175331353497936833698384581 m: 1000000000000000000000000000000 c5: 190 c0: 71 skew: 0.82 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2500001) Primes: RFBsize:176302, AFBsize:176344, largePrimes:5725559 encountered Relations: rels:5654649, finalFF:438134 Max relations in full relation-set: 28 Initial matrix: 352713 x 438134 with sparse part having weight 46113828. Pruned matrix : 323557 x 325384 with weight 31379717. Total sieving time: 33.71 hours. Total relation processing time: 0.15 hours. Matrix solve time: 1.52 hours. Time per square root: 0.17 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 35.56 hours. --------- CPU info (if available) ----------

Jun 15, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve
(82·10¹⁸⁵-1)/9 = 9(1)_185<186> = 773 · C184
C184 = P88 · P96
P88 = 4548789624633850866889146735134298403699896616070473264408962177272708854038293242583257_<88>
P96 = 259117053935733073539510463672622076339997265026506332376996259338801062100873517406377001946451_<96>

Number: n N=1178668966508552537013080350725887595227828086819031191605577116573235590053183843610751760816443869483972976857841023429639212304154089406353313209716831967802213597815150208423170907 ( 184 digits) SNFS difficulty: 186 digits. Divisors found: Mon Jun 16 00:16:49 2008 prp88 factor: 4548789624633850866889146735134298403699896616070473264408962177272708854038293242583257 Mon Jun 16 00:16:49 2008 prp96 factor: 259117053935733073539510463672622076339997265026506332376996259338801062100873517406377001946451 Mon Jun 16 00:16:49 2008 elapsed time 02:53:05 (Msieve 1.34) Version: GGNFS-0.77.1-20050930-k8 Total time: 96.97 hours. Scaled time: 81.16 units (timescale=0.837). Factorization parameters were as follows: name: KA_9_1_185 n: 1178668966508552537013080350725887595227828086819031191605577116573235590053183843610751760816443869483972976857841023429639212304154089406353313209716831967802213597815150208423170907 type: snfs skew: 0.41 deg: 5 c5: 82 c0: -1 m: 10000000000000000000000000000000000000 rlim: 7000000 alim: 7000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 7000000/7000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 13400077) Primes: RFBsize:476648, AFBsize:476605, largePrimes:9021915 encountered Relations: rels:8836726, finalFF:1037910 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 96.58 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,186,5,0,0,0,0,0,0,0,0,7000000,7000000,28,28,48,48,2.6,2.6,100000 total time: 96.97 hours. --------- CPU info (if available) ----------

Jun 15, 2008 (2nd)

By Sinkiti Sibata / GGNFS
(19·10¹⁴⁸+71)/9 = 2(1)₁₄₇9_<149> = 7 · 47 · 417006279637_<12> · C135
C135 = P37 · P48 · P51
P37 = 1665401849509587677728439136819520339_<37>
P48 = 396630940851504929651395216684056457143555288557_<48>
P51 = 232952280196970654163617482290594633816545512331261_<51>

Number: 21119_148 N=153876605963533264497237871153137488274836088714222638533355576644654978814571391424895423745228899363662939247215583153132173003687803 ( 135 digits) SNFS difficulty: 149 digits. Divisors found: r1=1665401849509587677728439136819520339 (pp37) r2=396630940851504929651395216684056457143555288557 (pp48) r3=232952280196970654163617482290594633816545512331261 (pp51) Version: GGNFS-0.77.1-20060513-k8 Total time: 41.46 hours. Scaled time: 83.04 units (timescale=2.003). Factorization parameters were as follows: name: 21119_148 n: 153876605963533264497237871153137488274836088714222638533355576644654978814571391424895423745228899363662939247215583153132173003687803 m: 100000000000000000000000000000 c5: 19000 c0: 71 skew: 0.33 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [750000, 5650001) Primes: RFBsize:114155, AFBsize:114198, largePrimes:3268956 encountered Relations: rels:3440669, finalFF:266667 Max relations in full relation-set: 28 Initial matrix: 228420 x 266667 with sparse part having weight 36402146. Pruned matrix : 218879 x 220085 with weight 29047573. Total sieving time: 40.45 hours. Total relation processing time: 0.18 hours. Matrix solve time: 0.70 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: snfs,149,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 41.46 hours. --------- CPU info (if available) ----------

Jun 15, 2008

By Kenji Ibusuki / GGNFS
(5·10¹⁷⁵+1)/3 = 1(6)₁₇₄7_<176> = 827 · C173
C173 = P80 · P93
P80 = 74865668108657376632912517989779780300464176273350461362789666667834688689397123_<80>
P93 = 269190999771828025899329511919947740033568840333403347746509215638814772035381976837532003227_<93>

Number: 16667_175 N=20153164046755340588472390165255945183393792825473599355098750503829101168883514711809754131398629584844820636839983877468762595727529222087867795243853284965739621120515921 ( 173 digits) SNFS difficulty: 175 digits. Divisors found: r1=74865668108657376632912517989779780300464176273350461362789666667834688689397123 (pp80) r2=269190999771828025899329511919947740033568840333403347746509215638814772035381976837532003227 (pp93) Version: GGNFS-0.77.1 Total time: 127.09 hours. Scaled time: 369.83 units (timescale=2.910). Factorization parameters were as follows: n: 20153164046755340588472390165255945183393792825473599355098750503829101168883514711809754131398629584844820636839983877468762595727529222087867795243853284965739621120515921 m: 100000000000000000000000000000000000 c5: 5 c0: 1 skew: 0.725 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [3700000, 9800001) Relations: rels:6928497, finalFF:1184727 Initial matrix: 1003098 x 1184727 with sparse part having weight 67068111. Pruned matrix : 926698 x 931777 with weight 43275106. Total sieving time: 122.35 hours. Total relation processing time: 0.14 hours. Matrix solve time: 4.46 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,175,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 127.09 hours. --------- CPU info (if available) ----------

Jun 14, 2008 (4th)

By Wataru Sakai / GGNFS
10¹⁸⁹-9 = (9)₁₈₈1_<189> = 680546965633716247679_<21> · 210016417538123401200815971279_<30> · C139
C139 = P49 · P90
P49 = 8147900155250040965434833800626154533552907527597_<49>
P90 = 858702947397860145236409007951942850049599814990863975327405594646045661188912043740978083_<90>

Number: 99991_189 N=6996625878416692438029157723410875624263386189411081125190307294339622079250688809160942796831099033973415942935043602179220749546094656551 ( 139 digits) SNFS difficulty: 190 digits. Divisors found: r1=8147900155250040965434833800626154533552907527597 (pp49) r2=858702947397860145236409007951942850049599814990863975327405594646045661188912043740978083 (pp90) Version: GGNFS-0.77.1-20060722-nocona Total time: 1147.35 hours. Scaled time: 2311.91 units (timescale=2.015). Factorization parameters were as follows: n: 6996625878416692438029157723410875624263386189411081125190307294339622079250688809160942796831099033973415942935043602179220749546094656551 m: 100000000000000000000000000000000000000 c5: 1 c0: -90 skew: 2.46 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 19900001) Primes: RFBsize:501962, AFBsize:502106, largePrimes:7170030 encountered Relations: rels:7740301, finalFF:1148030 Max relations in full relation-set: 32 Initial matrix: 1004132 x 1148030 with sparse part having weight 138656677. Pruned matrix : 902449 x 907533 with weight 118637521. Total sieving time: 1134.16 hours. Total relation processing time: 0.15 hours. Matrix solve time: 12.76 hours. Time per square root: 0.28 hours. Prototype def-par.txt line would be: snfs,190,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 1147.35 hours.

(7·10¹⁶⁹-61)/9 = (7)₁₆₈1_<169> = 83 · 10855381 · C160
C160 = P34 · P37 · P90
P34 = 2283299320810328736384747634415821_<34>
P37 = 7182607341442258629005707341782603917_<37>
P90 = 526365474032812165742184427823758439905684973552785490890082763434216262625675882189775261_<90>

Number: 77771_169 N=8632416125912358472599711150945987261239466130360599340201719910084255418766178636140990039845884947093500679833045032154108060156156409675885963645590464968677 ( 160 digits) SNFS difficulty: 170 digits. Divisors found: r1=2283299320810328736384747634415821 (pp34) r2=7182607341442258629005707341782603917 (pp37) r3=526365474032812165742184427823758439905684973552785490890082763434216262625675882189775261 (pp90) Version: GGNFS-0.77.1-20060722-nocona Total time: 169.71 hours. Scaled time: 340.62 units (timescale=2.007). Factorization parameters were as follows: n: 8632416125912358472599711150945987261239466130360599340201719910084255418766178636140990039845884947093500679833045032154108060156156409675885963645590464968677 m: 10000000000000000000000000000000000 c5: 7 c0: -610 skew: 2.44 type: snfsFactor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3000000, 9400001) Primes: RFBsize:412849, AFBsize:413557, largePrimes:6523136 encountered Relations: rels:6974496, finalFF:1087069 Max relations in full relation-set: 32 Initial matrix: 826471 x 1087069 with sparse part having weight 90460735. Pruned matrix : 620311 x 624507 with weight 73420826. Total sieving time: 165.44 hours. Total relation processing time: 0.11 hours. Matrix solve time: 3.97 hours. Time per square root: 0.20 hours. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000 total time: 169.71 hours.

Jun 14, 2008 (3rd)

By Wataru Sakai / GGNFS
(8·10¹⁶⁸-53)/9 = (8)₁₆₇3_<168> = 115509593 · C160
C160 = P25 · P36 · P100
P25 = 4168773560957646476042689_<25>
P36 = 496029423131682367523442139895210347_<36>
P100 = 3721462779361461935113578380790887976223197458450833632455359550260813918839667749389547619007630657_<100>

Number: 88883_168 N=7695368547345577513106542492006606662434425588261651037839678725981563184010949539826435791258383958541771408448204720874472208458815095027552290733886395815531 ( 160 digits) SNFS difficulty: 168 digits. Divisors found: r1=4168773560957646476042689 (pp25) r2=496029423131682367523442139895210347 (pp36) r3=3721462779361461935113578380790887976223197458450833632455359550260813918839667749389547619007630657 (pp100) Version: GGNFS-0.77.1-20060722-nocona Total time: 143.40 hours. Scaled time: 283.22 units (timescale=1.975). Factorization parameters were as follows: n: 7695368547345577513106542492006606662434425588261651037839678725981563184010949539826435791258383958541771408448204720874472208458815095027552290733886395815531 m: 2000000000000000000000000000000000 c5: 250 c0: -53 skew: 0.73 type: snfs Factor base limits: 5500000/5500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2750000, 7750001) Primes: RFBsize:380800, AFBsize:380967, largePrimes:6441404 encountered Relations: rels:6900311, finalFF:1078860 Max relations in full relation-set: 32 Initial matrix: 761833 x 1078860 with sparse part having weight 88535141. Pruned matrix : 523358 x 527231 with weight 78341106. Total sieving time: 140.02 hours. Total relation processing time: 0.10 hours. Matrix solve time: 3.11 hours. Time per square root: 0.17 hours. Prototype def-par.txt line would be: snfs,168,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.6,2.6,100000 total time: 143.40 hours.

Jun 14, 2008 (2nd)

By Sinkiti Sibata / GGNFS
(19·10¹⁴⁷+71)/9 = 2(1)₁₄₆9_<148> = 13 · 59 · 887 · C142
C142 = P46 · P96
P46 = 3726369897506049222488673132552815264516392147_<46>
P96 = 832733708305847517955059751402619654460601103742913699994890502633673002797961698240750355056813_<96>

Number: 21119_147 N=3103073823269493305608185320794955251225673330272722625540159409801891601138730101334958690738026912142670841770836038315449012332431972047511 ( 142 digits) SNFS difficulty: 148 digits. Divisors found: r1=3726369897506049222488673132552815264516392147 (pp46) r2=832733708305847517955059751402619654460601103742913699994890502633673002797961698240750355056813 (pp96) Version: GGNFS-0.77.1-20060513-k8 Total time: 32.77 hours. Scaled time: 65.86 units (timescale=2.010). Factorization parameters were as follows: name: 21119_147 n: 3103073823269493305608185320794955251225673330272722625540159409801891601138730101334958690738026912142670841770836038315449012332431972047511 m: 100000000000000000000000000000 c5: 1900 c0: 71 skew: 0.52 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [750000, 4450001) Primes: RFBsize:114155, AFBsize:114603, largePrimes:3082436 encountered Relations: rels:3151468, finalFF:259813 Max relations in full relation-set: 28 Initial matrix: 228825 x 259813 with sparse part having weight 32779060. Pruned matrix : 220551 x 221759 with weight 26667026. Total sieving time: 31.77 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.74 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,148,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 32.77 hours. --------- CPU info (if available) ----------

Jun 14, 2008

By Robert Backstrom / GGNFS, Msieve
8·10¹⁶⁹-7 = 7(9)₁₆₈3_<170> = 73 · 8753 · C165
C165 = P39 · P47 · P79
P39 = 473048713356314168354682550298167494871_<39>
P47 = 36110938960348331268870320405592134697102786337_<47>
P79 = 7329351527850956899400617896031539095927171138622765905330195821735845789339911_<79>

Number: n N=125201692100868743241064902992163939095636877532399850383977939461851826927440924364092780713931348782178791146362343087066821708095384909127046852038205296344580097 ( 165 digits) SNFS difficulty: 170 digits. Divisors found: Sat Jun 14 02:35:32 2008 prp39 factor: 473048713356314168354682550298167494871 Sat Jun 14 02:35:32 2008 prp47 factor: 36110938960348331268870320405592134697102786337 Sat Jun 14 02:35:32 2008 prp79 factor: 7329351527850956899400617896031539095927171138622765905330195821735845789339911 Sat Jun 14 02:35:32 2008 elapsed time 02:21:24 (Msieve 1.36) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 105.41 hours. Scaled time: 88.65 units (timescale=0.841). Factorization parameters were as follows: name: KA_7_9_168_3 n: 125201692100868743241064902992163939095636877532399850383977939461851826927440924364092780713931348782178791146362343087066821708095384909127046852038205296344580097 skew: 1.54 deg: 5 c5: 4 c0: -35 m: 10000000000000000000000000000000000 type: snfs rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 4500163) Primes: RFBsize:230209, AFBsize:230217, largePrimes:7834629 encountered Relations: rels:7288384, finalFF:441299 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 105.03 hours. Total relation processing time: 0.38 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000 total time: 105.41 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

Jun 13, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve
(4·10¹⁶⁸+23)/9 = (4)₁₆₇7_<168> = 3⁴ · 1265197 · C160
C160 = P79 · P82
P79 = 1058672780199082273664589389440212686058586452944274704237975222290582762325807_<79>
P82 = 4096496258940085111741497387505341221216333433858971073571460415594977424825412453_<82>

Number: n N=4336849083527239547972258343025079717439059867917162838793986325132038379037038505060451811007624025646486151026521390158802326996657968801408094232028341074571 ( 160 digits) SNFS difficulty: 168 digits. Divisors found: Fri Jun 13 23:45:43 2008 prp79 factor: 1058672780199082273664589389440212686058586452944274704237975222290582762325807 Fri Jun 13 23:45:43 2008 prp82 factor: 4096496258940085111741497387505341221216333433858971073571460415594977424825412453 Fri Jun 13 23:45:43 2008 elapsed time 02:28:18 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 70.39 hours. Scaled time: 101.99 units (timescale=1.449). Factorization parameters were as follows: name: KA_4_167_7 n: 4336849083527239547972258343025079717439059867917162838793986325132038379037038505060451811007624025646486151026521390158802326996657968801408094232028341074571 skew: 0.71 deg: 5 c5: 125 c0: 23 m: 2000000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 3500269) Primes: RFBsize:250150, AFBsize:250086, largePrimes:7571750 encountered Relations: rels:7011455, finalFF:533831 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 70.12 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,168,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 70.39 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

Jun 13, 2008

By Sinkiti Sibata / GGNFS
(19·10¹⁴³+71)/9 = 2(1)₁₄₂9_<144> = 3² · 211 · C141
C141 = P63 · P78
P63 = 773537122612256721050443498792233896398463284176095668716900509_<63>
P78 = 143715948709430888732671112113368641464136741032198092002947921700020431129809_<78>

Number: 21119_143 N=111169621438183839447662512433444502954771517172780995845766777836288104850506114329179100111169621438183839447662512433444502954771517172781 ( 141 digits) SNFS difficulty: 144 digits. Divisors found: r1=773537122612256721050443498792233896398463284176095668716900509 (pp63) r2=143715948709430888732671112113368641464136741032198092002947921700020431129809 (pp78) Version: GGNFS-0.77.1-20060513-k8 Total time: 22.98 hours. Scaled time: 46.18 units (timescale=2.010). Factorization parameters were as follows: name: 21119_143 n: 111169621438183839447662512433444502954771517172780995845766777836288104850506114329179100111169621438183839447662512433444502954771517172781 m: 10000000000000000000000000000 c5: 19000 c0: 71 skew: 0.33 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [650000, 3350001) Primes: RFBsize:100021, AFBsize:99934, largePrimes:3035935 encountered Relations: rels:3122816, finalFF:265596 Max relations in full relation-set: 28 Initial matrix: 200022 x 265596 with sparse part having weight 33581023. Pruned matrix : 184436 x 185500 with weight 22513251. Total sieving time: 22.36 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.38 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,144,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 22.98 hours. --------- CPU info (if available) ----------

(19·10¹⁴⁴+71)/9 = 2(1)₁₄₃9_<145> = 1999 · 4507 · C138
C138 = P60 · P78
P60 = 279576733790481204623483289144205990927420007608424299189687_<60>
P78 = 838126770218144510957697953206157504729388016127259238924760043036739444411909_<78>

Number: 21119_144 N=234320744919953998644664146041415550365721035702132307679367874653003350034359437441275675680208765477825568110337741658838195568952782483 ( 138 digits) SNFS difficulty: 146 digits. Divisors found: r1=279576733790481204623483289144205990927420007608424299189687 (pp60) r2=838126770218144510957697953206157504729388016127259238924760043036739444411909 (pp78) Version: GGNFS-0.77.1-20060513-k8 Total time: 24.32 hours. Scaled time: 48.56 units (timescale=1.997). Factorization parameters were as follows: name: 21119_144 n: 234320744919953998644664146041415550365721035702132307679367874653003350034359437441275675680208765477825568110337741658838195568952782483 m: 100000000000000000000000000000 c5: 19 c0: 710 skew: 2.06 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [750000, 3450001) Primes: RFBsize:114155, AFBsize:114373, largePrimes:2976517 encountered Relations: rels:3009909, finalFF:285451 Max relations in full relation-set: 28 Initial matrix: 228593 x 285451 with sparse part having weight 32777468. Pruned matrix : 212266 x 213472 with weight 22989071. Total sieving time: 23.51 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.56 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 24.32 hours. --------- CPU info (if available) ----------

Jun 12, 2008

By Sinkiti Sibata / GGNFS, Msieve
(19·10¹⁴¹+71)/9 = 2(1)₁₄₀9_<142> = 13 · 29 · 347 · 941 · 8111 · 16967418035004781_<17> · C114
C114 = P48 · P66
P48 = 650231791063999630808600501041274974102363870523_<48>
P66 = 191642700766968311023323590286528352074786023369003402963652968777_<66>

Number: 21119_141 N=124612176564047940613189812872850872746123053929396105024813316924095670437315190625530573100811253768993389660371 ( 114 digits) SNFS difficulty: 142 digits. Divisors found: r1=650231791063999630808600501041274974102363870523 (pp48) r2=191642700766968311023323590286528352074786023369003402963652968777 (pp66) Version: GGNFS-0.77.1-20060513-k8 Total time: 18.56 hours. Scaled time: 37.06 units (timescale=1.997). Factorization parameters were as follows: name: 21119_141 n: 124612176564047940613189812872850872746123053929396105024813316924095670437315190625530573100811253768993389660371 m: 10000000000000000000000000000 c5: 190 c0: 71 skew: 0.82 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [650000, 2750001) Primes: RFBsize:100021, AFBsize:100044, largePrimes:2926502 encountered Relations: rels:2964235, finalFF:258827 Max relations in full relation-set: 28 Initial matrix: 200132 x 258827 with sparse part having weight 31021926. Pruned matrix : 185082 x 186146 with weight 20907215. Total sieving time: 17.93 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.41 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,142,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 18.56 hours. --------- CPU info (if available) ----------

(19·10¹³²+71)/9 = 2(1)₁₃₁9_<133> = 5750351 · 3070993112983_<13> · 345044156871461_<15> · C99
C99 = P32 · P68
P32 = 24188464339752121280456516669389_<32>
P68 = 14323690221972322118217528148496229598451511026018742414164385860167_<68>

Msieve v. 1.36 Wed Jun 11 20:43:23 2008 random seeds: 525b3299 f77d553e factoring 3464680701478336600321379322542504153075346018260327430665746703964294 14515780339704184084723327963 (99 digits) no P-1/P+1/ECM available, skipping commencing quadratic sieve (99-digit input) using multiplier of 1 using 64kb Pentium 4 sieve core sieve interval: 18 blocks of size 65536 processing polynomials in batches of 6 using a sieve bound of 2608121 (95294 primes) using large prime bound of 391218150 (28 bits) using double large prime bound of 2926537886090700 (43-52 bits) using trial factoring cutoff of 52 bits polynomial 'A' values have 13 factors sieving in progress (press Ctrl-C to pause) 95438 relations (21959 full + 73479 combined from 1457579 partial), need 95390 95438 relations (21959 full + 73479 combined from 1457579 partial), need 95390 sieving complete, commencing postprocessing begin with 1479538 relations reduce to 254860 relations in 12 passes attempting to read 254860 relations recovered 254860 relations recovered 246051 polynomials attempting to build 95438 cycles found 95438 cycles in 6 passes distribution of cycle lengths: length 1 : 21959 length 2 : 16209 length 3 : 15947 length 4 : 12888 length 5 : 10074 length 6 : 6948 length 7 : 4671 length 9+: 6742 largest cycle: 22 relations matrix is 95294 x 95438 (26.0 MB) with weight 6442385 (67.50/col) sparse part has weight 6442385 (67.50/col) filtering completed in 3 passes matrix is 91866 x 91930 (25.2 MB) with weight 6238098 (67.86/col) sparse part has weight 6238098 (67.86/col) saving the first 48 matrix rows for later matrix is 91818 x 91930 (14.9 MB) with weight 4870259 (52.98/col) sparse part has weight 3352459 (36.47/col) matrix includes 64 packed rows using block size 21845 for processor cache size 512 kB commencing Lanczos iteration memory use: 14.9 MB linear algebra completed 88334 out of 91930 dimensions (96.1%) lanczos halted after 1453 iterations (dim = 91814) recovered 14 nontrivial dependencies prp32 factor: 24188464339752121280456516669389 prp68 factor: 143236902219723221182175281484962295984515110260187424141643858601 67 elapsed time 17:08:08

(19·10¹⁴²+71)/9 = 2(1)₁₄₁9_<143> = 7 · 97 · 2348733871051_<13> · C128
C128 = P32 · P47 · P50
P32 = 16065327225299271269093343103523_<32>
P47 = 35702000102923126067043311456968363449168793523_<47>
P50 = 23079446206702040089175443834158184126317648059459_<50>

Number: 21119_142 N=13237546736842859505402038877708992687784678505751658372756797808700605511230085366853429133351356265970701486042520921806832811 ( 128 digits) SNFS difficulty: 143 digits. Divisors found: r1=16065327225299271269093343103523 (pp32) r2=35702000102923126067043311456968363449168793523 (pp47) r3=23079446206702040089175443834158184126317648059459 (pp50) Version: GGNFS-0.77.1-20060513-k8 Total time: 17.07 hours. Scaled time: 34.10 units (timescale=1.997). Factorization parameters were as follows: name: 21119_142 n: 13237546736842859505402038877708992687784678505751658372756797808700605511230085366853429133351356265970701486042520921806832811 m: 10000000000000000000000000000 c5: 1900 c0: 71 skew: 0.52 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [650000, 2550001) Primes: RFBsize:100021, AFBsize:100279, largePrimes:2828872 encountered Relations: rels:2812879, finalFF:226712 Max relations in full relation-set: 28 Initial matrix: 200367 x 226712 with sparse part having weight 25694109. Pruned matrix : 193388 x 194453 with weight 20533623. Total sieving time: 16.39 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.49 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,143,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 17.07 hours. --------- CPU info (if available) ----------

Jun 11, 2008 (3rd)

By Sinkiti Sibata / Msieve, GGNFS
(19·10¹³⁷+71)/9 = 2(1)₁₃₆9_<138> = 3 · 17 · 53 · 760317572544031769_<18> · 6801356722860337047229446691_<28> · C89
C89 = P37 · P52
P37 = 4250715591941833113363929326424495917_<37>
P52 = 3553140787460875292162304042118460409815632172652911_<52>

Msieve v. 1.36 Wed Jun 11 06:15:26 2008 random seeds: 842cce61 e20be948 factoring 1510339094562442555697562556990930700341045654578517230076181491079231 5112232985777664387 (89 digits) no P-1/P+1/ECM available, skipping commencing quadratic sieve (89-digit input) using multiplier of 3 using 64kb Pentium 4 sieve core sieve interval: 14 blocks of size 65536 processing polynomials in batches of 8 using a sieve bound of 1533041 (58333 primes) using large prime bound of 122643280 (26 bits) using double large prime bound of 362709283500240 (42-49 bits) using trial factoring cutoff of 49 bits polynomial 'A' values have 11 factors sieving in progress (press Ctrl-C to pause) 58569 relations (15723 full + 42846 combined from 617873 partial), need 58429 58569 relations (15723 full + 42846 combined from 617873 partial), need 58429 sieving complete, commencing postprocessing begin with 633596 relations reduce to 142553 relations in 9 passes attempting to read 142553 relations recovered 142553 relations recovered 122273 polynomials attempting to build 58569 cycles found 58569 cycles in 5 passes distribution of cycle lengths: length 1 : 15723 length 2 : 10979 length 3 : 10473 length 4 : 7863 length 5 : 5457 length 6 : 3524 length 7 : 2049 length 9+: 2501 largest cycle: 19 relations matrix is 58333 x 58569 (14.2 MB) with weight 3487711 (59.55/col) sparse part has weight 3487711 (59.55/col) filtering completed in 3 passes matrix is 54502 x 54566 (13.3 MB) with weight 3275180 (60.02/col) sparse part has weight 3275180 (60.02/col) saving the first 48 matrix rows for later matrix is 54454 x 54566 (9.3 MB) with weight 2650970 (48.58/col) sparse part has weight 2107434 (38.62/col) matrix includes 64 packed rows using block size 21826 for processor cache size 512 kB commencing Lanczos iteration memory use: 8.6 MB lanczos halted after 863 iterations (dim = 54450) recovered 15 nontrivial dependencies prp37 factor: 4250715591941833113363929326424495917 prp52 factor: 3553140787460875292162304042118460409815632172652911 elapsed time 01:41:49

(19·10¹³⁶+71)/9 = 2(1)₁₃₅9_<137> = 7 · 151 · 5652617 · 847338798749_<12> · 16543089495237673789393867_<26> · C90
C90 = P42 · P49
P42 = 133603222497974916207566236359895495592119_<42>
P49 = 1886669803486077342881805363901015169384078657663_<49>

Msieve v. 1.36 Wed Jun 11 08:06:37 2008 random seeds: 96543fac dba2f462 factoring 2520651655353610024525327841485970561287114260186228248857235222627385 01167092198881757897 (90 digits) no P-1/P+1/ECM available, skipping commencing quadratic sieve (90-digit input) using multiplier of 17 using 64kb Pentium 4 sieve core sieve interval: 18 blocks of size 65536 processing polynomials in batches of 6 using a sieve bound of 1575269 (59429 primes) using large prime bound of 126021520 (26 bits) using double large prime bound of 380890718607520 (42-49 bits) using trial factoring cutoff of 49 bits polynomial 'A' values have 12 factors sieving in progress (press Ctrl-C to pause) 59947 relations (16155 full + 43792 combined from 629724 partial), need 59525 59947 relations (16155 full + 43792 combined from 629724 partial), need 59525 sieving complete, commencing postprocessing begin with 645879 relations reduce to 144865 relations in 10 passes attempting to read 144865 relations recovered 144865 relations recovered 123874 polynomials attempting to build 59947 cycles found 59947 cycles in 5 passes distribution of cycle lengths: length 1 : 16155 length 2 : 11799 length 3 : 10594 length 4 : 7866 length 5 : 5532 length 6 : 3513 length 7 : 2054 length 9+: 2434 largest cycle: 17 relations matrix is 59429 x 59947 (14.3 MB) with weight 3521971 (58.75/col) sparse part has weight 3521971 (58.75/col) filtering completed in 3 passes matrix is 55467 x 55530 (13.3 MB) with weight 3266995 (58.83/col) sparse part has weight 3266995 (58.83/col) saving the first 48 matrix rows for later matrix is 55419 x 55530 (8.1 MB) with weight 2513840 (45.27/col) sparse part has weight 1789178 (32.22/col) matrix includes 64 packed rows using block size 21845 for processor cache size 512 kB commencing Lanczos iteration memory use: 8.1 MB lanczos halted after 878 iterations (dim = 55419) recovered 18 nontrivial dependencies prp42 factor: 133603222497974916207566236359895495592119 prp49 factor: 1886669803486077342881805363901015169384078657663 elapsed time 02:05:15

(19·10¹¹²+71)/9 = 2(1)₁₁₁9_<113> = 7 · 565391 · C106
C106 = P45 · P62
P45 = 192943753209624529109523104943977732198649113_<45>
P62 = 27646072217246202886997945868549461853782928111418179513056399_<62>

Number: 21119_112 N=5334136935099808580284923205132405491095318135366526656801882265322610145927107109722326448450493580324087 ( 106 digits) SNFS difficulty: 113 digits. Divisors found: r1=192943753209624529109523104943977732198649113 (pp45) r2=27646072217246202886997945868549461853782928111418179513056399 (pp62) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 2.53 hours. Scaled time: 1.72 units (timescale=0.677). Factorization parameters were as follows: name: 21119_112 n: 5334136935099808580284923205132405491095318135366526656801882265322610145927107109722326448450493580324087 m: 10000000000000000000000 c5: 1900 c0: 71 skew: 0.52 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 550001) Primes: RFBsize:49098, AFBsize:64189, largePrimes:2361199 encountered Relations: rels:2768899, finalFF:523002 Max relations in full relation-set: 28 Initial matrix: 113354 x 523002 with sparse part having weight 43837723. Pruned matrix : 64947 x 65577 with weight 6285656. Total sieving time: 2.33 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.08 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,113,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.53 hours. --------- CPU info (if available) ----------

(19·10¹³⁴+71)/9 = 2(1)₁₃₃9_<135> = 3³ · 457257134670580393_<18> · C116
C116 = P38 · P79
P38 = 10698206939899017923623609042878690937_<38>
P79 = 1598364563201131516546710489349534778051921624547529288544666400228846159595517_<79>

Number: 21119_134 N=17099634862527007633774249557468016889650724451448309765314701595321185322430397101421106833371432310268550373729429 ( 116 digits) SNFS difficulty: 136 digits. Divisors found: r1=10698206939899017923623609042878690937 (pp38) r2=1598364563201131516546710489349534778051921624547529288544666400228846159595517 (pp79) Version: GGNFS-0.77.1-20060513-k8 Total time: 9.94 hours. Scaled time: 19.86 units (timescale=1.997). Factorization parameters were as follows: name: 21119_134 n: 17099634862527007633774249557468016889650724451448309765314701595321185322430397101421106833371432310268550373729429 m: 1000000000000000000000000000 c5: 19 c0: 710 skew: 2.06 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 1675001) Primes: RFBsize:78498, AFBsize:64144, largePrimes:1647026 encountered Relations: rels:1684261, finalFF:198191 Max relations in full relation-set: 28 Initial matrix: 142707 x 198191 with sparse part having weight 19597404. Pruned matrix : 128343 x 129120 with weight 11138560. Total sieving time: 9.69 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.12 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,136,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 9.94 hours. --------- CPU info (if available) ----------

(19·10¹¹⁴+71)/9 = 2(1)₁₁₃9_<115> = 73 · 691 · C110
C110 = P46 · P64
P46 = 8668069487682906600652956127049454670277290771_<46>
P64 = 4828228328398470071417068118715193261966974633062620905686001823_<64>

Number: 21119_114 N=41851418652957022998455902922330375098846442739549810897668875981030293818986006207226198106994253139407075533 ( 110 digits) SNFS difficulty: 116 digits. Divisors found: r1=8668069487682906600652956127049454670277290771 (pp46) r2=4828228328398470071417068118715193261966974633062620905686001823 (pp64) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 2.38 hours. Scaled time: 1.62 units (timescale=0.678). Factorization parameters were as follows: name: 21119_114 n: 41851418652957022998455902922330375098846442739549810897668875981030293818986006207226198106994253139407075533 m: 100000000000000000000000 c5: 19 c0: 710 skew: 2.06 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 550001) Primes: RFBsize:49098, AFBsize:64144, largePrimes:2134265 encountered Relations: rels:2237799, finalFF:245661 Max relations in full relation-set: 28 Initial matrix: 113307 x 245661 with sparse part having weight 20999251. Pruned matrix : 83577 x 84207 with weight 4754404. Total sieving time: 2.17 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.11 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,116,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.38 hours. --------- CPU info (if available) ----------

(19·10¹²⁴+71)/9 = 2(1)₁₂₃9_<125> = 7 · 23 · 53 · 545437 · 2033243 · 384102041 · C100
C100 = P40 · P61
P40 = 1253918638360010980630156828555485474091_<40>
P61 = 4631903386600872960769452069902828289819525693679554924387983_<61>

Number: 21119_124 N=5808029987541690152973383463236766090906255370289806657893139849685671618439794418005456394778248453 ( 100 digits) SNFS difficulty: 126 digits. Divisors found: r1=1253918638360010980630156828555485474091 (pp40) r2=4631903386600872960769452069902828289819525693679554924387983 (pp61) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 4.21 hours. Scaled time: 2.85 units (timescale=0.678). Factorization parameters were as follows: name: 21119_124 n: 5808029987541690152973383463236766090906255370289806657893139849685671618439794418005456394778248453 m: 10000000000000000000000000 c5: 19 c0: 710 skew: 2.06 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 750001) Primes: RFBsize:49098, AFBsize:64144, largePrimes:2250891 encountered Relations: rels:2388831, finalFF:237058 Max relations in full relation-set: 28 Initial matrix: 113307 x 237058 with sparse part having weight 23832349. Pruned matrix : 93307 x 93937 with weight 7260611. Total sieving time: 3.90 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.16 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,126,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 4.21 hours. --------- CPU info (if available) ----------

(19·10¹³⁸+71)/9 = 2(1)₁₃₇9_<139> = 73 · 997 · 195919 · 66563467303261_<14> · C115
C115 = P34 · P82
P34 = 1603870692511431841860591622009493_<34>
P82 = 1386791687162605489137851193896744499618556517677168287616017596826355620762034277_<82>

Number: 21119_138 N=2224234543658585009229052576859222565158549335853153762487314124689686259971732751014408988258302505370921285391561 ( 115 digits) SNFS difficulty: 139 digits. Divisors found: r1=1603870692511431841860591622009493 (pp34) r2=1386791687162605489137851193896744499618556517677168287616017596826355620762034277 (pp82) Version: GGNFS-0.77.1-20060513-k8 Total time: 17.15 hours. Scaled time: 34.34 units (timescale=2.003). Factorization parameters were as follows: name: 21119_138 n: 2224234543658585009229052576859222565158549335853153762487314124689686259971732751014408988258302505370921285391561 m: 1000000000000000000000000000 c5: 19000 c0: 71 skew: 0.33 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 2725001) Primes: RFBsize:78498, AFBsize:63999, largePrimes:1750118 encountered Relations: rels:1816378, finalFF:175667 Max relations in full relation-set: 28 Initial matrix: 142564 x 175667 with sparse part having weight 21332623. Pruned matrix : 135273 x 136049 with weight 15303043. Total sieving time: 16.81 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.18 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,139,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 17.15 hours. --------- CPU info (if available) ----------

Jun 11, 2008 (2nd)

By Robert Backstrom / GMP-ECM, GGNFS
(19·10¹⁰²+71)/9 = 2(1)₁₀₁9_<103> = 23 · 47 · 101611 · 763513 · 100996333 · C81
C81 = P30 · P51
P30 = 980156943101230219900359753653_<30>
P51 = 254288669710884780374892372181242723179308431072557_<51>
(19·10¹⁰⁸+71)/9 = 2(1)₁₀₇9_<109> = 8243 · 19120670782441660997_<20> · C86
C86 = P36 · P50
P36 = 450603619990888308306431347840461433_<36>
P50 = 29725419435685684489852635686211058845046578616633_<50>

Number: n N=13394381603467477755945469483667385640135036286832826097295226247555419210533528815089 ( 86 digits) SNFS difficulty: 109 digits. Divisors found: r1=450603619990888308306431347840461433 (pp36) r2=29725419435685684489852635686211058845046578616633 (pp50) Version: GGNFS-0.77.1-20051202-athlon Total time: 0.73 hours. Scaled time: 1.33 units (timescale=1.818). Factorization parameters were as follows: name: KA_2_1_107_9 n: 13394381603467477755945469483667385640135036286832826097295226247555419210533528815089 skew: 0.33 deg: 5 c5: 19000 c0: 71 m: 1000000000000000000000 type: snfs rlim: 500000 alim: 500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 500000/500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 180001) Primes: RFBsize:41538, AFBsize:41668, largePrimes:3476528 encountered Relations: rels:2873720, finalFF:99266 Max relations in full relation-set: 48 Initial matrix: 83273 x 99266 with sparse part having weight 7851229. Pruned matrix : 77272 x 77752 with weight 4272405. Total sieving time: 0.63 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.02 hours. Total square root time: 0.03 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,109,5,0,0,0,0,0,0,0,0,500000,500000,28,28,48,48,2.5,2.5,50000 total time: 0.73 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

(19·10¹²⁵+71)/9 = 2(1)₁₂₄9_<126> = 3² · 107 · C123
C123 = P34 · P90
P34 = 1413942013724739012664646934719861_<34>
P90 = 155043371987302231298493040834790288681640158330016874349793071994628235823840962820138833_<90>
(86·10¹⁹³+31)/9 = 9(5)₁₉₂9_<194> = 3 · 11 · 2699 · 46103930161_<11> · 8491960607515969_<16> · 193493468565567926104105693906747_<33> · C131
C131 = P41 · P90
P41 = 14340220886360533482512595413716049258071_<41>
P90 = 987577181992017289168545019941442943274336687209294613113211426445489576560981167267446169_<90>
(19·10¹²⁶+71)/9 = 2(1)₁₂₅9_<127> = 422096513 · 5145216763_<10> · 3313220862453003712927_<22> · C87
C87 = P37 · P50
P37 = 5784939440621316381615971654557277699_<37>
P50 = 50716169772551226915531892187055375653717528087137_<50>

Number: n N=293389970794478209096552836142598741462779930913674529100775827845706558862965578857763 ( 87 digits) SNFS difficulty: 127 digits. Divisors found: r1=5784939440621316381615971654557277699 (pp37) r2=50716169772551226915531892187055375653717528087137 (pp50) Version: GGNFS-0.77.1-20051202-athlon Total time: 2.33 hours. Scaled time: 4.27 units (timescale=1.829). Factorization parameters were as follows: name: KA_2_1_125_9 n: 293389970794478209096552836142598741462779930913674529100775827845706558862965578857763 skew: 0.82 deg: 5 c5: 190 c0: 71 m: 10000000000000000000000000 type: snfs rlim: 1000000 alim: 1000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 400001) Primes: RFBsize:78498, AFBsize:78712, largePrimes:5072487 encountered Relations: rels:4367200, finalFF:184214 Max relations in full relation-set: 48 Initial matrix: 157277 x 184214 with sparse part having weight 17282688. Pruned matrix : 146383 x 147233 with weight 10383105. Total sieving time: 2.11 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.12 hours. Total square root time: 0.02 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,127,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.5,2.5,50000 total time: 2.33 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

Jun 11, 2008

The factor table of 211...119 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.

Jun 10, 2008 (2nd)

By matsui
8·10¹⁷¹-3 = 7(9)₁₇₀7_<172> = 11 · 26691667 · C164
C164 = P57 · P108
P57 = 161588169710480273544767312890977071902081766318608100651_<57>
P108 = 168621148114846076028702461887800700665968272691501216143530445055605532067216607241423609435786388774673031_<108>

055605532067216607241423609435786388774673031 results=N=27247182698357778580381387467209420555384297551469051098504740347342384899649494625896811642647599614993221394799834992423937880210806139336567953109587620463243181 ( 164 digits) SNFS difficulty: 172 digits. Divisors found: r1=161588169710480273544767312890977071902081766318608100651 (pp57) r2=168621148114846076028702461887800700665968272691501216143530445055605532067216607241423609435786388774673031 (pp108) Version: GGNFS-0.77.1-20060513-prescott Total time: 109.34 hours. Scaled time: 185.99 units (timescale=1.701). Factorization parameters were as follows: n: 27247182698357778580381387467209420555384297551469051098504740347342384899649494625896811642647599614993221394799834992423937880210806139336567953109587620463243181 m: 20000000000000000000000000000000000 c5: 5 c0: -6 skew: 1.04 type: snfs Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3000000, 7100001) Primes: RFBsize:412849, AFBsize:411941, largePrimes:6008728 encountered Relations: rels:6280371, finalFF:935359 Max relations in full relation-set: 28 Initial matrix: 824855 x 935359 with sparse part having weight 54634880. Pruned matrix : 732551 x 736739 with weight 40305644. Total sieving time: 100.86 hours. Total relation processing time: 0.17 hours. Matrix solve time: 8.11 hours. Time per square root: 0.20 hours. Prototype def-par.txt line would be: snfs,172,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000 total time: 109.34 hours.

Jun 10, 2008

By Robert Backstrom / GGNFS, Msieve, GMP-ECM
(19·10¹⁶⁷+53)/9 = 2(1)₁₆₆7_<168> = 31 · 320083 · 17760384342751_<14> · C148
C148 = P52 · P96
P52 = 2570425101530933072476288537139463003096717765694241_<52>
P96 = 466046740920626307089573465132231484958654650900514236799839493101275990757147969483111772494719_<96>

Number: n N=1197938241349061336458522844018218127092204612969583280105998588522712770492267602126630070931892286913675016319536632794797252743959696031541213279 ( 148 digits) SNFS difficulty: 168 digits. Divisors found: Tue Jun 10 16:41:52 2008 prp52 factor: 2570425101530933072476288537139463003096717765694241 Tue Jun 10 16:41:52 2008 prp96 factor: 466046740920626307089573465132231484958654650900514236799839493101275990757147969483111772494719 Tue Jun 10 16:41:52 2008 elapsed time 03:13:45 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 114.73 hours. Scaled time: 199.06 units (timescale=1.735). Factorization parameters were as follows: name: KA_2_1_166_7 n: 1197938241349061336458522844018218127092204612969583280105998588522712770492267602126630070931892286913675016319536632794797252743959696031541213279 type: snfs skew: 0.49 deg: 5 c5: 1900 c0: 53 m: 1000000000000000000000000000000000 rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 5300001) Primes: RFBsize:230209, AFBsize:229847, largePrimes:7977913 encountered Relations: rels:7375544, finalFF:472087 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 114.37 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,168,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.6,2.6,100000 total time: 114.73 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(17·10¹⁶⁸-53)/9 = 1(8)₁₆₇3_<169> = 3371 · 48487 · 520151 · C155
C155 = P39 · P117
P39 = 149492575450278766064355105465537861991_<39>
P117 = 148618640254097296463041504915115243088101259415265146325211387004955010597261896312036315375075730295290862505541119_<117>

Jun 9, 2008

By Robert Backstrom / GGNFS, Msieve
(19·10¹⁶⁷+17)/9 = 2(1)₁₆₆3_<168> = 3³ · 7 · 12719167273_<11> · C155
C155 = P72 · P84
P72 = 331020430061825622240821487692762096553201092980731173026412142307290539_<72>
P84 = 265299120281487299747115556364341636867465798157268399080428918610074877812977268511_<84>

Number: n N=87819428890601930193174578949148272157511969157371746212193242682491669105644340286172556451630474536351991658958191443143132235435038495193586597492917429 ( 155 digits) SNFS difficulty: 168 digits. Divisors found: Mon Jun 09 13:43:34 2008 prp72 factor: 331020430061825622240821487692762096553201092980731173026412142307290539 Mon Jun 09 13:43:34 2008 prp84 factor: 265299120281487299747115556364341636867465798157268399080428918610074877812977268511 Mon Jun 09 13:43:34 2008 elapsed time 02:21:05 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 86.64 hours. Scaled time: 125.88 units (timescale=1.453). Factorization parameters were as follows: name: KA_2_1_166_3 n: 87819428890601930193174578949148272157511969157371746212193242682491669105644340286172556451630474536351991658958191443143132235435038495193586597492917429 skew: 0.39 deg: 5 c5: 1900 c0: 17 m: 1000000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 4400001) Primes: RFBsize:250150, AFBsize:249376, largePrimes:7844574 encountered Relations: rels:7268414, finalFF:533461 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 86.33 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,168,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 86.64 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+

Jun 8, 2008

By matsui / GGNFS
8·10¹⁷⁰-3 = 7(9)₁₆₉7_<171> = 19 · 283 · 313 · 12939739 · C158
C158 = P79 · P80
P79 = 1329287407066634342417708533382270111835295739849982262342044058728813534610871_<79>
P80 = 27635110530649598980061095653778265322075333231930656337853079914922096864534713_<80>

N=36735004421287046871645786893404694611759911810832769307831335234685028075163714623640129986468296706960744230461691070339391812014777047625593680940926665023 ( 158 digits) SNFS difficulty: 170 digits. Divisors found: r1=1329287407066634342417708533382270111835295739849982262342044058728813534610871 (pp79) r2=27635110530649598980061095653778265322075333231930656337853079914922096864534713 (pp80) Version: GGNFS-0.77.1-20060513-prescott Total time: 108.76 hours. Scaled time: 123.12 units (timescale=1.132). Factorization parameters were as follows: n: 36735004421287046871645786893404694611759911810832769307831335234685028075163714623640129986468296706960744230461691070339391812014777047625593680940926665023 m: 10000000000000000000000000000000000 c5: 8 c0: -3 skew: 0.82 type: snfs Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3000000, 6800001) Primes: RFBsize:412849, AFBsize:412856, largePrimes:5993930 encountered Relations: rels:6267516, finalFF:937691 Max relations in full relation-set: 28 Initial matrix: 825770 x 937691 with sparse part having weight 51657631. Pruned matrix : 732164 x 736356 with weight 37657512. Total sieving time: 100.31 hours. Total relation processing time: 0.18 hours. Matrix solve time: 7.99 hours. Time per square root: 0.28 hours. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000 total time: 108.76 hours.

Jun 7, 2008

By Robert Backstrom / GGNFS, Msieve, GMP-ECM
(19·10¹⁷¹+53)/9 = 2(1)₁₇₀7_<172> = 29 · 73 · C168
C168 = P78 · P91
P78 = 168661868577202193078498353096651456486993533110668327480176859986366715725113_<78>
P91 = 5912529573202205892596710183074556787793902601590008372374823072400078491492372186687664177_<91>

Number: n N=997218285834251823859759617907941006665616963207893770009972182858342518238597596179079410066656169632078937700099721828583425182385975961790794100666561696320789377001 ( 168 digits) SNFS difficulty: 172 digits. Divisors found: Sat Jun 07 11:15:53 2008 prp78 factor: 168661868577202193078498353096651456486993533110668327480176859986366715725113 Sat Jun 07 11:15:53 2008 prp91 factor: 5912529573202205892596710183074556787793902601590008372374823072400078491492372186687664177 Sat Jun 07 11:15:53 2008 elapsed time 01:54:10 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 62.34 hours. Scaled time: 114.01 units (timescale=1.829). Factorization parameters were as follows: name: KA_2_1_170_7 n: 997218285834251823859759617907941006665616963207893770009972182858342518238597596179079410066656169632078937700099721828583425182385975961790794100666561696320789377001 skew: 0.77 deg: 5 c5: 190 c0: 53 m: 10000000000000000000000000000000000 type: snfs rlim: 3800000 alim: 3800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3800000/3800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 8399990) Primes: RFBsize:269987, AFBsize:270102, largePrimes:8759196 encountered Relations: rels:8275802, finalFF:614142 Max relations in full relation-set: 28 Initial matrix: 540156 x 614142 with sparse part having weight 104508632. Pruned matrix : Total sieving time: 62.04 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,172,5,0,0,0,0,0,0,0,0,3800000,3800000,28,28,48,48,2.5,2.5,100000 total time: 62.34 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

(52·10¹⁶⁶-7)/9 = 5(7)_166<167> = 3 · 8537 · 255757 · 525541 · 542555873 · C143
C143 = P39 · P105
P39 = 194347402850767085232324193773663394853_<39>
P105 = 159175768603678496522767736976312094223274142566031220136596573878529488740968790595578468802481799156919_<105>

Number: n N=30935397224899588137032400403776143825219089737083473114490349480239274430387787920586369380476002430395991417734593542513905288852266803937907 ( 143 digits) SNFS difficulty: 168 digits. Divisors found: Sat Jun 07 21:27:14 2008 prp39 factor: 194347402850767085232324193773663394853 Sat Jun 07 21:27:14 2008 prp105 factor: 159175768603678496522767736976312094223274142566031220136596573878529488740968790595578468802481799156919 Sat Jun 07 21:27:14 2008 elapsed time 02:26:22 (Msieve 1.36) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 117.71 hours. Scaled time: 154.31 units (timescale=1.311). Factorization parameters were as follows: name: KA_5_7_166 n: 30935397224899588137032400403776143825219089737083473114490349480239274430387787920586369380476002430395991417734593542513905288852266803937907 skew: 0.84 deg: 5 c5: 65 c0: -28 m: 2000000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 4300573) Primes: RFBsize:216816, AFBsize:217161, largePrimes:7714153 encountered Relations: rels:7106257, finalFF:456914 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 117.23 hours. Total relation processing time: 0.48 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,168,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 117.71 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(82·10¹⁹⁶-1)/9 = 9(1)_196<197> = 6529 · 2016943147_<10> · 4747717717776043_<16> · 52903728369300534371_<20> · 7068156580783016438441_<22> · C127
C127 = P44 · P83
P44 = 81658001383391490714853549764552732910419977_<44>
P83 = 47725989393250425685698093318853962668514004436283556924989693866905105524709738757_<83>

Jun 5, 2008 (2nd)

By matsui / GGNFS
6·10¹⁷¹+7 = 6(0)₁₇₀7_<172> = 71 · 59218811 · C163
C163 = P33 · P130
P33 = 474552042132264250970127542339833_<33>
P130 = 3007110393444661684023615721112945500024818563987365700417287479523557838981587406237779335223878760263992906197715985864050125259_<130>

N=1427030378126320819926009326355609214191592305614026387757663739937321748163843163823614696626347803048833326070026186799440477847153697330073801556443529595141747 ( 163 digits) SNFS difficulty: 171 digits. Divisors found: r1=474552042132264250970127542339833 (pp33) r2=3007110393444661684023615721112945500024818563987365700417287479523557838981587406237779335223878760263992906197715985864050125259 (pp130) Version: GGNFS-0.77.1-20060513-prescott Total time: 263.39 hours. Scaled time: 447.23 units (timescale=1.698). Factorization parameters were as follows: n: 1427030378126320819926009326355609214191592305614026387757663739937321748163843163823614696626347803048833326070026186799440477847153697330073801556443529595141747 m: 10000000000000000000000000000000000 c5: 60 c0: 7 skew: 0.65 type: snfs Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3000000, 9100001) Primes: RFBsize:412849, AFBsize:413211, largePrimes:6243772 encountered Relations: rels:6522967, finalFF:932713 Max relations in full relation-set: 28 Initial matrix: 826127 x 932713 with sparse part having weight 72156280. Pruned matrix : 744394 x 748588 with weight 56055920. Total sieving time: 252.14 hours. Total relation processing time: 0.27 hours. Matrix solve time: 10.74 hours. Time per square root: 0.23 hours. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000 total time: 263.39 hours.

Jun 5, 2008

By Robert Backstrom / GGNFS, Msieve
(19·10¹⁵³+53)/9 = 2(1)₁₅₂7_<154> = 1879 · 18211 · 657339007961513351528016261555491_<33> · C113
C113 = P41 · P73
P41 = 49440282722308466810657310201766051159457_<41>
P73 = 1898366959062654878216846059729855418347441491497031988617483026838153539_<73>

Number: n N=93855799166746640492272622125497718479246182956099212617130611814947101236895121008505256986359336706235937868323 ( 113 digits) Divisors found: Thu Jun 5 01:27:19 2008 prp41 factor: 49440282722308466810657310201766051159457 Thu Jun 5 01:27:19 2008 prp73 factor: 1898366959062654878216846059729855418347441491497031988617483026838153539 Thu Jun 5 01:27:19 2008 elapsed time 00:54:53 (Msieve 1.34) Version: GGNFS-0.77.1-20050930-k8 Total time: 25.54 hours. Scaled time: 21.33 units (timescale=0.835). Factorization parameters were as follows: name: KA_2_1_152_7 n: 93855799166746640492272622125497718479246182956099212617130611814947101236895121008505256986359336706235937868323 skew: 11116.69 # norm 1.92e+15 c5: 103440 c4: 11953367872 c3: 15928492693912 c2: -722423903459076173 c1: 1332711082941591543402 c0: -5152737654335827118703105 # alpha -5.25 Y1: 725795780941 Y0: -3904385166972887532266 # Murphy_E 6.57e-10 # M 41592232628683845462355480330603808426187404799596563145996588259114680645002794406922771259457385042957096841561 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved special-q in [100000, 1600097) Primes: RFBsize:250150, AFBsize:250146, largePrimes:6949358 encountered Relations: rels:6614567, finalFF:545217 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 25.35 hours. Total relation processing time: 0.20 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 25.54 hours. --------- CPU info (if available) ----------

Jun 4, 2008 (4th)

By Robert Backstrom / GGNFS, Msieve
(4·10¹⁶⁶-7)/3 = 1(3)₁₆₅1_<167> = 29 · 53 · 277 · 617 · 5838767041_<10> · 7353513077_<10> · C139
C139 = P54 · P85
P54 = 192731134450942355826572331465468888732090323885616437_<54>
P85 = 6133834322965081225387775111756706302035506281288803413842786108108282065805336181223_<85>

Number: n N=1182180847599188046818857534724658900852626590739814972842019783607392083840022685023727597960406156943676045299525683368653969430899562451 ( 139 digits) SNFS difficulty: 166 digits. Divisors found: Wed Jun 04 17:41:20 2008 prp54 factor: 192731134450942355826572331465468888732090323885616437 Wed Jun 04 17:41:20 2008 prp85 factor: 6133834322965081225387775111756706302035506281288803413842786108108282065805336181223 Wed Jun 04 17:41:20 2008 elapsed time 00:53:13 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 36.64 hours. Scaled time: 66.69 units (timescale=1.820). Factorization parameters were as follows: name: KA_1_3_165_1 n: 1182180847599188046818857534724658900852626590739814972842019783607392083840022685023727597960406156943676045299525683368653969430899562451 skew: 0.32 deg: 5 c5: 40 c0: -7 m: 1000000000000000000000000000000000 type: snfs rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2500529) Primes: RFBsize:230209, AFBsize:229712, largePrimes:7212995 encountered Relations: rels:6635279, finalFF:484405 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 36.46 hours. Total relation processing time: 0.18 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000 total time: 36.64 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

Jun 4, 2008 (3rd)

By Sinkiti Sibata / GGNFS
(19·10¹⁴³+53)/9 = 2(1)₁₄₂7_<144> = 29 · 642821741 · 4284759633206018989819201_<25> · C109
C109 = P45 · P65
P45 = 113218888779812679914545263801430398846511411_<45>
P65 = 23344102690036781800016467479390952616696847561433570010070708823_<65>

Number: 21117_143 N=2642993366127800393414430806581459942303114996968280892797448071154662899280821918339828161151241489527879253 ( 109 digits) SNFS difficulty: 144 digits. Divisors found: r1=113218888779812679914545263801430398846511411 (pp45) r2=23344102690036781800016467479390952616696847561433570010070708823 (pp65) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 29.34 hours. Scaled time: 19.86 units (timescale=0.677). Factorization parameters were as follows: name: 21117_143 n: 2642993366127800393414430806581459942303114996968280892797448071154662899280821918339828161151241489527879253 m: 10000000000000000000000000000 c5: 19000 c0: 53 skew: 0.31 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [650000, 3550001) Primes: RFBsize:100021, AFBsize:100113, largePrimes:3009325 encountered Relations: rels:3070164, finalFF:227045 Max relations in full relation-set: 28 Initial matrix: 200201 x 227045 with sparse part having weight 29056454. Pruned matrix : 193665 x 194730 with weight 23731295. Total sieving time: 27.51 hours. Total relation processing time: 0.25 hours. Matrix solve time: 1.46 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,144,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 29.34 hours. --------- CPU info (if available) ----------

Jun 4, 2008 (2nd)

By matsui / GGNFS
2·10¹⁶⁹-1 = 1(9)_169<170> = 9479 · 22528741 · C158
C158 = P47 · P112
P47 = 58898760265545578947543164298726379592443127301_<47>
P112 = 1590099849864182210494369250009957128474833068460631622744916529265419584880420247201933949436069843089442684241_<112>

N=93654909855430485828763065681998364104412095025723340870348581107002829762155361242962287920426721940792480679499437178241372396724687925920080647933909563541 ( 158 digits) SNFS difficulty: 170 digits. Divisors found: r1=58898760265545578947543164298726379592443127301 (pp47) r2=1590099849864182210494369250009957128474833068460631622744916529265419584880420247201933949436069843089442684241 (pp112) Version: GGNFS-0.77.1-20060513-prescott Total time: 177.49 hours. Scaled time: 151.40 units (timescale=0.853). Factorization parameters were as follows: n: 93654909855430485828763065681998364104412095025723340870348581107002829762155361242962287920426721940792480679499437178241372396724687925920080647933909563541 m: 10000000000000000000000000000000000 c5: 1 c0: -5 skew: 1.38 type: snfs Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3000000, 6500001) Primes: RFBsize:412849, AFBsize:412271, largePrimes:5956885 encountered Relations: rels:6224596, finalFF:933623 Max relations in full relation-set: 28 Initial matrix: 825184 x 933623 with sparse part having weight 47674635. Pruned matrix : 733184 x 737373 with weight 34636533. Total sieving time: 165.67 hours. Total relation processing time: 0.23 hours. Matrix solve time: 11.27 hours. Time per square root: 0.32 hours. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000 total time: 177.49 hours.

Jun 4, 2008

GMP-ECM 6.2.1 has been released.
HOW TO for Japanese

Jun 3, 2008 (4th)

By Wataru Sakai / GGNFS
(10¹⁷⁵+11)/3 = (3)₁₇₄7_<175> = 7 · 66593 · C169
C169 = P38 · P132
P38 = 31384625954292517272083270912284988437_<38>
P132 = 227842725978933038527191595324104875211606210309617485656031157323032196340886078968896526888348315502943618148510280830511973874051_<132>

Number: 33337_175 N=7150758731255179830855952970889976280933288426568501050803995557948676144282289072282014483146734284241229415647147240557959402282379171842028298412603069248662629348287 ( 169 digits) SNFS difficulty: 175 digits. Divisors found: r1=31384625954292517272083270912284988437 (pp38) r2=227842725978933038527191595324104875211606210309617485656031157323032196340886078968896526888348315502943618148510280830511973874051 (pp132) Version: GGNFS-0.77.1-20060722-nocona Total time: 176.55 hours. Scaled time: 353.46 units (timescale=2.002). Factorization parameters were as follows: n: 7150758731255179830855952970889976280933288426568501050803995557948676144282289072282014483146734284241229415647147240557959402282379171842028298412603069248662629348287 m: 100000000000000000000000000000000000 c5: 1 c0: 11 skew: 1.62 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 9400001) Primes: RFBsize:501962, AFBsize:502027, largePrimes:6547456 encountered Relations: rels:7183440, finalFF:1298613 Max relations in full relation-set: 32 Initial matrix: 1004053 x 1298613 with sparse part having weight 71578861. Pruned matrix : 741890 x 746974 with weight 50609168. Total sieving time: 172.03 hours. Total relation processing time: 0.10 hours. Matrix solve time: 4.25 hours. Time per square root: 0.17 hours. Prototype def-par.txt line would be: snfs,175,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 176.55 hours.

Jun 3, 2008 (3rd)

By Jo Yeong Uk / GGNFS
(19·10¹⁶³+53)/9 = 2(1)₁₆₂7_<164> = 3³ · 73 · 2689 · 10424563 · 923076685159_<12> · 2946551431987_<13> · 34825517084278748077301_<23> · C103
C103 = P52 · P52
P52 = 1651232239649515659508639079209693572743461625197213_<52>
P52 = 2442970742799471533588610599827101256283903212427009_<52>

Number: 21117_163 N=4033912051031012261593993832795928814631065204377255803288434374957097404460879570195369709261992725917 ( 103 digits) Divisors found: r1=1651232239649515659508639079209693572743461625197213 (pp52) r2=2442970742799471533588610599827101256283903212427009 (pp52) Version: GGNFS-0.77.1-20050930-nocona Total time: 5.38 hours. Scaled time: 12.75 units (timescale=2.370). Factorization parameters were as follows: name: 21117_163 n: 4033912051031012261593993832795928814631065204377255803288434374957097404460879570195369709261992725917 skew: 7340.12 # norm 1.81e+14 c5: 146160 c4: -398831628 c3: -29546363044896 c2: 15604863772449401 c1: 569711961235965527372 c0: 29241800285831870731743 # alpha -5.87 Y1: 45608002259 Y0: -30773715148705995392 # Murphy_E 2.35e-09 # M 3172093150204558832540147395143702792889572096330200074127881341980114758822844799745116817020563794105 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 60000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [900000, 1680001) Primes: RFBsize:135072, AFBsize:135442, largePrimes:4395510 encountered Relations: rels:4347033, finalFF:334703 Max relations in full relation-set: 28 Initial matrix: 270597 x 334703 with sparse part having weight 27697377. Pruned matrix : 229725 x 231141 with weight 16357860. Polynomial selection time: 0.35 hours. Total sieving time: 4.66 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.23 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000 total time: 5.38 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: 8047200k/8912896k available (2440k kernel code, 339088k reserved, 1234k data, 192k init) Calibrating delay using timer specific routine.. 5347.62 BogoMIPS (lpj=2673811) Calibrating delay using timer specific routine.. 5214.21 BogoMIPS (lpj=2607107) Calibrating delay using timer specific routine.. 5344.19 BogoMIPS (lpj=2672095) Calibrating delay using timer specific routine.. 5344.70 BogoMIPS (lpj=2672350)

Jun 3, 2008 (2nd)

By Sinkiti Sibata / GGNFS
(19·10¹³⁴+53)/9 = 2(1)₁₃₃7_<135> = 7 · 47 · 4597 · 8609 · C125
C125 = P43 · P82
P43 = 5403622215874456846832096554592058096621793_<43>
P82 = 3000564753507592297355998545136918553987659979517034764910691658674627703147614257_<82>

Number: 21117_134 N=16213918362223489302223535692633389562153429015595671952321814050862732998694287615956975520679013858527672865365139183702801 ( 125 digits) SNFS difficulty: 136 digits. Divisors found: r1=5403622215874456846832096554592058096621793 (pp43) r2=3000564753507592297355998545136918553987659979517034764910691658674627703147614257 (pp82) Version: GGNFS-0.77.1-20060513-k8 Total time: 10.54 hours. Scaled time: 20.86 units (timescale=1.979). Factorization parameters were as follows: name: 21117_134 n: 16213918362223489302223535692633389562153429015595671952321814050862732998694287615956975520679013858527672865365139183702801 m: 1000000000000000000000000000 c5: 19 c0: 530 skew: 1.95 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 1675001) Primes: RFBsize:78498, AFBsize:64098, largePrimes:1614720 encountered Relations: rels:1625307, finalFF:171469 Max relations in full relation-set: 28 Initial matrix: 142661 x 171469 with sparse part having weight 16936085. Pruned matrix : 134817 x 135594 with weight 11860232. Total sieving time: 10.24 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.15 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,136,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 10.54 hours. --------- CPU info (if available) ----------

(19·10¹⁵¹+53)/9 = 2(1)₁₅₀7_<152> = 3 · 59 · 113 · 19777 · 496132729 · 255184099217_<12> · C123
C123 = P35 · P39 · P50
P35 = 10802596959816835717153878679789093_<35>
P39 = 510747305679292439904818708357078624189_<39>
P50 = 76403494685203056879146028205246866036211171137461_<50>

Number: 21117_151 N=421548434642298635067245499858189780855963517184294121673147892868581238049980895146232704403663085255385064268683122684997 ( 123 digits) SNFS difficulty: 152 digits. Divisors found: r1=10802596959816835717153878679789093 (pp35) r2=510747305679292439904818708357078624189 (pp39) r3=76403494685203056879146028205246866036211171137461 (pp50) Version: GGNFS-0.77.1-20060513-k8 Total time: 30.64 hours. Scaled time: 61.38 units (timescale=2.003). Factorization parameters were as follows: name: 21117_151 n: 421548434642298635067245499858189780855963517184294121673147892868581238049980895146232704403663085255385064268683122684997 m: 1000000000000000000000000000000 c5: 190 c0: 53 skew: 0.77 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2300001) Primes: RFBsize:176302, AFBsize:176488, largePrimes:5745499 encountered Relations: rels:5739824, finalFF:530707 Max relations in full relation-set: 28 Initial matrix: 352857 x 530707 with sparse part having weight 50577699. Pruned matrix : 289862 x 291690 with weight 27680081. Total sieving time: 29.18 hours. Total relation processing time: 0.15 hours. Matrix solve time: 1.16 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 30.64 hours. --------- CPU info (if available) ----------

Jun 3, 2008

By Robert Backstrom / GGNFS, Msieve, GMP-ECM
(17·10¹⁸⁵-53)/9 = 1(8)₁₈₄3_<186> = 3³ · 31 · C183
C183 = P82 · P102
P82 = 1597997386322290245461276699108764584415883034598743632467843957463923933713820829_<82>
P102 = 141222823208483395121283940637151729989074192145153563988529735450619888690572081943928291407031714371_<102>

Number: n N=225673702376211336784813487322447895924598433559007035709544670118146820655781229257931766892340369042878003451480153989114562591265100225673702376211336784813487322447895924598433559 ( 183 digits) SNFS difficulty: 186 digits. Divisors found: Tue Jun 3 00:59:42 2008 prp82 factor: 1597997386322290245461276699108764584415883034598743632467843957463923933713820829 Tue Jun 3 00:59:42 2008 prp102 factor: 141222823208483395121283940637151729989074192145153563988529735450619888690572081943928291407031714371 Tue Jun 3 00:59:42 2008 elapsed time 03:01:31 (Msieve 1.34) Version: GGNFS-0.77.1-20050930-k8 Total time: 96.19 hours. Scaled time: 80.61 units (timescale=0.838). Factorization parameters were as follows: name: KA_1_8_184_3 n: 225673702376211336784813487322447895924598433559007035709544670118146820655781229257931766892340369042878003451480153989114562591265100225673702376211336784813487322447895924598433559 type: snfs deg: 5 c5: 17 c0: -53 skew: 1.26 m: 10000000000000000000000000000000000000 rlim: 7000000 alim: 7000000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 7000000/7000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 13400077) Primes: RFBsize:476648, AFBsize:476034, largePrimes:6576115 encountered Relations: rels:6884940, finalFF:988009 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 95.96 hours. Total relation processing time: 0.24 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,186,5,0,0,0,0,0,0,0,0,7000000,7000000,27,27,48,48,2.5,2.5,100000 total time: 96.19 hours. --------- CPU info (if available) ----------

(19·10¹⁵⁷+53)/9 = 2(1)₁₅₆7_<158> = 3 · 137 · 1669 · 2416956391_<10> · C143
C143 = P43 · P100
P43 = 9327754593722757997158137149780069754362391_<43>
P100 = 1365107984440039824790803736415625965715893749320105011201077904595167216578438035906087890833714123_<100>
(19·10¹⁴¹+53)/9 = 2(1)₁₄₀7_<142> = 137 · 40690807 · C132
C132 = P41 · P92
P41 = 27198025104878136528579769327922885245327_<41>
P92 = 13923770326764645462911775434681406383095756757842407468021553475546864212753687318351193869_<92>

Number: n N=378699054901902081739421275414128653081310010809454075711845569972130486756125779321498871746559742832580196694097046465935403300163 ( 132 digits) SNFS difficulty: 142 digits. Divisors found: Tue Jun 03 04:22:47 2008 prp41 factor: 27198025104878136528579769327922885245327 Tue Jun 03 04:22:47 2008 prp92 factor: 13923770326764645462911775434681406383095756757842407468021553475546864212753687318351193869 Tue Jun 03 04:22:47 2008 elapsed time 00:24:28 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 5.78 hours. Scaled time: 10.50 units (timescale=1.817). Factorization parameters were as follows: name: KA_2_1_140_7 n: 378699054901902081739421275414128653081310010809454075711845569972130486756125779321498871746559742832580196694097046465935403300163 skew: 0.77 deg: 5 c5: 190 c0: 53 m: 10000000000000000000000000000 type: snfs rlim: 2000000 alim: 2000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 960581) Primes: RFBsize:148933, AFBsize:149140, largePrimes:6361799 encountered Relations: rels:5656427, finalFF:321577 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 5.59 hours. Total relation processing time: 0.19 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,142,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,100000 total time: 5.78 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

(19·10¹⁴⁶+53)/9 = 2(1)₁₄₅7_<147> = 7 · 1190149 · C140
C140 = P68 · P72
P68 = 58331886632896092336330712812119256134195174608064860440080724285391_<68>
P72 = 434415879950414804346950736783159062697316149855191019881795289997876609_<72>

Number: n N=25340297860797394889344720836408011711272059346124022059556181754326692481494947404678035044484959579624197247704892546000676159168919319119 ( 140 digits) SNFS difficulty: 147 digits. Divisors found: r1=58331886632896092336330712812119256134195174608064860440080724285391 (pp68) r2=434415879950414804346950736783159062697316149855191019881795289997876609 (pp72) Version: GGNFS-0.77.1-20051202-athlon Total time: 9.19 hours. Scaled time: 16.71 units (timescale=1.819). Factorization parameters were as follows: name: KA_2_1_145_7 n: 25340297860797394889344720836408011711272059346124022059556181754326692481494947404678035044484959579624197247704892546000676159168919319119 skew: 0.77 deg: 5 c5: 190 c0: 53 m: 100000000000000000000000000000 type: snfs rlim: 2400000 alim: 2400000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1500001) Primes: RFBsize:176302, AFBsize:176488, largePrimes:6869920 encountered Relations: rels:6255073, finalFF:414560 Max relations in full relation-set: 48 Initial matrix: 352857 x 414560 with sparse part having weight 36005432. Pruned matrix : 309414 x 311242 with weight 21939980. Total sieving time: 8.14 hours. Total relation processing time: 0.20 hours. Matrix solve time: 0.76 hours. Total square root time: 0.10 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,147,5,0,0,0,0,0,0,0,0,2400000,2400000,28,28,48,48,2.5,2.5,100000 total time: 9.19 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

(19·10¹⁶⁰+53)/9 = 2(1)₁₅₉7_<161> = 3 · 173 · 4217 · 22205549 · 356050365606344610424786395461843_<33> · C115
C115 = P40 · P75
P40 = 1942156014418176018702442345855437715753_<40>
P75 = 628178499120351639880606186016433190873849204059410375565924824840997233549_<75>

Jun 2, 2008 (4th)

By Jo Yeong Uk / GMP-ECM, Msieve, GGNFS
(19·10¹³⁹+53)/9 = 2(1)₁₃₈7_<140> = 3 · 73 · 269 · 1314345485719339431777602851_<28> · C108
C108 = P33 · P36 · P39
P33 = 510099375329014604799283301482189_<33>
P36 = 838519257079062659185170193098878123_<36>
P39 = 637437084815224855533017008762999621951_<39>

Mon Jun 2 11:12:44 2008 Mon Jun 2 11:12:44 2008 Mon Jun 2 11:12:44 2008 Msieve v. 1.34 Mon Jun 2 11:12:44 2008 random seeds: eb11b0bc f0692308 Mon Jun 2 11:12:44 2008 factoring 534503270793905799138212310001265257409229574257419045318153661011224477973 (75 digits) Mon Jun 2 11:12:44 2008 no P-1/P+1/ECM available, skipping Mon Jun 2 11:12:44 2008 commencing quadratic sieve (75-digit input) Mon Jun 2 11:12:44 2008 using multiplier of 29 Mon Jun 2 11:12:44 2008 using 32kb Intel Core sieve core Mon Jun 2 11:12:44 2008 sieve interval: 12 blocks of size 32768 Mon Jun 2 11:12:44 2008 processing polynomials in batches of 17 Mon Jun 2 11:12:44 2008 using a sieve bound of 667091 (26908 primes) Mon Jun 2 11:12:44 2008 using large prime bound of 66709100 (25 bits) Mon Jun 2 11:12:44 2008 using trial factoring cutoff of 26 bits Mon Jun 2 11:12:44 2008 polynomial 'A' values have 10 factors Mon Jun 2 11:15:58 2008 27434 relations (14226 full + 13208 combined from 147476 partial), need 27004 Mon Jun 2 11:15:58 2008 begin with 161702 relations Mon Jun 2 11:15:58 2008 reduce to 38984 relations in 2 passes Mon Jun 2 11:15:58 2008 attempting to read 38984 relations Mon Jun 2 11:15:58 2008 recovered 38984 relations Mon Jun 2 11:15:58 2008 recovered 30274 polynomials Mon Jun 2 11:15:58 2008 attempting to build 27434 cycles Mon Jun 2 11:15:58 2008 found 27434 cycles in 1 passes Mon Jun 2 11:15:58 2008 distribution of cycle lengths: Mon Jun 2 11:15:58 2008 length 1 : 14226 Mon Jun 2 11:15:58 2008 length 2 : 13208 Mon Jun 2 11:15:58 2008 largest cycle: 2 relations Mon Jun 2 11:15:58 2008 matrix is 26908 x 27434 (4.0 MB) with weight 827908 (30.18/col) Mon Jun 2 11:15:58 2008 sparse part has weight 827908 (30.18/col) Mon Jun 2 11:15:58 2008 filtering completed in 5 passes Mon Jun 2 11:15:58 2008 matrix is 23022 x 23086 (3.3 MB) with weight 677687 (29.35/col) Mon Jun 2 11:15:58 2008 sparse part has weight 677687 (29.35/col) Mon Jun 2 11:15:59 2008 saving the first 48 matrix rows for later Mon Jun 2 11:15:59 2008 matrix is 22974 x 23086 (2.3 MB) with weight 496279 (21.50/col) Mon Jun 2 11:15:59 2008 sparse part has weight 359701 (15.58/col) Mon Jun 2 11:15:59 2008 matrix includes 64 packed rows Mon Jun 2 11:15:59 2008 commencing Lanczos iteration Mon Jun 2 11:15:59 2008 memory use: 3.1 MB Mon Jun 2 11:16:04 2008 lanczos halted after 364 iterations (dim = 22967) Mon Jun 2 11:16:05 2008 recovered 14 nontrivial dependencies Mon Jun 2 11:16:05 2008 prp36 factor: 838519257079062659185170193098878123 Mon Jun 2 11:16:05 2008 prp39 factor: 637437084815224855533017008762999621951 Mon Jun 2 11:16:05 2008 elapsed time 00:03:21

(19·10¹⁵⁸+53)/9 = 2(1)₁₅₇7_<159> = 7² · 551826959 · C148
C148 = P39 · P110
P39 = 460989874520911044064786431843221905337_<39>
P110 = 16936384759591687512192175264040477850108231701305445403165968977141397799585486877387463283782557291612041451_<110>
(19·10¹⁵⁰+53)/9 = 2(1)₁₄₉7_<151> = C151
C151 = P31 · P120
P31 = 9985015037288028821227614289837_<31>
P120 = 211427935083460583094406150513915501270969623409084899062206666680722548922350472589902425296793812587271223307267489441_<120>

Number: 21117_150 N=2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111117 ( 151 digits) SNFS difficulty: 151 digits. Divisors found: r1=9985015037288028821227614289837 (pp31) r2=211427935083460583094406150513915501270969623409084899062206666680722548922350472589902425296793812587271223307267489441 (pp120) Version: GGNFS-0.77.1-20050930-nocona Total time: 14.11 hours. Scaled time: 33.61 units (timescale=2.382). Factorization parameters were as follows: n: 2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111117 m: 1000000000000000000000000000000 c5: 19 c0: 53 skew: 1.23 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2200001) Primes: RFBsize:176302, AFBsize:177173, largePrimes:5510831 encountered Relations: rels:5384542, finalFF:442565 Max relations in full relation-set: 28 Initial matrix: 353540 x 442565 with sparse part having weight 39552834. Pruned matrix : 316742 x 318573 with weight 24798877. Total sieving time: 13.43 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.57 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 14.11 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: 8047200k/8912896k available (2440k kernel code, 339088k reserved, 1234k data, 192k init) Calibrating delay using timer specific routine.. 5347.62 BogoMIPS (lpj=2673811) Calibrating delay using timer specific routine.. 5214.21 BogoMIPS (lpj=2607107) Calibrating delay using timer specific routine.. 5344.19 BogoMIPS (lpj=2672095) Calibrating delay using timer specific routine.. 5344.70 BogoMIPS (lpj=2672350)

Jun 2, 2008 (3rd)

By Sinkiti Sibata / GGNFS, Msieve
(19·10¹²⁴+53)/9 = 2(1)₁₂₃7_<125> = 3 · 306525654222521_<15> · C110
C110 = P52 · P58
P52 = 2320545677943061507893706868698246585867969028650453_<52>
P58 = 9893111122056882575541062637026092122141686702534903437003_<58>

Number: 21117_124 N=22957416255699530501295404822326167390114094473872188918375242049826145386407603389399279197768288688392912359 ( 110 digits) SNFS difficulty: 126 digits. Divisors found: r1=2320545677943061507893706868698246585867969028650453 (pp52) r2=9893111122056882575541062637026092122141686702534903437003 (pp58) Version: GGNFS-0.77.1-20060513-k8 Total time: 3.45 hours. Scaled time: 6.93 units (timescale=2.010). Factorization parameters were as follows: name: 21117_124 n: 22957416255699530501295404822326167390114094473872188918375242049826145386407603389399279197768288688392912359 m: 10000000000000000000000000 c5: 19 c0: 530 skew: 1.95 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 750001) Primes: RFBsize:49098, AFBsize:64098, largePrimes:2259309 encountered Relations: rels:2381189, finalFF:206711 Max relations in full relation-set: 28 Initial matrix: 113261 x 206711 with sparse part having weight 21468806. Pruned matrix : 99556 x 100186 with weight 8063758. Total sieving time: 3.27 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.07 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,126,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 3.45 hours. --------- CPU info (if available) ----------

(19·10¹⁰⁸+53)/9 = 2(1)₁₀₇7_<109> = 262411 · 460121017 · C95
C95 = P32 · P63
P32 = 40715325956793234293671007002897_<32>
P63 = 429436612371250961547371918499935905158308605193850743956973903_<63>

Sun Jun 1 23:08:03 2008 Msieve v. 1.35 Sun Jun 1 23:08:03 2008 random seeds: a3301bb0 3d53df02 Sun Jun 1 23:08:03 2008 factoring 17484651650476548830770449081096030553402318344900536526344925522349690719762578371973674396991 (95 digits) Sun Jun 1 23:08:04 2008 searching for 15-digit factors Sun Jun 1 23:08:06 2008 commencing quadratic sieve (95-digit input) Sun Jun 1 23:08:06 2008 using multiplier of 11 Sun Jun 1 23:08:07 2008 using 64kb Pentium 4 sieve core Sun Jun 1 23:08:07 2008 sieve interval: 18 blocks of size 65536 Sun Jun 1 23:08:07 2008 processing polynomials in batches of 6 Sun Jun 1 23:08:07 2008 using a sieve bound of 2128183 (78667 primes) Sun Jun 1 23:08:07 2008 using large prime bound of 310714718 (28 bits) Sun Jun 1 23:08:07 2008 using double large prime bound of 1933086450144842 (43-51 bits) Sun Jun 1 23:08:07 2008 using trial factoring cutoff of 51 bits Sun Jun 1 23:08:07 2008 polynomial 'A' values have 12 factors Mon Jun 2 06:07:09 2008 78793 relations (19031 full + 59762 combined from 1177846 partial), need 78763 Mon Jun 2 06:07:13 2008 begin with 1196877 relations Mon Jun 2 06:07:15 2008 reduce to 206885 relations in 12 passes Mon Jun 2 06:07:15 2008 attempting to read 206885 relations Mon Jun 2 06:07:21 2008 recovered 206885 relations Mon Jun 2 06:07:21 2008 recovered 192966 polynomials Mon Jun 2 06:07:22 2008 attempting to build 78793 cycles Mon Jun 2 06:07:22 2008 found 78793 cycles in 6 passes Mon Jun 2 06:07:22 2008 distribution of cycle lengths: Mon Jun 2 06:07:22 2008 length 1 : 19031 Mon Jun 2 06:07:22 2008 length 2 : 13437 Mon Jun 2 06:07:22 2008 length 3 : 13297 Mon Jun 2 06:07:22 2008 length 4 : 10751 Mon Jun 2 06:07:22 2008 length 5 : 8138 Mon Jun 2 06:07:22 2008 length 6 : 5588 Mon Jun 2 06:07:22 2008 length 7 : 3479 Mon Jun 2 06:07:22 2008 length 9+: 5072 Mon Jun 2 06:07:22 2008 largest cycle: 21 relations Mon Jun 2 06:07:22 2008 matrix is 78667 x 78793 (21.6 MB) with weight 5352964 (67.94/col) Mon Jun 2 06:07:22 2008 sparse part has weight 5352964 (67.94/col) Mon Jun 2 06:07:24 2008 filtering completed in 3 passes Mon Jun 2 06:07:24 2008 matrix is 75293 x 75357 (20.8 MB) with weight 5158753 (68.46/col) Mon Jun 2 06:07:24 2008 sparse part has weight 5158753 (68.46/col) Mon Jun 2 06:07:25 2008 saving the first 48 matrix rows for later Mon Jun 2 06:07:25 2008 matrix is 75245 x 75357 (14.5 MB) with weight 4257881 (56.50/col) Mon Jun 2 06:07:25 2008 sparse part has weight 3344104 (44.38/col) Mon Jun 2 06:07:25 2008 matrix includes 64 packed rows Mon Jun 2 06:07:25 2008 using block size 21845 for processor cache size 512 kB Mon Jun 2 06:07:26 2008 commencing Lanczos iteration Mon Jun 2 06:07:26 2008 memory use: 13.1 MB Mon Jun 2 06:08:33 2008 lanczos halted after 1192 iterations (dim = 75245) Mon Jun 2 06:08:34 2008 recovered 18 nontrivial dependencies Mon Jun 2 06:08:35 2008 prp32 factor: 40715325956793234293671007002897 Mon Jun 2 06:08:35 2008 prp63 factor: 429436612371250961547371918499935905158308605193850743956973903 Mon Jun 2 06:08:35 2008 elapsed time 07:00:32

(19·10¹²⁶+53)/9 = 2(1)₁₂₅7_<127> = 6903268719584384055121_<22> · C105
C105 = P48 · P58
P48 = 103864082049619335708579914537850517920687452179_<48>
P58 = 2944360108581633473932191940997116495964585541314631028463_<58>

Number: 21117_126 N=305813259901348875505100926497148986989091453916083398966422966908277463737129647551735449182057900370877 ( 105 digits) SNFS difficulty: 127 digits. Divisors found: r1=103864082049619335708579914537850517920687452179 (pp48) r2=2944360108581633473932191940997116495964585541314631028463 (pp58) Version: GGNFS-0.77.1-20060513-k8 Total time: 3.39 hours. Scaled time: 6.76 units (timescale=1.997). Factorization parameters were as follows: name: 21117_126 n: 305813259901348875505100926497148986989091453916083398966422966908277463737129647551735449182057900370877 m: 10000000000000000000000000 c5: 190 c0: 53 skew: 0.77 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 750001) Primes: RFBsize:49098, AFBsize:63698, largePrimes:2194925 encountered Relations: rels:2237426, finalFF:145939 Max relations in full relation-set: 28 Initial matrix: 112863 x 145939 with sparse part having weight 14497090. Pruned matrix : 107817 x 108445 with weight 8805731. Total sieving time: 3.20 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.07 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,127,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 3.39 hours. --------- CPU info (if available) ----------

(19·10¹²⁷+53)/9 = 2(1)₁₂₆7_<128> = 3² · 6983 · 9613105129_<10> · 61692263912471_<14> · C99
C99 = P42 · P58
P42 = 291916727489587673555967133607481146004727_<42>
P58 = 1940319099666381182533341297772978664273656217246287082027_<58>

Number: 21117_127 N=566411601860153100701394847632673604425475046837779231967780131659685243669308032364681161978741629 ( 99 digits) SNFS difficulty: 128 digits. Divisors found: r1=291916727489587673555967133607481146004727 (pp42) r2=1940319099666381182533341297772978664273656217246287082027 (pp58) Version: GGNFS-0.77.1-20060513-k8 Total time: 4.45 hours. Scaled time: 8.94 units (timescale=2.010). Factorization parameters were as follows: name: 21117_127 n: 566411601860153100701394847632673604425475046837779231967780131659685243669308032364681161978741629 m: 10000000000000000000000000 c5: 1900 c0: 53 skew: 0.49 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [400000, 950001) Primes: RFBsize:63951, AFBsize:63753, largePrimes:1434124 encountered Relations: rels:1402381, finalFF:144834 Max relations in full relation-set: 28 Initial matrix: 127771 x 144834 with sparse part having weight 9933985. Pruned matrix : 122878 x 123580 with weight 7074809. Total sieving time: 4.27 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.08 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,128,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 4.45 hours. --------- CPU info (if available) ----------

(19·10¹²⁹+53)/9 = 2(1)₁₂₈7_<130> = 699157 · 830191 · C118
C118 = P38 · P81
P38 = 32446483245581804133518445040362730189_<38>
P81 = 112096158128274832108557939489689899902140999040333373890236189338415740274281619_<81>

Number: 21117_129 N=3637126116603157908916080743469907732373168181016890173585191244364727938683418468784020814756624198363984843499095991 ( 118 digits) SNFS difficulty: 131 digits. Divisors found: r1=32446483245581804133518445040362730189 (pp38) r2=112096158128274832108557939489689899902140999040333373890236189338415740274281619 (pp81) Version: GGNFS-0.77.1-20060513-k8 Total time: 6.11 hours. Scaled time: 12.20 units (timescale=1.997). Factorization parameters were as follows: name: 21117_129 n: 3637126116603157908916080743469907732373168181016890173585191244364727938683418468784020814756624198363984843499095991 m: 100000000000000000000000000 c5: 19 c0: 530 skew: 1.95 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [400000, 1150001) Primes: RFBsize:63951, AFBsize:64098, largePrimes:1511991 encountered Relations: rels:1492598, finalFF:146143 Max relations in full relation-set: 28 Initial matrix: 128114 x 146143 with sparse part having weight 13064371. Pruned matrix : 123752 x 124456 with weight 9702245. Total sieving time: 5.90 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.10 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 6.11 hours. --------- CPU info (if available) ----------

(19·10¹³⁸+53)/9 = 2(1)₁₃₇7_<139> = 49169 · 59530109 · 361883017 · 1553270333_<10> · 1742932671511_<13> · C96
C96 = P30 · P67
P30 = 153982827554613533780693879837_<30>
P67 = 4780957545125991811271590664511031750645306007121798055625197067351_<67>

Mon Jun 2 06:17:46 2008 Msieve v. 1.35 Mon Jun 2 06:17:46 2008 random seeds: fbc554e4 1547fed8 Mon Jun 2 06:17:46 2008 factoring 736185361217064049236247539127012918759713514368891194303392952937676728083414902290966389901787 (96 digits) Mon Jun 2 06:17:48 2008 searching for 15-digit factors Mon Jun 2 06:17:50 2008 commencing quadratic sieve (96-digit input) Mon Jun 2 06:17:50 2008 using multiplier of 3 Mon Jun 2 06:17:50 2008 using 64kb Pentium 4 sieve core Mon Jun 2 06:17:50 2008 sieve interval: 18 blocks of size 65536 Mon Jun 2 06:17:50 2008 processing polynomials in batches of 6 Mon Jun 2 06:17:50 2008 using a sieve bound of 2299951 (84630 primes) Mon Jun 2 06:17:50 2008 using large prime bound of 344992650 (28 bits) Mon Jun 2 06:17:50 2008 using double large prime bound of 2333767984535850 (43-52 bits) Mon Jun 2 06:17:50 2008 using trial factoring cutoff of 52 bits Mon Jun 2 06:17:50 2008 polynomial 'A' values have 12 factors Mon Jun 2 15:43:57 2008 84765 relations (20102 full + 64663 combined from 1294956 partial), need 84726 Mon Jun 2 15:44:02 2008 begin with 1315058 relations Mon Jun 2 15:44:04 2008 reduce to 225164 relations in 11 passes Mon Jun 2 15:44:04 2008 attempting to read 225164 relations Mon Jun 2 15:44:11 2008 recovered 225164 relations Mon Jun 2 15:44:11 2008 recovered 212776 polynomials Mon Jun 2 15:44:12 2008 attempting to build 84765 cycles Mon Jun 2 15:44:12 2008 found 84765 cycles in 6 passes Mon Jun 2 15:44:12 2008 distribution of cycle lengths: Mon Jun 2 15:44:12 2008 length 1 : 20102 Mon Jun 2 15:44:12 2008 length 2 : 14231 Mon Jun 2 15:44:12 2008 length 3 : 13930 Mon Jun 2 15:44:12 2008 length 4 : 11635 Mon Jun 2 15:44:12 2008 length 5 : 9103 Mon Jun 2 15:44:12 2008 length 6 : 6090 Mon Jun 2 15:44:12 2008 length 7 : 3877 Mon Jun 2 15:44:12 2008 length 9+: 5797 Mon Jun 2 15:44:12 2008 largest cycle: 19 relations Mon Jun 2 15:44:12 2008 matrix is 84630 x 84765 (23.9 MB) with weight 5923925 (69.89/col) Mon Jun 2 15:44:12 2008 sparse part has weight 5923925 (69.89/col) Mon Jun 2 15:44:14 2008 filtering completed in 3 passes Mon Jun 2 15:44:14 2008 matrix is 81223 x 81287 (23.1 MB) with weight 5721340 (70.38/col) Mon Jun 2 15:44:14 2008 sparse part has weight 5721340 (70.38/col) Mon Jun 2 15:44:15 2008 saving the first 48 matrix rows for later Mon Jun 2 15:44:15 2008 matrix is 81175 x 81287 (17.2 MB) with weight 4837727 (59.51/col) Mon Jun 2 15:44:15 2008 sparse part has weight 4015307 (49.40/col) Mon Jun 2 15:44:15 2008 matrix includes 64 packed rows Mon Jun 2 15:44:15 2008 using block size 21845 for processor cache size 512 kB Mon Jun 2 15:44:16 2008 commencing Lanczos iteration Mon Jun 2 15:44:16 2008 memory use: 15.0 MB Mon Jun 2 15:45:40 2008 lanczos halted after 1285 iterations (dim = 81173) Mon Jun 2 15:45:40 2008 recovered 16 nontrivial dependencies Mon Jun 2 15:45:42 2008 prp30 factor: 153982827554613533780693879837 Mon Jun 2 15:45:42 2008 prp67 factor: 4780957545125991811271590664511031750645306007121798055625197067351 Mon Jun 2 15:45:42 2008 elapsed time 09:27:56

(19·10¹⁴⁸+53)/9 = 2(1)₁₄₇7_<149> = 3 · 109 · 163 · 24029 · 182617 · 368507 · 1351981 · 253573542341957_<15> · 63117301189870715519_<20> · C89
C89 = P39 · P50
P39 = 362057969379015044200712589221264255659_<39>
P50 = 31264539269177925749669527557963065564867851547731_<50>

Mon Jun 2 15:54:31 2008 Msieve v. 1.35 Mon Jun 2 15:54:31 2008 random seeds: 05a7b83d b339eb60 Mon Jun 2 15:54:31 2008 factoring 11319575601369034829580537568191960657052642282608078063135992672601045638966210825359729 (89 digits) Mon Jun 2 15:54:33 2008 searching for 15-digit factors Mon Jun 2 15:54:34 2008 commencing quadratic sieve (89-digit input) Mon Jun 2 15:54:34 2008 using multiplier of 1 Mon Jun 2 15:54:34 2008 using 64kb Pentium 4 sieve core Mon Jun 2 15:54:34 2008 sieve interval: 14 blocks of size 65536 Mon Jun 2 15:54:34 2008 processing polynomials in batches of 8 Mon Jun 2 15:54:34 2008 using a sieve bound of 1536389 (58333 primes) Mon Jun 2 15:54:34 2008 using large prime bound of 122911120 (26 bits) Mon Jun 2 15:54:34 2008 using double large prime bound of 364136361200880 (42-49 bits) Mon Jun 2 15:54:34 2008 using trial factoring cutoff of 49 bits Mon Jun 2 15:54:34 2008 polynomial 'A' values have 11 factors Mon Jun 2 17:24:07 2008 58499 relations (15792 full + 42707 combined from 617918 partial), need 58429 Mon Jun 2 17:24:09 2008 begin with 633710 relations Mon Jun 2 17:24:10 2008 reduce to 142214 relations in 11 passes Mon Jun 2 17:24:10 2008 attempting to read 142214 relations Mon Jun 2 17:24:13 2008 recovered 142214 relations Mon Jun 2 17:24:13 2008 recovered 118727 polynomials Mon Jun 2 17:24:14 2008 attempting to build 58499 cycles Mon Jun 2 17:24:14 2008 found 58499 cycles in 5 passes Mon Jun 2 17:24:14 2008 distribution of cycle lengths: Mon Jun 2 17:24:14 2008 length 1 : 15792 Mon Jun 2 17:24:14 2008 length 2 : 11349 Mon Jun 2 17:24:14 2008 length 3 : 10193 Mon Jun 2 17:24:14 2008 length 4 : 7776 Mon Jun 2 17:24:14 2008 length 5 : 5432 Mon Jun 2 17:24:14 2008 length 6 : 3467 Mon Jun 2 17:24:14 2008 length 7 : 2040 Mon Jun 2 17:24:14 2008 length 9+: 2450 Mon Jun 2 17:24:14 2008 largest cycle: 18 relations Mon Jun 2 17:24:14 2008 matrix is 58333 x 58499 (13.8 MB) with weight 3374198 (57.68/col) Mon Jun 2 17:24:14 2008 sparse part has weight 3374198 (57.68/col) Mon Jun 2 17:24:15 2008 filtering completed in 3 passes Mon Jun 2 17:24:15 2008 matrix is 54272 x 54335 (12.9 MB) with weight 3169633 (58.34/col) Mon Jun 2 17:24:15 2008 sparse part has weight 3169633 (58.34/col) Mon Jun 2 17:24:15 2008 saving the first 48 matrix rows for later Mon Jun 2 17:24:15 2008 matrix is 54224 x 54335 (8.5 MB) with weight 2506354 (46.13/col) Mon Jun 2 17:24:15 2008 sparse part has weight 1906309 (35.08/col) Mon Jun 2 17:24:15 2008 matrix includes 64 packed rows Mon Jun 2 17:24:15 2008 using block size 21734 for processor cache size 512 kB Mon Jun 2 17:24:16 2008 commencing Lanczos iteration Mon Jun 2 17:24:16 2008 memory use: 8.2 MB Mon Jun 2 17:24:47 2008 lanczos halted after 858 iterations (dim = 54222) Mon Jun 2 17:24:47 2008 recovered 15 nontrivial dependencies Mon Jun 2 17:24:48 2008 prp39 factor: 362057969379015044200712589221264255659 Mon Jun 2 17:24:48 2008 prp50 factor: 31264539269177925749669527557963065564867851547731 Mon Jun 2 17:24:48 2008 elapsed time 01:30:17

(19·10¹³²+53)/9 = 2(1)₁₃₁7_<133> = 229637 · 624509 · 1096168133_<10> · 2996578231_<10> · C103
C103 = P30 · P74
P30 = 274774136419884955287483432737_<30>
P74 = 16309921890964946701578150469724656682279803131647250107014492259289394799_<74>

Number: 21117_132 N=4481544702665670260142350017053071939841557981489925134501982700492970878648611368462978938115754134863 ( 103 digits) SNFS difficulty: 133 digits. Divisors found: r1=274774136419884955287483432737 (pp30) r2=16309921890964946701578150469724656682279803131647250107014492259289394799 (pp74) Version: GGNFS-0.77.1-20060513-k8 Total time: 7.69 hours. Scaled time: 15.49 units (timescale=2.016). Factorization parameters were as follows: name: 21117_132 n: 4481544702665670260142350017053071939841557981489925134501982700492970878648611368462978938115754134863 m: 100000000000000000000000000 c5: 1900 c0: 53 skew: 0.49 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [400000, 1450001) Primes: RFBsize:63951, AFBsize:63753, largePrimes:1604706 encountered Relations: rels:1630922, finalFF:175301 Max relations in full relation-set: 28 Initial matrix: 127771 x 175301 with sparse part having weight 17797755. Pruned matrix : 117290 x 117992 with weight 10304530. Total sieving time: 7.45 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.11 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,133,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 7.69 hours. --------- CPU info (if available) ----------

(19·10¹⁴⁴+53)/9 = 2(1)₁₄₃7_<145> = 43 · 9819072943_<10> · 10619340031061_<14> · 1221482300914250354995629197_<28> · C93
C93 = P32 · P61
P32 = 59460061664238851775266882472133_<32>
P61 = 6482792018674955359906067036006848637517667147841276577049253_<61>

Mon Jun 2 17:39:49 2008 Msieve v. 1.35 Mon Jun 2 17:39:49 2008 random seeds: ecb5fe42 7f1f0941 Mon Jun 2 17:39:49 2008 factoring 385467213186848311654808549004712309847359247130531463837047964694710049428655567891140966649 (93 digits) Mon Jun 2 17:39:51 2008 searching for 15-digit factors Mon Jun 2 17:39:53 2008 commencing quadratic sieve (93-digit input) Mon Jun 2 17:39:53 2008 using multiplier of 1 Mon Jun 2 17:39:53 2008 using 64kb Pentium 4 sieve core Mon Jun 2 17:39:53 2008 sieve interval: 18 blocks of size 65536 Mon Jun 2 17:39:53 2008 processing polynomials in batches of 6 Mon Jun 2 17:39:53 2008 using a sieve bound of 1914511 (71765 primes) Mon Jun 2 17:39:53 2008 using large prime bound of 231655831 (27 bits) Mon Jun 2 17:39:53 2008 using double large prime bound of 1139509009637394 (42-51 bits) Mon Jun 2 17:39:53 2008 using trial factoring cutoff of 51 bits Mon Jun 2 17:39:53 2008 polynomial 'A' values have 12 factors Mon Jun 2 21:14:02 2008 72278 relations (18172 full + 54106 combined from 957428 partial), need 71861 Mon Jun 2 21:14:06 2008 begin with 975600 relations Mon Jun 2 21:14:07 2008 reduce to 184070 relations in 13 passes Mon Jun 2 21:14:07 2008 attempting to read 184070 relations Mon Jun 2 21:14:12 2008 recovered 184070 relations Mon Jun 2 21:14:12 2008 recovered 162815 polynomials Mon Jun 2 21:14:13 2008 attempting to build 72278 cycles Mon Jun 2 21:14:13 2008 found 72278 cycles in 6 passes Mon Jun 2 21:14:13 2008 distribution of cycle lengths: Mon Jun 2 21:14:13 2008 length 1 : 18172 Mon Jun 2 21:14:13 2008 length 2 : 13053 Mon Jun 2 21:14:13 2008 length 3 : 12368 Mon Jun 2 21:14:13 2008 length 4 : 9884 Mon Jun 2 21:14:13 2008 length 5 : 7240 Mon Jun 2 21:14:13 2008 length 6 : 4805 Mon Jun 2 21:14:13 2008 length 7 : 2998 Mon Jun 2 21:14:13 2008 length 9+: 3758 Mon Jun 2 21:14:13 2008 largest cycle: 22 relations Mon Jun 2 21:14:13 2008 matrix is 71765 x 72278 (17.3 MB) with weight 4257237 (58.90/col) Mon Jun 2 21:14:13 2008 sparse part has weight 4257237 (58.90/col) Mon Jun 2 21:14:15 2008 filtering completed in 3 passes Mon Jun 2 21:14:15 2008 matrix is 67846 x 67910 (16.3 MB) with weight 4001883 (58.93/col) Mon Jun 2 21:14:15 2008 sparse part has weight 4001883 (58.93/col) Mon Jun 2 21:14:15 2008 saving the first 48 matrix rows for later Mon Jun 2 21:14:15 2008 matrix is 67798 x 67910 (8.9 MB) with weight 2957170 (43.55/col) Mon Jun 2 21:14:15 2008 sparse part has weight 1922201 (28.31/col) Mon Jun 2 21:14:15 2008 matrix includes 64 packed rows Mon Jun 2 21:14:15 2008 using block size 21845 for processor cache size 512 kB Mon Jun 2 21:14:16 2008 commencing Lanczos iteration Mon Jun 2 21:14:16 2008 memory use: 9.6 MB Mon Jun 2 21:14:59 2008 lanczos halted after 1073 iterations (dim = 67795) Mon Jun 2 21:14:59 2008 recovered 15 nontrivial dependencies Mon Jun 2 21:15:02 2008 prp32 factor: 59460061664238851775266882472133 Mon Jun 2 21:15:02 2008 prp61 factor: 6482792018674955359906067036006848637517667147841276577049253 Mon Jun 2 21:15:02 2008 elapsed time 03:35:13

Jun 2, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM
(19·10¹²⁸+53)/9 = 2(1)₁₂₇7_<129> = 7 · C128
C128 = P51 · P78
P51 = 271141390923736296890969959857913248646126105732399_<51>
P78 = 111228794895475322398277643129562837424306229357728734610117553484069301696869_<78>

Number: n N=30158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158731 ( 128 digits) SNFS difficulty: 129 digits. Divisors found: r1=271141390923736296890969959857913248646126105732399 (pp51) r2=111228794895475322398277643129562837424306229357728734610117553484069301696869 (pp78) Version: GGNFS-0.77.1-20051202-athlon Total time: 2.76 hours. Scaled time: 5.03 units (timescale=1.823). Factorization parameters were as follows: name: KA_2_1_127_7 n: 30158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158730158731 skew: 0.49 deg: 5 c5: 19000 c0: 53 m: 10000000000000000000000000 type: snfs rlim: 1500000 alim: 1500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 420001) Primes: RFBsize:114155, AFBsize:114222, largePrimes:5215005 encountered Relations: rels:4612501, finalFF:288380 Max relations in full relation-set: 48 Initial matrix: 228444 x 288380 with sparse part having weight 17831781. Pruned matrix : 180854 x 182060 with weight 8358571. Total sieving time: 2.48 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.14 hours. Total square root time: 0.04 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,129,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,50000 total time: 2.76 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

(11·10¹⁷²+61)/9 = 1(2)₁₇₁9_<173> = 7 · 17 · C171
C171 = P41 · P51 · P80
P41 = 12028479575122500852357107894999807304683_<41>
P51 = 731295526744164282624207366517572340820823022344947_<51>
P80 = 11676147223871752732879615382398657779764886931536666306447311056887715314521891_<80>

Number: n N=102707749766573295985060690943043884220354808590102707749766573295985060690943043884220354808590102707749766573295985060690943043884220354808590102707749766573295985060691 ( 171 digits) SNFS difficulty: 173 digits. Divisors found: Mon Jun 02 12:00:46 2008 prp41 factor: 12028479575122500852357107894999807304683 Mon Jun 02 12:00:46 2008 prp51 factor: 731295526744164282624207366517572340820823022344947 Mon Jun 02 12:00:46 2008 prp80 factor: 11676147223871752732879615382398657779764886931536666306447311056887715314521891 Mon Jun 02 12:00:46 2008 elapsed time 02:16:33 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 132.61 hours. Scaled time: 241.74 units (timescale=1.823). Factorization parameters were as follows: name: KA_1_2_171_9 n: 102707749766573295985060690943043884220354808590102707749766573295985060690943043884220354808590102707749766573295985060690943043884220354808590102707749766573295985060691 skew: 0.56 deg: 5 c5: 1100 c0: 61 m: 10000000000000000000000000000000000 type: snfs rlim: 3800000 alim: 3800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3800000/3800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 8900279) Primes: RFBsize:269987, AFBsize:269319, largePrimes:8671566 encountered Relations: rels:8126828, finalFF:570564 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 132.21 hours. Total relation processing time: 0.40 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,173,5,0,0,0,0,0,0,0,0,3800000,3800000,28,28,48,48,2.5,2.5,100000 total time: 132.61 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

(19·10¹³³+53)/9 = 2(1)₁₃₂7_<134> = 3 · 71 · 137 · C129
C129 = P37 · P93
P37 = 4513613610675304606872458634030936047_<37>
P93 = 160282660468278098339555574832288507693386513616326522786634467104125332769066378678664671231_<93>

Number: n N=723453997844868616946338751623011929375659199859878383575309657349340704948806110520924954974507765707518971629180326620441763857 ( 129 digits) SNFS difficulty: 134 digits. Divisors found: Mon Jun 02 13:50:41 2008 prp37 factor: 4513613610675304606872458634030936047 Mon Jun 02 13:50:41 2008 prp93 factor: 160282660468278098339555574832288507693386513616326522786634467104125332769066378678664671231 Mon Jun 02 13:50:41 2008 elapsed time 00:18:55 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 3.56 hours. Scaled time: 6.52 units (timescale=1.829). Factorization parameters were as follows: name: KA_2_1_132_7 n: 723453997844868616946338751623011929375659199859878383575309657349340704948806110520924954974507765707518971629180326620441763857 skew: 0.31 deg: 5 c5: 19000 c0: 53 m: 100000000000000000000000000 type: snfs rlim: 1600000 alim: 1600000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 1600000/1600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 560001) Primes: RFBsize:121127, AFBsize:121110, largePrimes:5674008 encountered Relations: rels:5002947, finalFF:281155 Max relations in full relation-set: 28 Initial matrix: 242304 x 281155 with sparse part having weight 20748030. Pruned matrix : Total sieving time: 3.46 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,134,5,0,0,0,0,0,0,0,0,1600000,1600000,28,28,48,48,2.5,2.5,75000 total time: 3.56 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

(19·10¹⁶⁶+53)/9 = 2(1)₁₆₅7_<167> = 3 · 94597 · 2198191 · 12154976546378825893_<20> · 22397921288742578946556385747021_<32> · C105
C105 = P33 · P72
P33 = 334551636295269131863698068034581_<33>
P72 = 371554093246116187712128253073382931231925606666989345072655834471049849_<72>

Jun 2, 2008

By Tyler Cadigan / GGNFS, Msieve
8·10¹⁹⁷+9 = 8(0)₁₉₆9_<198> = 7 · 12219247 · 15213705288655807_<17> · 4865154059575323971503_<22> · 37114608851460783280897610347_<29> · C124
C124 = P62 · P63
P62 = 16621692800680584305294747562998773325126469691178650296201467_<62>
P63 = 204831038833285778102275560455244890057538477743970633200511049_<63>

Number: 80009_197 N=3404638603531151408492144608513648227826645811936364923836164689727994762576449290071236221548482768741339116814127863508883 ( 124 digits) Divisors found: r1=16621692800680584305294747562998773325126469691178650296201467 r2=204831038833285778102275560455244890057538477743970633200511049 Version: Total time: 81.57 hours. Scaled time: 206.94 units (timescale=2.537). Factorization parameters were as follows: name: 80009_197 n: 3404638603531151408492144608513648227826645811936364923836164689727994762576449290071236221548482768741339116814127863508883 skew: 70717.79 # norm 3.61e+017 c5: 478800 c4: 81917542588 c3: -13839480355966165 c2: -262680385946951499111 c1: 21383762814069117708461157 c0: 68693812172939743478896238955 # alpha -6.89 Y1: 27372789176161 Y0: -371862411727914405008552 # Murphy_E 1.72e-010 # M 1446656491575742184387572950846474116950583333787238843359449638130640620324693639485660327461752000793094567024696147419232 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, 6100001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 737464 x 737712 Polynomial selection time: 9.10 hours. Total sieving time: 72.47 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,5000000,5000000,27,27,50,50,2.4,2.4,60000 total time: 81.57 hours. --------- CPU info (if available) ----------

Jun 1, 2008 (4th)

By Sinkiti Sibata / GGNFS
(19·10¹¹⁷+53)/9 = 2(1)₁₁₆7_<118> = 137 · 173 · C113
C113 = P48 · P66
P48 = 340739379185554837829678627965128592230514605529_<48>
P66 = 261409937598548866812402751089866267362790132318322972151795257473_<66>

Number: 21117_117 N=89072659850264170756976967685376613269951103797776933931526564748791659048610232104599430872583904101561584368217 ( 113 digits) SNFS difficulty: 118 digits. Divisors found: r1=340739379185554837829678627965128592230514605529 (pp48) r2=261409937598548866812402751089866267362790132318322972151795257473 (pp66) Version: GGNFS-0.77.1-20060513-k8 Total time: 3.90 hours. Scaled time: 7.82 units (timescale=2.003). Factorization parameters were as follows: name: 21117_117 n: 89072659850264170756976967685376613269951103797776933931526564748791659048610232104599430872583904101561584368217 m: 100000000000000000000000 c5: 1900 c0: 53 skew: 0.49 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 650001) Primes: RFBsize:49098, AFBsize:63753, largePrimes:2477594 encountered Relations: rels:2999016, finalFF:614924 Max relations in full relation-set: 28 Initial matrix: 112918 x 614924 with sparse part having weight 56713889. Pruned matrix : 73573 x 74201 with weight 7485835. Total sieving time: 3.76 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.04 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,118,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 3.90 hours. --------- CPU info (if available) ----------

(19·10¹¹⁸+53)/9 = 2(1)₁₁₇7_<119> = 3² · 647 · 16240958219_<11> · C105
C105 = P36 · P69
P36 = 355681218568581823872236281324646653_<36>
P69 = 627612694100122250224375210065246217931458194520185206310045788028397_<69>

Number: 21117_118 N=223230047826642066205521963974483683939638118880420228496218591190724410961696681286005167031723555005241 ( 105 digits) SNFS difficulty: 119 digits. Divisors found: r1=355681218568581823872236281324646653 (pp36) r2=627612694100122250224375210065246217931458194520185206310045788028397 (pp69) Version: GGNFS-0.77.1-20060513-k8 Total time: 3.31 hours. Scaled time: 6.60 units (timescale=1.991). Factorization parameters were as follows: name: 21117_118 n: 223230047826642066205521963974483683939638118880420228496218591190724410961696681286005167031723555005241 m: 100000000000000000000000 c5: 19000 c0: 53 skew: 0.31 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 650001) Primes: RFBsize:49098, AFBsize:63858, largePrimes:2468293 encountered Relations: rels:2965236, finalFF:582489 Max relations in full relation-set: 28 Initial matrix: 113023 x 582489 with sparse part having weight 56724991. Pruned matrix : 76137 x 76766 with weight 9107278. Total sieving time: 3.16 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.04 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,119,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 3.31 hours. --------- CPU info (if available) ----------

(16·10¹⁶⁴-7)/9 = 1(7)_164<165> = 3 · 2579 · 51439 · 4963080423026380935320657_<25> · C131
C131 = P62 · P70
P62 = 27077574071931379632102132928358669855145747323367902682258041_<62>
P70 = 3323925597838468353082294553807010837436662578376074591306828959271647_<70>

Number: 17777_164 N=90003841585059920924224866844440249713658946274123664702277080206963969563210631887340234268972054822694480502697694149336669063527 ( 131 digits) SNFS difficulty: 165 digits. Divisors found: r1=27077574071931379632102132928358669855145747323367902682258041 (pp62) r2=3323925597838468353082294553807010837436662578376074591306828959271647 (pp70) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 131.28 hours. Scaled time: 88.88 units (timescale=0.677). Factorization parameters were as follows: name: 17777_164 n: 90003841585059920924224866844440249713658946274123664702277080206963969563210631887340234268972054822694480502697694149336669063527 m: 1000000000000000000000000000000000 c5: 8 c0: -35 skew: 1.34 type: snfs Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2500000, 5500001) Primes: RFBsize:348513, AFBsize:349436, largePrimes:5872683 encountered Relations: rels:6032223, finalFF:800929 Max relations in full relation-set: 28 Initial matrix: 698014 x 800929 with sparse part having weight 49993017. Pruned matrix : 618137 x 621691 with weight 36216756. Total sieving time: 112.92 hours. Total relation processing time: 0.41 hours. Matrix solve time: 17.71 hours. Time per square root: 0.25 hours. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000 total time: 131.28 hours. --------- CPU info (if available) ----------

Jun 1, 2008 (3rd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve
(19·10¹⁰⁵+53)/9 = 2(1)₁₀₄7_<106> = 753148849 · C97
C97 = P33 · P64
P33 = 911966845446144824010461085219467_<33>
P64 = 3073627441612605884921881130730293562533139400059580806969126199_<64>
(19·10¹¹³+53)/9 = 2(1)₁₁₂7_<114> = 55057 · C109
C109 = P38 · P71
P38 = 58757645619987456838275424826062650763_<38>
P71 = 65258060544098108161363500386786898008268259644863574985134074625486487_<71>
(19·10¹²²+53)/9 = 2(1)₁₂₁7_<123> = 7 · 31 · 229 · 7699981 · 260740884419_<12> · C100
C100 = P48 · P52
P48 = 589368244104645491805519232085371347662733937127_<48>
P52 = 3590296830419907767433446957296372459019708981878273_<52>

Number: n N=2116006938759055201081299150385079711667157232288061779372701201257089798938424952493683560749341671 ( 100 digits) SNFS difficulty: 123 digits. Divisors found: Mon Jun 02 00:23:15 2008 prp48 factor: 589368244104645491805519232085371347662733937127 Mon Jun 02 00:23:15 2008 prp52 factor: 3590296830419907767433446957296372459019708981878273 Mon Jun 02 00:23:15 2008 elapsed time 00:13:21 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 1.61 hours. Scaled time: 2.94 units (timescale=1.823). Factorization parameters were as follows: name: KA_2_1_121_7 n: 2116006938759055201081299150385079711667157232288061779372701201257089798938424952493683560749341671 skew: 0.49 deg: 5 c5: 1900 c0: 53 m: 1000000000000000000000000 type: snfs rlim: 1000000 alim: 1000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 280337) Primes: RFBsize:78498, AFBsize:78301, largePrimes:4407787 encountered Relations: rels:3743887, finalFF:172633 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 1.55 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,123,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.5,2.5,50000 total time: 1.61 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+

Jun 1, 2008 (2nd)

By Wataru Sakai / GGNFS
(61·10¹⁶⁷-7)/9 = 6(7)_167<168> = 114611656331_<12> · C157
C157 = P74 · P83
P74 = 93444174992472819257688502885450481471938296013132895952362893249876854697_<74>
P83 = 63285804116327054211214121309466806760944769236184213402549280405475070400939982011_<83>

Number: 67777_167 N=5913689754385421924941064638506622593709715696454659744653592670342697115329570254212974844663993897741044747015015353375643536731026442195443240180440855667 ( 157 digits) SNFS difficulty: 168 digits. Divisors found: r1=93444174992472819257688502885450481471938296013132895952362893249876854697 (pp74) r2=63285804116327054211214121309466806760944769236184213402549280405475070400939982011 (pp83) Version: GGNFS-0.77.1-20060722-nocona Total time: 150.31 hours. Scaled time: 302.28 units (timescale=2.011). Factorization parameters were as follows: n: 5913689754385421924941064638506622593709715696454659744653592670342697115329570254212974844663993897741044747015015353375643536731026442195443240180440855667 m: 1000000000000000000000000000000000 c5: 6100 c0: -7 skew: 0.26 type: snfs Factor base limits: 5500000/5500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2750000, 8450001) Primes: RFBsize:380800, AFBsize:380633, largePrimes:6496633 encountered Relations: rels:6945548, finalFF:1064739 Max relations in full relation-set: 32 Initial matrix: 761500 x 1064739 with sparse part having weight 95376348. Pruned matrix : 538647 x 542518 with weight 86032135. Total sieving time: 146.14 hours. Total relation processing time: 0.11 hours. Matrix solve time: 3.87 hours. Time per square root: 0.20 hours. Prototype def-par.txt line would be: snfs,168,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.6,2.6,100000 total time: 150.31 hours.

Jun 1, 2008

The factor table of 211...117 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.