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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