News and updates, October 2009

Home > Math > Factorizations >

News and updates, October 2009

Oct 31, 2009 (4th): By Sinkiti Sibata / GGNFS, Msieve / Oct 30, 2009
(67·10¹³⁵-13)/9 = 7(4)₁₃₄3_<136> = 3 · 6366299 · 343322550875497_<15> · 18427413715447589_<17> · C98
C98 = P39 · P60
P39 = 209356080628475924973631219217832056833_<39>
P60 = 294287428717985459743101905958444395235619064479793257863671_<60>

Number: 74443_135 N=61610862654629425320461097325772360749579711146654232773145044842857294758491948071998405438013943 ( 98 digits) SNFS difficulty: 136 digits. Divisors found: r1=209356080628475924973631219217832056833 (pp39) r2=294287428717985459743101905958444395235619064479793257863671 (pp60) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 8.70 hours. Scaled time: 4.09 units (timescale=0.470). Factorization parameters were as follows: name: 74443_135 n: 61610862654629425320461097325772360749579711146654232773145044842857294758491948071998405438013943 m: 1000000000000000000000000000 deg: 5 c5: 67 c0: -13 skew: 0.72 type: snfs lss: 1 rlim: 1340000 alim: 1340000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1340000/1340000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [670000, 1345001) Primes: RFBsize:102852, AFBsize:102619, largePrimes:3220602 encountered Relations: rels:3134916, finalFF:237995 Max relations in full relation-set: 28 Initial matrix: 205536 x 237995 with sparse part having weight 19742667. Pruned matrix : 195806 x 196897 with weight 13765686. Total sieving time: 7.72 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.78 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,136,5,0,0,0,0,0,0,0,0,1340000,1340000,26,26,48,48,2.3,2.3,75000 total time: 8.70 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS, Msieve / Oct 31, 2009
(62·10¹⁴²-53)/9 = 6(8)₁₄₁3_<143> = 3 · 38231 · C138
C138 = P31 · P108
P31 = 1897221955530729728636794936489_<31>
P108 = 316587764021525936138950181020917122053434327967423987470819925009163201030651339553471066974369806252970879_<108>

Number: 68883_142 N=600637256754020636733618345399360805706441447070779288089847583452249822472939838428577933168448718656665087571943264967250737960371503831 ( 138 digits) SNFS difficulty: 144 digits. Divisors found: r1=1897221955530729728636794936489 (pp31) r2=316587764021525936138950181020917122053434327967423987470819925009163201030651339553471066974369806252970879 (pp108) Version: GGNFS-0.77.1-20060513-k8 Total time: 23.85 hours. Scaled time: 46.67 units (timescale=1.957). Factorization parameters were as follows: name: 68883_142 n: 600637256754020636733618345399360805706441447070779288089847583452249822472939838428577933168448718656665087571943264967250737960371503831 m: 20000000000000000000000000000 deg: 5 c5: 775 c0: -212 skew: 0.77 type: snfs lss: 1 rlim: 1790000 alim: 1790000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1790000/1790000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [895000, 2995001) Primes: RFBsize:134359, AFBsize:134018, largePrimes:4285211 encountered Relations: rels:4611288, finalFF:372028 Max relations in full relation-set: 28 Initial matrix: 268444 x 372028 with sparse part having weight 44790153. Pruned matrix : 239391 x 240797 with weight 28079612. Total sieving time: 22.68 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.91 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: snfs,144,5,0,0,0,0,0,0,0,0,1790000,1790000,26,26,49,49,2.3,2.3,100000 total time: 23.85 hours. --------- CPU info (if available) ----------
(62·10¹⁴⁶-17)/9 = 6(8)₁₄₅7_<147> = 3 · 467 · 8199181 · C137
C137 = P34 · P104
P34 = 1362518920977791402556581436857353_<34>
P104 = 44014728682733656162984696344578934532017463783335918028526772701777175353463305906690407115138338099859_<104>

Number: 68887_146 N=59970900631928507134678788225256830909677272320730651392923130286217054871587593448388419881377479427147482375478201781976233202452413227 ( 137 digits) SNFS difficulty: 148 digits. Divisors found: r1=1362518920977791402556581436857353 (pp34) r2=44014728682733656162984696344578934532017463783335918028526772701777175353463305906690407115138338099859 (pp104) Version: Msieve-1.40 Total time: 13.52 hours. Scaled time: 28.20 units (timescale=2.085). Factorization parameters were as follows: name: 68887_146 n: 59970900631928507134678788225256830909677272320730651392923130286217054871587593448388419881377479427147482375478201781976233202452413227 m: 200000000000000000000000000000 deg: 5 c5: 155 c0: -136 skew: 0.97 type: snfs lss: 1 rlim: 2100000 alim: 2100000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 2100000/2100000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [1050000, 2650001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 356196 x 356425 Total sieving time: 12.87 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.44 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,148.000,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,49,49,2.3,2.3,100000 total time: 13.52 hours. --------- CPU info (if available) ----------
(67·10¹³⁶-13)/9 = 7(4)₁₃₅3_<137> = 107071636716652010184212485927_<30> · C108
C108 = P49 · P60
P49 = 1388497017615733774323439876017921362377077183293_<49>
P60 = 500740709756802603000974713552278904512748721414586970310513_<60>

Number: 73339_136 N=695276982096106176900642839859448798309712051367578561086347155086278922700828965871905561126372859625859309 ( 108 digits) SNFS difficulty: 139 digits. Divisors found: r1=1388497017615733774323439876017921362377077183293 (pp49) r2=500740709756802603000974713552278904512748721414586970310513 (pp60) Version: GGNFS-0.77.1-20060513-k8 Total time: 9.04 hours. Scaled time: 17.71 units (timescale=1.960). Factorization parameters were as follows: name: 73339_136 n: 695276982096106176900642839859448798309712051367578561086347155086278922700828965871905561126372859625859309 m: 2000000000000000000000000000 deg: 5 c5: 335 c0: -208 skew: 0.91 type: snfs lss: 1 rlim: 1450000 alim: 1450000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1450000/1450000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [725000, 1550001) Primes: RFBsize:110630, AFBsize:110649, largePrimes:3508814 encountered Relations: rels:3522800, finalFF:297635 Max relations in full relation-set: 28 Initial matrix: 221346 x 297635 with sparse part having weight 27324926. Pruned matrix : 198752 x 199922 with weight 15189467. Total sieving time: 8.42 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.42 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,139,5,0,0,0,0,0,0,0,0,1450000,1450000,26,26,48,48,2.3,2.3,75000 total time: 9.04 hours. --------- CPU info (if available) ----------
(64·10¹⁸⁵+71)/9 = 7(1)₁₈₄9_<186> = 593707 · 594449 · 4422329046727_<13> · 40284292656009544724056072361587_<32> · 9116432441824664823352631671213357_<34> · C97
C97 = P47 · P50
P47 = 13226685334951086277235559910788997247553626789_<47>
P50 = 93796786332729755561282648937916873301551400163929_<50>

Sat Oct 31 07:48:36 2009 Msieve v. 1.40 Sat Oct 31 07:48:36 2009 random seeds: 95692308 2fbe9ed9 Sat Oct 31 07:48:36 2009 factoring 1240620578252657138397677340020548602052064584196378623862760965588007134959583060094673085893981 (97 digits) Sat Oct 31 07:48:37 2009 no P-1/P+1/ECM available, skipping Sat Oct 31 07:48:37 2009 commencing quadratic sieve (97-digit input) Sat Oct 31 07:48:37 2009 using multiplier of 1 Sat Oct 31 07:48:37 2009 using 32kb Intel Core sieve core Sat Oct 31 07:48:37 2009 sieve interval: 36 blocks of size 32768 Sat Oct 31 07:48:37 2009 processing polynomials in batches of 6 Sat Oct 31 07:48:37 2009 using a sieve bound of 2319689 (85882 primes) Sat Oct 31 07:48:37 2009 using large prime bound of 347953350 (28 bits) Sat Oct 31 07:48:37 2009 using double large prime bound of 2369942626511550 (43-52 bits) Sat Oct 31 07:48:37 2009 using trial factoring cutoff of 52 bits Sat Oct 31 07:48:37 2009 polynomial 'A' values have 12 factors Sat Oct 31 12:43:57 2009 86053 relations (20821 full + 65232 combined from 1294325 partial), need 85978 Sat Oct 31 12:43:58 2009 begin with 1315146 relations Sat Oct 31 12:43:58 2009 reduce to 225963 relations in 11 passes Sat Oct 31 12:43:58 2009 attempting to read 225963 relations Sat Oct 31 12:44:00 2009 recovered 225963 relations Sat Oct 31 12:44:00 2009 recovered 211772 polynomials Sat Oct 31 12:44:00 2009 attempting to build 86053 cycles Sat Oct 31 12:44:00 2009 found 86053 cycles in 6 passes Sat Oct 31 12:44:00 2009 distribution of cycle lengths: Sat Oct 31 12:44:00 2009 length 1 : 20821 Sat Oct 31 12:44:00 2009 length 2 : 14726 Sat Oct 31 12:44:00 2009 length 3 : 14389 Sat Oct 31 12:44:00 2009 length 4 : 11723 Sat Oct 31 12:44:00 2009 length 5 : 8681 Sat Oct 31 12:44:00 2009 length 6 : 6191 Sat Oct 31 12:44:00 2009 length 7 : 3942 Sat Oct 31 12:44:00 2009 length 9+: 5580 Sat Oct 31 12:44:00 2009 largest cycle: 21 relations Sat Oct 31 12:44:00 2009 matrix is 85882 x 86053 (23.8 MB) with weight 5898371 (68.54/col) Sat Oct 31 12:44:00 2009 sparse part has weight 5898371 (68.54/col) Sat Oct 31 12:44:01 2009 filtering completed in 3 passes Sat Oct 31 12:44:01 2009 matrix is 82214 x 82278 (22.9 MB) with weight 5679157 (69.02/col) Sat Oct 31 12:44:01 2009 sparse part has weight 5679157 (69.02/col) Sat Oct 31 12:44:01 2009 saving the first 48 matrix rows for later Sat Oct 31 12:44:01 2009 matrix is 82166 x 82278 (16.5 MB) with weight 4746522 (57.69/col) Sat Oct 31 12:44:01 2009 sparse part has weight 3827985 (46.53/col) Sat Oct 31 12:44:01 2009 matrix includes 64 packed rows Sat Oct 31 12:44:01 2009 using block size 32911 for processor cache size 8192 kB Sat Oct 31 12:44:01 2009 commencing Lanczos iteration Sat Oct 31 12:44:01 2009 memory use: 14.7 MB Sat Oct 31 12:44:26 2009 lanczos halted after 1301 iterations (dim = 82164) Sat Oct 31 12:44:26 2009 recovered 16 nontrivial dependencies Sat Oct 31 12:44:27 2009 prp47 factor: 13226685334951086277235559910788997247553626789 Sat Oct 31 12:44:27 2009 prp50 factor: 93796786332729755561282648937916873301551400163929 Sat Oct 31 12:44:27 2009 elapsed time 04:55:51
(59·10¹⁷⁴+31)/9 = 6(5)₁₇₃9_<175> = 41 · 251 · 3754148753_<10> · 182442596131_<12> · 247407888474658786954353161_<27> · 3665302763719338852949381637894473_<34> · C91
C91 = P34 · P57
P34 = 1673659438408664325758148924770227_<34>
P57 = 612806996955643428028548588301906533880212069329060037253_<57>

Sat Oct 31 11:29:05 2009 Msieve v. 1.42 Sat Oct 31 11:29:05 2009 random seeds: 27e0594c 2c6ccd51 Sat Oct 31 11:29:05 2009 factoring 1025630214377682248913408120542627988922255145298292474518193455947066469922875791085266431 (91 digits) Sat Oct 31 11:29:06 2009 searching for 15-digit factors Sat Oct 31 11:29:07 2009 commencing quadratic sieve (91-digit input) Sat Oct 31 11:29:07 2009 using multiplier of 39 Sat Oct 31 11:29:07 2009 using 32kb Intel Core sieve core Sat Oct 31 11:29:07 2009 sieve interval: 36 blocks of size 32768 Sat Oct 31 11:29:07 2009 processing polynomials in batches of 6 Sat Oct 31 11:29:07 2009 using a sieve bound of 1652503 (62270 primes) Sat Oct 31 11:29:07 2009 using large prime bound of 145420264 (27 bits) Sat Oct 31 11:29:07 2009 using double large prime bound of 492861412574344 (42-49 bits) Sat Oct 31 11:29:07 2009 using trial factoring cutoff of 49 bits Sat Oct 31 11:29:07 2009 polynomial 'A' values have 12 factors Sat Oct 31 13:01:36 2009 62513 relations (16385 full + 46128 combined from 695793 partial), need 62366 Sat Oct 31 13:01:37 2009 begin with 712178 relations Sat Oct 31 13:01:38 2009 reduce to 153635 relations in 10 passes Sat Oct 31 13:01:38 2009 attempting to read 153635 relations Sat Oct 31 13:01:40 2009 recovered 153635 relations Sat Oct 31 13:01:40 2009 recovered 135212 polynomials Sat Oct 31 13:01:40 2009 attempting to build 62513 cycles Sat Oct 31 13:01:40 2009 found 62513 cycles in 5 passes Sat Oct 31 13:01:40 2009 distribution of cycle lengths: Sat Oct 31 13:01:40 2009 length 1 : 16385 Sat Oct 31 13:01:40 2009 length 2 : 11845 Sat Oct 31 13:01:40 2009 length 3 : 11127 Sat Oct 31 13:01:40 2009 length 4 : 8447 Sat Oct 31 13:01:40 2009 length 5 : 6027 Sat Oct 31 13:01:40 2009 length 6 : 3706 Sat Oct 31 13:01:40 2009 length 7 : 2267 Sat Oct 31 13:01:40 2009 length 9+: 2709 Sat Oct 31 13:01:40 2009 largest cycle: 17 relations Sat Oct 31 13:01:41 2009 matrix is 62270 x 62513 (15.3 MB) with weight 3763141 (60.20/col) Sat Oct 31 13:01:41 2009 sparse part has weight 3763141 (60.20/col) Sat Oct 31 13:01:41 2009 filtering completed in 3 passes Sat Oct 31 13:01:41 2009 matrix is 58420 x 58484 (14.4 MB) with weight 3545107 (60.62/col) Sat Oct 31 13:01:42 2009 sparse part has weight 3545107 (60.62/col) Sat Oct 31 13:01:42 2009 saving the first 48 matrix rows for later Sat Oct 31 13:01:42 2009 matrix is 58372 x 58484 (8.7 MB) with weight 2731776 (46.71/col) Sat Oct 31 13:01:42 2009 sparse part has weight 1934628 (33.08/col) Sat Oct 31 13:01:42 2009 matrix includes 64 packed rows Sat Oct 31 13:01:42 2009 using block size 23393 for processor cache size 1024 kB Sat Oct 31 13:01:42 2009 commencing Lanczos iteration Sat Oct 31 13:01:42 2009 memory use: 9.1 MB Sat Oct 31 13:02:02 2009 lanczos halted after 925 iterations (dim = 58372) Sat Oct 31 13:02:03 2009 recovered 19 nontrivial dependencies Sat Oct 31 13:02:04 2009 prp34 factor: 1673659438408664325758148924770227 Sat Oct 31 13:02:04 2009 prp57 factor: 612806996955643428028548588301906533880212069329060037253 Sat Oct 31 13:02:04 2009 elapsed time 01:32:59
(65·10¹⁸⁷+61)/9 = 7(2)₁₈₆9_<188> = 131 · 5507 · 220729284101_<12> · 2299975915314223_<16> · 1109471659166831215174847_<25> · 1512052274095148841868452958388463932723_<40> · C93
C93 = P42 · P51
P42 = 309843707618510847624745331660074576027487_<42>
P51 = 379380961349370970936336620824720600414315083305277_<51>

Sat Oct 31 13:27:52 2009 Msieve v. 1.42 Sat Oct 31 13:27:52 2009 random seeds: 12ba8844 239eac6d Sat Oct 31 13:27:52 2009 factoring 117548803664364063729993986270961475590052376474609853792498756031020401498410673032364148899 (93 digits) Sat Oct 31 13:27:53 2009 searching for 15-digit factors Sat Oct 31 13:27:53 2009 commencing quadratic sieve (93-digit input) Sat Oct 31 13:27:54 2009 using multiplier of 59 Sat Oct 31 13:27:54 2009 using 32kb Intel Core sieve core Sat Oct 31 13:27:54 2009 sieve interval: 36 blocks of size 32768 Sat Oct 31 13:27:54 2009 processing polynomials in batches of 6 Sat Oct 31 13:27:54 2009 using a sieve bound of 1850521 (69412 primes) Sat Oct 31 13:27:54 2009 using large prime bound of 209108873 (27 bits) Sat Oct 31 13:27:54 2009 using double large prime bound of 947698977581332 (42-50 bits) Sat Oct 31 13:27:54 2009 using trial factoring cutoff of 50 bits Sat Oct 31 13:27:54 2009 polynomial 'A' values have 12 factors Sat Oct 31 15:05:32 2009 69729 relations (18960 full + 50769 combined from 871863 partial), need 69508 Sat Oct 31 15:05:33 2009 begin with 890823 relations Sat Oct 31 15:05:34 2009 reduce to 171658 relations in 13 passes Sat Oct 31 15:05:34 2009 attempting to read 171658 relations Sat Oct 31 15:05:37 2009 recovered 171658 relations Sat Oct 31 15:05:37 2009 recovered 148129 polynomials Sat Oct 31 15:05:37 2009 attempting to build 69729 cycles Sat Oct 31 15:05:37 2009 found 69729 cycles in 5 passes Sat Oct 31 15:05:37 2009 distribution of cycle lengths: Sat Oct 31 15:05:37 2009 length 1 : 18960 Sat Oct 31 15:05:37 2009 length 2 : 13312 Sat Oct 31 15:05:37 2009 length 3 : 12246 Sat Oct 31 15:05:37 2009 length 4 : 9183 Sat Oct 31 15:05:37 2009 length 5 : 6467 Sat Oct 31 15:05:37 2009 length 6 : 4046 Sat Oct 31 15:05:37 2009 length 7 : 2505 Sat Oct 31 15:05:37 2009 length 9+: 3010 Sat Oct 31 15:05:37 2009 largest cycle: 20 relations Sat Oct 31 15:05:38 2009 matrix is 69412 x 69729 (17.5 MB) with weight 4296010 (61.61/col) Sat Oct 31 15:05:38 2009 sparse part has weight 4296010 (61.61/col) Sat Oct 31 15:05:39 2009 filtering completed in 3 passes Sat Oct 31 15:05:39 2009 matrix is 64555 x 64618 (16.3 MB) with weight 4009614 (62.05/col) Sat Oct 31 15:05:39 2009 sparse part has weight 4009614 (62.05/col) Sat Oct 31 15:05:39 2009 saving the first 48 matrix rows for later Sat Oct 31 15:05:39 2009 matrix is 64507 x 64618 (10.2 MB) with weight 3145901 (48.68/col) Sat Oct 31 15:05:39 2009 sparse part has weight 2297112 (35.55/col) Sat Oct 31 15:05:39 2009 matrix includes 64 packed rows Sat Oct 31 15:05:39 2009 using block size 25847 for processor cache size 1024 kB Sat Oct 31 15:05:39 2009 commencing Lanczos iteration Sat Oct 31 15:05:39 2009 memory use: 10.4 MB Sat Oct 31 15:06:15 2009 lanczos halted after 1022 iterations (dim = 64503) Sat Oct 31 15:06:15 2009 recovered 15 nontrivial dependencies Sat Oct 31 15:06:16 2009 prp42 factor: 309843707618510847624745331660074576027487 Sat Oct 31 15:06:16 2009 prp51 factor: 379380961349370970936336620824720600414315083305277 Sat Oct 31 15:06:16 2009 elapsed time 01:38:24
(22·10¹³⁷+17)/3 = 7(3)₁₃₆9_<138> = 99233 · 6090360415818263634173_<22> · C112
C112 = P35 · P77
P35 = 24060802183399412367506978238260797_<35>
P77 = 50430376250228200083232843381013952500349332497781653637769170585369111950243_<77>

Number: 73339_137 N=1213395306991144546783180912710761066871854197431551041872076438143619148233733680631064690192492448101121523671 ( 112 digits) SNFS difficulty: 138 digits. Divisors found: r1=24060802183399412367506978238260797 (pp35) r2=50430376250228200083232843381013952500349332497781653637769170585369111950243 (pp77) Version: GGNFS-0.77.1-20060513-k8 Total time: 9.84 hours. Scaled time: 19.18 units (timescale=1.949). Factorization parameters were as follows: name: 73339_137 n: 1213395306991144546783180912710761066871854197431551041872076438143619148233733680631064690192492448101121523671 m: 2000000000000000000000000000 deg: 5 c5: 275 c0: 68 skew: 0.76 type: snfs lss: 1 rlim: 1450000 alim: 1450000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1450000/1450000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [725000, 1550001) Primes: RFBsize:110630, AFBsize:110510, largePrimes:3624560 encountered Relations: rels:3789230, finalFF:422683 Max relations in full relation-set: 28 Initial matrix: 221207 x 422683 with sparse part having weight 40398695. Pruned matrix : 173233 x 174403 with weight 14551791. Total sieving time: 9.35 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.32 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,138,5,0,0,0,0,0,0,0,0,1450000,1450000,26,26,48,48,2.3,2.3,75000 total time: 9.84 hours. --------- CPU info (if available) ----------
(62·10¹³⁸-53)/9 = 6(8)₁₃₇3_<139> = 302791 · 77761357942084376053452253_<26> · C108
C108 = P34 · P75
P34 = 2598917760441813104579654155912123_<34>
P75 = 112577044979171717082980452895774413486489534296882540558515482893898057627_<75>

Number: 68883_138 N=292578481614426219363304516419595857892000196250239350859450480767231738398900672852889995261550968201912121 ( 108 digits) SNFS difficulty: 141 digits. Divisors found: r1=2598917760441813104579654155912123 (pp34) r2=112577044979171717082980452895774413486489534296882540558515482893898057627 (pp75) Version: Msieve-1.40 Total time: 9.15 hours. Scaled time: 30.73 units (timescale=3.357). Factorization parameters were as follows: name: 68883_138 n: 292578481614426219363304516419595857892000196250239350859450480767231738398900672852889995261550968201912121 m: 5000000000000000000000000000 deg: 5 c5: 496 c0: -1325 skew: 1.22 type: snfs lss: 1 rlim: 1580000 alim: 1580000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1580000/1580000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [790000, 1990001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 277070 x 277318 Total sieving time: 8.97 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.14 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,141.000,5,0,0,0,0,0,0,0,0,1580000,1580000,26,26,48,48,2.3,2.3,100000 total time: 9.15 hours. --------- CPU info (if available) ----------
(62·10¹³⁸-17)/9 = 6(8)₁₃₇3_<139> = 127867 · 32744763151_<11> · C124
C124 = P39 · P85
P39 = 971875626191891557665240752440339768261_<39>
P85 = 1692926721964495127439620152695166412870828555923484903620152946476576710419052305151_<85>

Number: 68887_138 N=1645314218006229997445207528172151195583233097326614361854592382318318016040391840164344928471593225843499909801429196612411 ( 124 digits) SNFS difficulty: 141 digits. Divisors found: r1=971875626191891557665240752440339768261 (pp39) r2=1692926721964495127439620152695166412870828555923484903620152946476576710419052305151 (pp85) Version: Msieve-1.40 Total time: 7.31 hours. Scaled time: 15.09 units (timescale=2.064). Factorization parameters were as follows: name: 68887_138 n: 1645314218006229997445207528172151195583233097326614361854592382318318016040391840164344928471593225843499909801429196612411 m: 5000000000000000000000000000 deg: 5 c5: 496 c0: -425 skew: 0.97 type: snfs lss: 1 rlim: 1580000 alim: 1580000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1580000/1580000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [790000, 1690001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 227733 x 227977 Total sieving time: 6.95 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.18 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: snfs,141.000,5,0,0,0,0,0,0,0,0,1580000,1580000,26,26,48,48,2.3,2.3,100000 total time: 7.31 hours. --------- CPU info (if available) ----------
Oct 31, 2009 (3rd): By Wataru Sakai / GMP-ECM 6.2.1 / Oct 31, 2009
(67·10¹⁶⁹-13)/9 = 7(4)₁₆₈3_<170> = 23 · 73 · 409 · 443 · 19531 · 28429 · 307440589 · 230276573803_<12> · 291650412038164334986511683_<27> · C107
C107 = P42 · P65
P42 = 393857077963053849631651147459903660023143_<42>
P65 = 54194634030097109172706023869603113274357441497744516636274957483_<65>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=750763233 Step 1 took 31013ms Step 2 took 12299ms ********** Factor found in step 2: 393857077963053849631651147459903660023143 Found probable prime factor of 42 digits: 393857077963053849631651147459903660023143 Probable prime cofactor 54194634030097109172706023869603113274357441497744516636274957483 has 65 digits
Oct 31, 2009 (2nd): By Dmitry Domanov / GGNFS/msieve / Oct 31, 2009
(67·10¹⁷⁴-13)/9 = 7(4)₁₇₃3_<175> = 3³ · 19 · 137 · 31440401 · 4039164379_<10> · 21853548229100149169939_<23> · 6941387106858984105338581430971_<31> · C100
C100 = P41 · P60
P41 = 45447270246285945938556880752125388129671_<41>
P60 = 120987005656784401807364834160943893119911420811939979029743_<60>

Number: g100 N=5498529142372807175182476307775514287810474350786223541016287633379554796119682890402386436049804553 ( 100 digits) Divisors found: r1=45447270246285945938556880752125388129671 (pp41) r2=120987005656784401807364834160943893119911420811939979029743 (pp60) Version: Msieve-1.40 Total time: 3.76 hours. Scaled time: 7.40 units (timescale=1.969). Factorization parameters were as follows: name: g100 n: 5498529142372807175182476307775514287810474350786223541016287633379554796119682890402386436049804553 skew: 28871.49 # norm 5.18e+013 c5: 1860 c4: -19207852 c3: -4079387662045 c2: 20205124276853681 c1: 1594619980425421631937 c0: -8929492543484694695004813 # alpha -5.55 Y1: 7628741191 Y0: -19685527873587608852 # Murphy_E 3.35e-009 # M 1964019609939265345418848352462673916351410918179450993688452056155422116082900383504670895533042190 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [900000, 1400001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 233609 x 233857 Polynomial selection time: 0.38 hours. Total sieving time: 3.13 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.15 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: gnfs,99,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000 total time: 3.76 hours. --------- CPU info (if available) ----------
(67·10¹⁶⁴-13)/9 = 7(4)₁₆₃3_<165> = 17 · 2859771989_<10> · 263447695627_<12> · 398722735777_<12> · 151262176674730970257358082173_<30> · C102
C102 = P39 · P64
P39 = 224280627189667359179586493987006022837_<39>
P64 = 4296991075348987428139366522540260942980725114590177648731306909_<64>

Number: g102 N=963731853407674093877908577792914764065479764108496015908002087521494488533136960353559408101309880833 ( 102 digits) Divisors found: r1=224280627189667359179586493987006022837 (pp39) r2=4296991075348987428139366522540260942980725114590177648731306909 (pp64) Version: Msieve-1.40 Total time: 5.24 hours. Scaled time: 10.31 units (timescale=1.969). Factorization parameters were as follows: name: g102 n: 963731853407674093877908577792914764065479764108496015908002087521494488533136960353559408101309880833 skew: 1562.33 # norm 1.03e+014 c5: 1528560 c4: 13594030180 c3: 3000195359306 c2: -30653164647004551 c1: 3594495509332078518 c0: 7733172680002833841155 # alpha -5.72 Y1: 89251703579 Y0: -14452067262770819782 # Murphy_E 2.76e-009 # M 129344431061528792284070628029008878021022211209342795954905427200961353231646508782196747326379618063 type: gnfs rlim: 2300000 alim: 2300000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1150000, 1750001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 276517 x 276742 Polynomial selection time: 0.50 hours. Total sieving time: 4.33 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.21 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: gnfs,101,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000 total time: 5.24 hours. --------- CPU info (if available) ----------
Oct 31, 2009: By Serge Batalov / Msieve / Oct 31, 2009
(67·10¹⁴⁴-13)/9 = 7(4)₁₄₃3_<145> = 3 · 29 · C143
C143 = P59 · P85
P59 = 43105680901206764377509983041410360068255898727809426039017_<59>
P85 = 1985082364056607809703148754055340488055249934086925223804597770313599535606384757717_<85>

SNFS difficulty: 146 digits. Divisors found: r1=43105680901206764377509983041410360068255898727809426039017 (pp59) r2=1985082364056607809703148754055340488055249934086925223804597770313599535606384757717 (pp85) Version: Msieve v. 1.44 SVN130 Total time: 5.35 hours. Scaled time: 12.83 units (timescale=2.400). Factorization parameters were as follows: n: 85568326947637292464878671775223499361430395913154533844189016602809706257982120051085568326947637292464878671775223499361430395913154533844189 m: 100000000000000000000000000000 deg: 5 c5: 67 c0: -130 skew: 1.14 type: snfs lss: 1 rlim: 1960000 alim: 1960000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1960000/1960000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [1225000, 2525001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 323954 x 324180 Total sieving time: 5.00 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.26 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,146.000,5,0,0,0,0,0,0,0,0,1960000,1960000,26,26,49,49,2.3,2.3,100000 total time: 5.35 hours.
(22·10¹⁴⁴+17)/3 = 7(3)₁₄₃9_<145> = 13 · 79 · C142
C142 = P39 · P49 · P55
P39 = 355704369772481560789194645513945473203_<39>
P49 = 5325835763078243037856500964485555354952804736467_<49>
P55 = 3769241919049291518517227454568595454414179901716545857_<55>

SNFS difficulty: 146 digits. Divisors found: r1=355704369772481560789194645513945473203 (pp39) r2=5325835763078243037856500964485555354952804736467 (pp49) r3=3769241919049291518517227454568595454414179901716545857 (pp55) Version: Msieve v. 1.44 SVN130 Total time: 5.14 hours. Scaled time: 12.33 units (timescale=2.400). Factorization parameters were as follows: n: 7140538786108406361570918532943849399545602077247646867900032456994482310938007140538786108406361570918532943849399545602077247646867900032457 m: 100000000000000000000000000000 deg: 5 c5: 11 c0: 85 skew: 1.51 type: snfs lss: 1 rlim: 1900000 alim: 1900000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1900000/1900000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [1187500, 2387501) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 328823 x 329048 Total sieving time: 4.60 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.41 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,146.000,5,0,0,0,0,0,0,0,0,1900000,1900000,26,26,49,49,2.3,2.3,100000 total time: 5.14 hours.
Oct 30, 2009 (11th): By Ignacio Santos / GGNFS, Msieve / Oct 30, 2009
(26·10¹⁷⁰-11)/3 = 8(6)₁₆₉3_<171> = 1574849 · C165
C165 = P64 · P101
P64 = 6879741969361830247705267902282155696253164397146995711289478697_<64>
P101 = 79990981245460272814684156404787112141167933425430834180983411533442461790764746144400168831077267471_<101>

Number: 86663_170 N=550317310844828086163604679983075626086479825473214680687905104976201951213523751589305810694654958454217938778045810529559765200769512928964406534637077374825565287 ( 165 digits) SNFS difficulty: 171 digits. Divisors found: r1=6879741969361830247705267902282155696253164397146995711289478697 (pp64) r2=79990981245460272814684156404787112141167933425430834180983411533442461790764746144400168831077267471 (pp101) Version: Msieve-1.40 Total time: 58.86 hours. Scaled time: 102.35 units (timescale=1.739). Factorization parameters were as follows: n: 550317310844828086163604679983075626086479825473214680687905104976201951213523751589305810694654958454217938778045810529559765200769512928964406534637077374825565287 m: 10000000000000000000000000000000000 deg: 5 c5: 26 c0: -11 skew: 0.84 type: snfs lss: 1 rlim: 5000000 alim: 5000000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2500000, 5600001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1074714 x 1074941 Total sieving time: 57.03 hours. Total relation processing time: 0.11 hours. Matrix solve time: 1.54 hours. Time per square root: 0.18 hours. Prototype def-par.txt line would be: snfs,171.000,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,100000 total time: 58.86 hours.
(83·10¹⁷⁰+7)/9 = 9(2)₁₆₉3_<171> = 13² · 1303 · C166
C166 = P44 · P46 · P76
P44 = 75175740784686081593779300770475028296195771_<44>
P46 = 7924410550370980851226220768780461448204670107_<46>
P76 = 7030072093617251150883355788994421962121941534602600580932819909233991111337_<76>

Number: 92223_170 N=4187978684702222101124043387459173515020967645089494077037615617224803127158638109697794448960397363490816469150491229716685764858620399089139864864523935307334563489 ( 166 digits) SNFS difficulty: 171 digits. Divisors found: r1=75175740784686081593779300770475028296195771 (pp44) r2=7924410550370980851226220768780461448204670107 (pp46) r3=7030072093617251150883355788994421962121941534602600580932819909233991111337 (pp76) Version: Msieve-1.40 Total time: 54.19 hours. Scaled time: 94.23 units (timescale=1.739). Factorization parameters were as follows: n: 4187978684702222101124043387459173515020967645089494077037615617224803127158638109697794448960397363490816469150491229716685764858620399089139864864523935307334563489 m: 10000000000000000000000000000000000 deg: 5 c5: 83 c0: 7 skew: 0.61 type: snfs lss: 1 rlim: 5100000 alim: 5100000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 5100000/5100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2550000, 5350001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 982004 x 982229 Total sieving time: 52.51 hours. Total relation processing time: 0.11 hours. Matrix solve time: 1.25 hours. Time per square root: 0.32 hours. Prototype def-par.txt line would be: snfs,171.000,5,0,0,0,0,0,0,0,0,5100000,5100000,27,27,52,52,2.4,2.4,100000 total time: 54.19 hours.
Oct 30, 2009 (10th): By Robert Backstrom / GGNFS / Oct 30, 2009
(62·10¹³⁹+1)/9 = 6(8)₁₃₈9_<140> = 3 · 17 · 45022889 · C131
C131 = P36 · P95
P36 = 484214506163729990618092275284042969_<36>
P95 = 61959492079224298660493435009803532533981674214668390763156707898945653153181452537824772870179_<95>

Number: n N=30001684859297133695920447411646111254476339752905477978706189100135479668056060999868132384792574078543187957473551055021294721451 ( 131 digits) SNFS difficulty: 141 digits. Divisors found: r1=484214506163729990618092275284042969 (pp36) r2=61959492079224298660493435009803532533981674214668390763156707898945653153181452537824772870179 (pp95) Version: GGNFS-0.77.1-20051202-athlon Total time: 4.64 hours. Scaled time: 8.46 units (timescale=1.823). Factorization parameters were as follows: name: KA_6_8_138_9 n: 30001684859297133695920447411646111254476339752905477978706189100135479668056060999868132384792574078543187957473551055021294721451 m: 10000000000000000000000000000 deg: 5 c5: 31 c0: 5 skew: 0.69 type: snfs lss: 1 rlim: 1600000 alim: 1600000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 qintsize: 10000 Factor base limits: 1600000/1600000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [800000, 1540001) Primes: RFBsize:121127, AFBsize:121136, largePrimes:3480094 encountered Relations: rels:3388656, finalFF:277961 Max relations in full relation-set: 48 Initial matrix: 242328 x 277961 with sparse part having weight 26767212. Pruned matrix : 230728 x 232003 with weight 17588153. Total sieving time: 4.07 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.43 hours. Total square root time: 0.07 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,141,5,0,0,0,0,0,0,0,0,1600000,1600000,26,26,48,48,2.3,2.3,100000 total time: 4.64 hours. --------- CPU info (if available) ----------
(67·10¹²⁴-13)/9 = 7(4)₁₂₃3_<125> = 167 · 2098015493895221_<16> · C108
C108 = P50 · P59
P50 = 18413459563540298067804775297170844243589025668543_<50>
P59 = 11539094725850237919675966907571710452758307093471194899943_<59>

Number: n N=212474654134304477312475815582067521840594360125311988630953593272073000222223112697185992344600977567593049 ( 108 digits) SNFS difficulty: 126 digits. Divisors found: r1=18413459563540298067804775297170844243589025668543 (pp50) r2=11539094725850237919675966907571710452758307093471194899943 (pp59) Version: GGNFS-0.77.1-20051202-athlon Total time: 1.71 hours. Scaled time: 3.11 units (timescale=1.823). Factorization parameters were as follows: name: KA_7_4_123_3 n: 212474654134304477312475815582067521840594360125311988630953593272073000222223112697185992344600977567593049 m: 10000000000000000000000000 deg: 5 c5: 67 c0: -130 skew: 1.14 type: snfs lss: 1 rlim: 910000 alim: 910000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 qintsize: 10000 Factor base limits: 910000/910000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [455000, 735001) Primes: RFBsize:72026, AFBsize:72442, largePrimes:2399626 encountered Relations: rels:2237187, finalFF:162283 Max relations in full relation-set: 48 Initial matrix: 144533 x 162283 with sparse part having weight 13056975. Pruned matrix : 138055 x 138841 with weight 8687947. Total sieving time: 1.51 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.10 hours. Total square root time: 0.06 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,126,5,0,0,0,0,0,0,0,0,910000,910000,26,26,46,46,2.3,2.3,50000 total time: 1.71 hours. --------- CPU info (if available) ----------
Oct 30, 2009 (9th): By Wataru Sakai / GMP-ECM 6.2.1 / Oct 30, 2009
(65·10¹⁸⁷+61)/9 = 7(2)₁₈₆9_<188> = 131 · 5507 · 220729284101_<12> · 2299975915314223_<16> · 1109471659166831215174847_<25> · C132
C132 = P40 · C93
P40 = 1512052274095148841868452958388463932723_<40>
C93 = [117548803664364063729993986270961475590052376474609853792498756031020401498410673032364148899_<93>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2945990577 Step 1 took 38221ms Step 2 took 14029ms ********** Factor found in step 2: 1512052274095148841868452958388463932723 Found probable prime factor of 40 digits: 1512052274095148841868452958388463932723 Composite cofactor 117548803664364063729993986270961475590052376474609853792498756031020401498410673032364148899 has 93 digits
(64·10¹⁸⁵+71)/9 = 7(1)₁₈₄9_<186> = 593707 · 594449 · 4422329046727_<13> · 40284292656009544724056072361587_<32> · C131
C131 = P34 · C97
P34 = 9116432441824664823352631671213357_<34>
C97 = [1240620578252657138397677340020548602052064584196378623862760965588007134959583060094673085893981_<97>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=630455973 Step 1 took 38243ms Step 2 took 13952ms ********** Factor found in step 2: 9116432441824664823352631671213357 Found probable prime factor of 34 digits: 9116432441824664823352631671213357 Composite cofactor 1240620578252657138397677340020548602052064584196378623862760965588007134959583060094673085893981 has 97 digits
(59·10¹⁶⁶+31)/9 = 6(5)₁₆₅9_<167> = 3 · 13 · 7259437319_<10> · 8758021819_<10> · 3392702120053749464840779_<25> · C121
C121 = P35 · P86
P35 = 80699902067736399108835652452339219_<35>
P86 = 96564428551450245513740093588018269772203313974459102582096055520689780511463138067621_<86>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1299118853 Step 1 took 34255ms Step 2 took 13280ms ********** Factor found in step 2: 80699902067736399108835652452339219 Found probable prime factor of 35 digits: 80699902067736399108835652452339219 Probable prime cofactor 96564428551450245513740093588018269772203313974459102582096055520689780511463138067621 has 86 digits
Oct 30, 2009 (8th): By Erik Branger / GGNFS, Msieve, YAFU / Oct 30, 2009
(67·10¹⁰⁵-13)/9 = 7(4)₁₀₄3_<106> = 3 · 73 · 5669 · 569057 · C95
C95 = P41 · P54
P41 = 60058359933313649972243137470065257329163_<41>
P54 = 175449640663427204253932925983205548218359311006550343_<54>

Number: 74443_105 N=10537217669134653717350764785332255258069098699759163662633735476197589541582812554582281552909 ( 95 digits) SNFS difficulty: 107 digits. Divisors found: r1=60058359933313649972243137470065257329163 (pp41) r2=175449640663427204253932925983205548218359311006550343 (pp54) Version: Msieve v. 1.43 Total time: 0.80 hours. Scaled time: 0.63 units (timescale=0.788). Factorization parameters were as follows: n: 10537217669134653717350764785332255258069098699759163662633735476197589541582812554582281552909 m: 200000000000000000000000000 deg: 4 c4: 335 c0: -104 skew: 0.75 type: snfs lss: 1 rlim: 440000 alim: 440000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 Factor base limits: 440000/440000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [220000, 300001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 36011 x 36238 Total sieving time: 0.78 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.01 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,107.000,4,0,0,0,0,0,0,0,0,440000,440000,25,25,44,44,2.2,2.2,20000 total time: 0.80 hours. --------- CPU info (if available) ----------
(22·10¹¹¹+17)/3 = 7(3)₁₁₀9_<112> = 4561 · C109
C109 = P41 · P69
P41 = 10353494998124320950439689240019536224501_<41>
P69 = 155293892497221396344263249494507201244620736494605530331157572978399_<69>

Number: 73339_111 N=1607834539209237740261638529562230505006212087992399327632829057955126799678433092158152451947672294087553899 ( 109 digits) SNFS difficulty: 113 digits. Divisors found: r1=10353494998124320950439689240019536224501 (pp41) r2=155293892497221396344263249494507201244620736494605530331157572978399 (pp69) Version: Msieve v. 1.43 Total time: 1.33 hours. Scaled time: 1.05 units (timescale=0.788). Factorization parameters were as follows: n: 1607834539209237740261638529562230505006212087992399327632829057955126799678433092158152451947672294087553899 m: 20000000000000000000000 deg: 5 c5: 55 c0: 136 skew: 1.20 type: snfs lss: 1 rlim: 540000 alim: 540000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 Factor base limits: 540000/540000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [270000, 420001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 64236 x 64465 Total sieving time: 1.28 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.02 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,113.000,5,0,0,0,0,0,0,0,0,540000,540000,25,25,45,45,2.2,2.2,50000 total time: 1.33 hours. --------- CPU info (if available) ----------
(62·10¹³⁷-53)/9 = 6(8)₁₃₆3_<138> = 13 · 379 · 9913338693829_<13> · C122
C122 = P41 · P81
P41 = 92016598929517614098722805673273505224217_<41>
P81 = 153278236964167015210420723223931171496148765949262538905208174029503679220103953_<81>

Number: 68883_137 N=14104142055355317759668354177413145279996340994172427429184656761606188941098694112179225964159993307036446344359313029801 ( 122 digits) SNFS difficulty: 139 digits. Divisors found: r1=92016598929517614098722805673273505224217 (pp41) r2=153278236964167015210420723223931171496148765949262538905208174029503679220103953 (pp81) Version: Msieve-1.40 Total time: 7.17 hours. Scaled time: 6.96 units (timescale=0.970). Factorization parameters were as follows: n: 14104142055355317759668354177413145279996340994172427429184656761606188941098694112179225964159993307036446344359313029801 m: 2000000000000000000000000000 deg: 5 c5: 775 c0: -212 skew: 0.77 type: snfs lss: 1 rlim: 1470000 alim: 1470000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1470000/1470000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [735000, 1860001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 261076 x 261302 Total sieving time: 6.82 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.15 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,139.000,5,0,0,0,0,0,0,0,0,1470000,1470000,26,26,48,48,2.3,2.3,75000 total time: 7.17 hours. --------- CPU info (if available) ----------
(22·10¹⁷³-7)/3 = 7(3)₁₇₂1_<174> = 97 · 541859 · 65483111511553_<14> · 29019575156728627496451041059487_<32> · 7085999215281227635840096984763449_<34> · C88
C88 = P43 · P45
P43 = 2918897382864143812189601638526072779141423_<43>
P45 = 354979371562529997440931835199505599882907401_<45>

10/29/09 19:43:40 v1.12 @ ERIK-DATOR, starting SIQS on c88: 1036148358624627286217516372248460715568726928814760434392187296717805689495977792371623 10/29/09 19:43:40 v1.12 @ ERIK-DATOR, random seeds: 1579246471, 485612288 10/29/09 19:43:40 v1.12 @ ERIK-DATOR, ==== sieve params ==== 10/29/09 19:43:40 v1.12 @ ERIK-DATOR, n = 88 digits, 291 bits 10/29/09 19:43:40 v1.12 @ ERIK-DATOR, factor base: 60488 primes (max prime = 1595317) 10/29/09 19:43:40 v1.12 @ ERIK-DATOR, single large prime cutoff: 175484870 (110 * pmax) 10/29/09 19:43:40 v1.12 @ ERIK-DATOR, double large prime range from 43 to 50 bits 10/29/09 19:43:40 v1.12 @ ERIK-DATOR, double large prime cutoff: 691244073679672 10/29/09 19:43:40 v1.12 @ ERIK-DATOR, using 0 large prime slices of factor base 10/29/09 19:43:40 v1.12 @ ERIK-DATOR, buckets hold 1024 elements 10/29/09 19:43:40 v1.12 @ ERIK-DATOR, sieve interval: 18 blocks of size 32768 10/29/09 19:43:40 v1.12 @ ERIK-DATOR, polynomial A has ~ 0 factors 10/29/09 19:43:40 v1.12 @ ERIK-DATOR, using multiplier of 3 10/29/09 19:43:40 v1.12 @ ERIK-DATOR, using small prime variation correction of 20 bits 10/29/09 19:43:40 v1.12 @ ERIK-DATOR, using SSE2 for trial division and x128 sieve scanning 10/29/09 19:43:40 v1.12 @ ERIK-DATOR, trial factoring cutoff at 97 bits 10/29/09 19:43:40 v1.12 @ ERIK-DATOR, ==== sieving started ( 2 threads) ==== 10/29/09 20:04:47 v1.12 @ ERIK-DATOR, sieve time = 379.8600, relation time = 165.2976, poly_time = 696.2156 10/29/09 20:04:47 v1.12 @ ERIK-DATOR, 60850 relations found: 20164 full + 40686 from 522236 partial, using 48318116 polys (613 A polys) 10/29/09 20:04:47 v1.12 @ ERIK-DATOR, on average, sieving found 0.01 rels/poly and 428.14 rels/sec 10/29/09 20:04:47 v1.12 @ ERIK-DATOR, trial division touched 13914331 sieve locations out of 56998368903168 10/29/09 20:04:47 v1.12 @ ERIK-DATOR, ==== post processing stage (msieve-1.38) ==== 10/29/09 20:04:47 v1.12 @ ERIK-DATOR, begin with 542400 relations 10/29/09 20:04:47 v1.12 @ ERIK-DATOR, reduce to 123655 relations in 8 passes 10/29/09 20:04:54 v1.12 @ ERIK-DATOR, recovered 123655 relations 10/29/09 20:04:54 v1.12 @ ERIK-DATOR, recovered 102177 polynomials 10/29/09 20:04:54 v1.12 @ ERIK-DATOR, attempting to build 60850 cycles 10/29/09 20:04:54 v1.12 @ ERIK-DATOR, found 60850 cycles in 4 passes 10/29/09 20:04:54 v1.12 @ ERIK-DATOR, distribution of cycle lengths: 10/29/09 20:04:54 v1.12 @ ERIK-DATOR, length 1 : 20164 10/29/09 20:04:54 v1.12 @ ERIK-DATOR, length 2 : 16960 10/29/09 20:04:54 v1.12 @ ERIK-DATOR, length 3 : 11354 10/29/09 20:04:54 v1.12 @ ERIK-DATOR, length 4 : 6358 10/29/09 20:04:54 v1.12 @ ERIK-DATOR, length 5 : 3250 10/29/09 20:04:54 v1.12 @ ERIK-DATOR, length 6 : 1545 10/29/09 20:04:54 v1.12 @ ERIK-DATOR, length 7 : 694 10/29/09 20:04:54 v1.12 @ ERIK-DATOR, length 9+: 525 10/29/09 20:04:54 v1.12 @ ERIK-DATOR, largest cycle: 15 relations 10/29/09 20:04:54 v1.12 @ ERIK-DATOR, matrix is 60488 x 60850 (12.1 MB) with weight 2920285 (47.99/col) 10/29/09 20:04:54 v1.12 @ ERIK-DATOR, sparse part has weight 2920285 (47.99/col) 10/29/09 20:04:54 v1.12 @ ERIK-DATOR, filtering completed in 3 passes 10/29/09 20:04:54 v1.12 @ ERIK-DATOR, matrix is 53491 x 53554 (10.8 MB) with weight 2626833 (49.05/col) 10/29/09 20:04:54 v1.12 @ ERIK-DATOR, sparse part has weight 2626833 (49.05/col) 10/29/09 20:04:54 v1.12 @ ERIK-DATOR, saving the first 48 matrix rows for later 10/29/09 20:04:55 v1.12 @ ERIK-DATOR, matrix is 53443 x 53554 (9.2 MB) with weight 2268111 (42.35/col) 10/29/09 20:04:55 v1.12 @ ERIK-DATOR, sparse part has weight 2086592 (38.96/col) 10/29/09 20:04:55 v1.12 @ ERIK-DATOR, matrix includes 64 packed rows 10/29/09 20:04:55 v1.12 @ ERIK-DATOR, using block size 21421 for processor cache size 2048 kB 10/29/09 20:04:55 v1.12 @ ERIK-DATOR, commencing Lanczos iteration 10/29/09 20:04:55 v1.12 @ ERIK-DATOR, memory use: 8.3 MB 10/29/09 20:05:13 v1.12 @ ERIK-DATOR, lanczos halted after 847 iterations (dim = 53443) 10/29/09 20:05:13 v1.12 @ ERIK-DATOR, recovered 18 nontrivial dependencies 10/29/09 20:05:14 v1.12 @ ERIK-DATOR, prp43 = 2918897382864143812189601638526072779141423 10/29/09 20:05:21 v1.12 @ ERIK-DATOR, prp45 = 354979371562529997440931835199505599882907401 10/29/09 20:05:21 v1.12 @ ERIK-DATOR, Lanczos elapsed time = 26.7540 seconds. 10/29/09 20:05:21 v1.12 @ ERIK-DATOR, Sqrt elapsed time = 7.7850 seconds. 10/29/09 20:05:21 v1.12 @ ERIK-DATOR, SIQS elapsed time = 1301.4064 seconds.
(22·10¹¹³+17)/3 = 7(3)₁₁₂9_<114> = 41 · 89 · 30226562196724237_<17> · C94
C94 = P40 · P55
P40 = 4742658220612723377993912832802326986709_<40>
P55 = 1401899815697364732864295246904507767152298674388612267_<55>

Number: 73339_113 N=6648731685392568673340087143484735074721518359722676856044541286039486751148900577046263359303 ( 94 digits) SNFS difficulty: 115 digits. Divisors found: r1=4742658220612723377993912832802326986709 (pp40) r2=1401899815697364732864295246904507767152298674388612267 (pp55) Version: Msieve v. 1.43 Total time: 1.39 hours. Scaled time: 1.10 units (timescale=0.788). Factorization parameters were as follows: n: 6648731685392568673340087143484735074721518359722676856044541286039486751148900577046263359303 m: 50000000000000000000000 deg: 5 c5: 176 c0: 425 skew: 1.19 type: snfs lss: 1 rlim: 590000 alim: 590000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 Factor base limits: 590000/590000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [295000, 445001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 63916 x 64141 Total sieving time: 1.34 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.02 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,115.000,5,0,0,0,0,0,0,0,0,590000,590000,25,25,45,45,2.2,2.2,50000 total time: 1.39 hours. --------- CPU info (if available) ----------
(67·10¹¹⁵-13)/9 = 7(4)₁₁₄3_<116> = 934023203657_<12> · C104
C104 = P46 · P59
P46 = 2363136207298356542813024663867821003977095941_<46>
P59 = 33727633771518272875025217406971537221298425870762282057639_<59>

Number: 74443_115 N=79702992551973656202412085387411627658370929220796610067063903154859269670308077208497397166333194943299 ( 104 digits) SNFS difficulty: 116 digits. Divisors found: r1=2363136207298356542813024663867821003977095941 (pp46) r2=33727633771518272875025217406971537221298425870762282057639 (pp59) Version: Msieve-1.40 Total time: 1.15 hours. Scaled time: 1.12 units (timescale=0.969). Factorization parameters were as follows: n: 79702992551973656202412085387411627658370929220796610067063903154859269670308077208497397166333194943299 m: 100000000000000000000000 deg: 5 c5: 67 c0: -13 skew: 0.72 type: snfs lss: 1 rlim: 620000 alim: 620000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 Factor base limits: 620000/620000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [310000, 510001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 68923 x 69148 Total sieving time: 1.12 hours. Total relation processing time: 0.01 hours. Matrix solve time: 0.01 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,116.000,5,0,0,0,0,0,0,0,0,620000,620000,25,25,45,45,2.2,2.2,50000 total time: 1.15 hours. --------- CPU info (if available) ----------
(22·10¹¹⁹+17)/3 = 7(3)₁₁₈9_<120> = 4871 · 88395289 · C109
C109 = P35 · P36 · P39
P35 = 50397412484330388603542395361078269_<35>
P36 = 284229425704179960225725802324609161_<36>
P39 = 118898643426182964310318249358540813809_<39>

Number: 73339_119 N=1703155010376173589245963363912844479505898920513548079792184363384189269662871013342757311335327814133864981 ( 109 digits) SNFS difficulty: 121 digits. Divisors found: r1=50397412484330388603542395361078269 (pp35) r2=284229425704179960225725802324609161 (pp36) r3=118898643426182964310318249358540813809 (pp39) Version: Msieve-1.40 Total time: 1.44 hours. Scaled time: 1.45 units (timescale=1.003). Factorization parameters were as follows: n: 1703155010376173589245963363912844479505898920513548079792184363384189269662871013342757311335327814133864981 m: 1000000000000000000000000 deg: 5 c5: 11 c0: 85 skew: 1.51 type: snfs lss: 1 rlim: 730000 alim: 730000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 730000/730000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [365000, 615001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 86095 x 86343 Total sieving time: 1.37 hours. Total relation processing time: 0.01 hours. Matrix solve time: 0.02 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,121.000,5,0,0,0,0,0,0,0,0,730000,730000,25,25,46,46,2.2,2.2,50000 total time: 1.44 hours. --------- CPU info (if available) ----------
(67·10¹²³-13)/9 = 7(4)₁₂₂3_<124> = 3 · 36172259 · 12953224991209_<14> · C103
C103 = P37 · P67
P37 = 1598370800869751930125360162910027197_<37>
P67 = 3313446482445314661395426297353620629334616744119570057380870392583_<67>

Number: 74443_123 N=5296116107785180025060234384281114220424865461631383972660953328631925645912935715468651123228597079851 ( 103 digits) SNFS difficulty: 126 digits. Divisors found: r1=1598370800869751930125360162910027197 (pp37) r2=3313446482445314661395426297353620629334616744119570057380870392583 (pp67) Version: Msieve-1.40 Total time: 1.93 hours. Scaled time: 1.73 units (timescale=0.894). Factorization parameters were as follows: n: 5296116107785180025060234384281114220424865461631383972660953328631925645912935715468651123228597079851 m: 5000000000000000000000000 deg: 5 c5: 536 c0: -325 skew: 0.90 type: snfs lss: 1 rlim: 890000 alim: 890000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 890000/890000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [445000, 745001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 120758 x 120983 Total sieving time: 1.83 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.04 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,126.000,5,0,0,0,0,0,0,0,0,890000,890000,26,26,46,46,2.3,2.3,50000 total time: 1.93 hours. --------- CPU info (if available) ----------
(65·10¹³⁸+61)/9 = 7(2)₁₃₇9_<139> = 7 · 820888039693842689_<18> · C121
C121 = P39 · P82
P39 = 231983952017062808710371389960379972197_<39>
P82 = 5417899396106871046513719119689905295688836403624747656508338369048000425620143559_<82>

Number: 72229_138 N=1256865713539729940732436596428989152859916869094343065781795420088325741227881969351681537465013212501751088675568629123 ( 121 digits) SNFS difficulty: 140 digits. Divisors found: r1=231983952017062808710371389960379972197 (pp39) r2=5417899396106871046513719119689905295688836403624747656508338369048000425620143559 (pp82) Version: Msieve-1.40 Total time: 5.96 hours. Scaled time: 5.98 units (timescale=1.003). Factorization parameters were as follows: n: 1256865713539729940732436596428989152859916869094343065781795420088325741227881969351681537465013212501751088675568629123 m: 5000000000000000000000000000 deg: 5 c5: 104 c0: 305 skew: 1.24 type: snfs lss: 1 rlim: 1540000 alim: 1540000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1540000/1540000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [770000, 1670001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 260716 x 260941 Total sieving time: 5.73 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.15 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,140.000,5,0,0,0,0,0,0,0,0,1540000,1540000,26,26,48,48,2.3,2.3,100000 total time: 5.96 hours. --------- CPU info (if available) ----------
(22·10¹³²+17)/3 = 7(3)₁₃₁9_<133> = 13 · 12133421 · 30027659 · 3606149550515935321_<19> · C99
C99 = P47 · P53
P47 = 12453067396570738943402028834555057839784395671_<47>
P53 = 34477300948705518718980721337704600617529621152055447_<53>

Number: 73339_132 N=429348152366082101879424461334080508049160634782916238895467141839271983897081546365941358378769937 ( 99 digits) SNFS difficulty: 133 digits. Divisors found: r1=12453067396570738943402028834555057839784395671 (pp47) r2=34477300948705518718980721337704600617529621152055447 (pp53) Version: Msieve v. 1.43 Total time: 5.61 hours. Scaled time: 4.43 units (timescale=0.789). Factorization parameters were as follows: n: 429348152366082101879424461334080508049160634782916238895467141839271983897081546365941358378769937 m: 200000000000000000000000000 deg: 5 c5: 275 c0: 68 skew: 0.76 type: snfs lss: 1 rlim: 1200000 alim: 1200000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [600000, 1125001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 163998 x 164223 Total sieving time: 5.36 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.14 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,133.000,5,0,0,0,0,0,0,0,0,1200000,1200000,26,26,47,47,2.3,2.3,75000 total time: 5.61 hours. --------- CPU info (if available) ----------
(22·10¹³⁶+17)/3 = 7(3)₁₃₅9_<137> = 7 · 8980812433_<10> · C127
C127 = P61 · P66
P61 = 4113360418876992191345184069972901753084088769096918837906397_<61>
P66 = 283590053967020542468512853768491642154157101023860518632668590177_<66>

Number: 73339_136 N=1166508103175132439655105140329176295856416365286589900933541796885056511509952662674708395223890149826768594586479376279662269 ( 127 digits) SNFS difficulty: 138 digits. Divisors found: r1=4113360418876992191345184069972901753084088769096918837906397 (pp61) r2=283590053967020542468512853768491642154157101023860518632668590177 (pp66) Version: Msieve-1.40 Total time: 4.90 hours. Scaled time: 4.82 units (timescale=0.983). Factorization parameters were as follows: n: 1166508103175132439655105140329176295856416365286589900933541796885056511509952662674708395223890149826768594586479376279662269 m: 2000000000000000000000000000 deg: 5 c5: 55 c0: 136 skew: 1.20 type: snfs lss: 1 rlim: 1410000 alim: 1410000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1410000/1410000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [705000, 1455001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 214678 x 214903 Total sieving time: 4.73 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.10 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,138.000,5,0,0,0,0,0,0,0,0,1410000,1410000,26,26,48,48,2.3,2.3,75000 total time: 4.90 hours. --------- CPU info (if available) ----------
Oct 30, 2009 (7th): By Sinkiti Sibata / Msieve, GGNFS / Oct 30, 2009
(62·10¹⁴⁸-53)/9 = 6(8)₁₄₇3_<149> = 3 · 2957 · 554396173829032040309_<21> · 80618323734034493160877932323_<29> · C96
C96 = P41 · P56
P41 = 15649311336687670483003413809050773543817_<41>
P56 = 11102668729253886618598862637858746443379270194714314067_<56>

Number: 68883_148 N=173749119612200540250170808346984527455185833744652662545780871322071342123571560550077923973739 ( 96 digits) Divisors found: r1=15649311336687670483003413809050773543817 (pp41) r2=11102668729253886618598862637858746443379270194714314067 (pp56) Version: Msieve-1.40 Total time: 7.06 hours. Scaled time: 14.35 units (timescale=2.032). Factorization parameters were as follows: name: 68883_148 n: 173749119612200540250170808346984527455185833744652662545780871322071342123571560550077923973739 m: 6500700344411699054074 deg: 4 c4: 97293096 c3: -223649123332 c2: -642136958186635483 c1: 738328517650567800 c0: 471523111539404624724519 skew: 1635.250 type: gnfs # adj. I(F,S) = 55.605 # E(F1,F2) = 2.998325e-05 # GGNFS version 0.77.1-20060722-pentium4 polyselect. # Options were: # lcd=1, enumLCD=24, maxS1=60.00000000, seed=1256814568. # maxskew=2000.0 # These parameters should be manually set: rlim: 1200000 alim: 1200000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.4 alambda: 2.4 qintsize: 60000 type: gnfs Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved algebraic special-q in [600000, 1500001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 179842 x 180070 Polynomial selection time: 0.17 hours. Total sieving time: 6.60 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.11 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: gnfs,95,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000 total time: 7.06 hours. --------- CPU info (if available) ----------
(62·10¹⁴⁸+1)/9 = 6(8)₁₄₇9_<149> = 3 · 968893963 · 1010325931287078378105743_<25> · 26271799596027579924616943_<26> · C90
C90 = P40 · P51
P40 = 1154296887283017820556565817700236598461_<40>
P51 = 773540093204736296456243349622971513303636130557709_<51>

Fri Oct 30 07:07:22 2009 Msieve v. 1.42 Fri Oct 30 07:07:22 2009 random seeds: dc8593b8 2e6a889f Fri Oct 30 07:07:22 2009 factoring 892894921774842591947278084980579648441470220219533682231568136751789747957843249021085849 (90 digits) Fri Oct 30 07:07:23 2009 searching for 15-digit factors Fri Oct 30 07:07:24 2009 commencing quadratic sieve (90-digit input) Fri Oct 30 07:07:24 2009 using multiplier of 1 Fri Oct 30 07:07:24 2009 using 32kb Intel Core sieve core Fri Oct 30 07:07:24 2009 sieve interval: 36 blocks of size 32768 Fri Oct 30 07:07:24 2009 processing polynomials in batches of 6 Fri Oct 30 07:07:24 2009 using a sieve bound of 1606249 (61176 primes) Fri Oct 30 07:07:24 2009 using large prime bound of 134924916 (27 bits) Fri Oct 30 07:07:24 2009 using double large prime bound of 430690990940364 (42-49 bits) Fri Oct 30 07:07:24 2009 using trial factoring cutoff of 49 bits Fri Oct 30 07:07:24 2009 polynomial 'A' values have 11 factors Fri Oct 30 08:13:01 2009 61413 relations (16479 full + 44934 combined from 660424 partial), need 61272 Fri Oct 30 08:13:02 2009 begin with 676903 relations Fri Oct 30 08:13:03 2009 reduce to 149572 relations in 11 passes Fri Oct 30 08:13:03 2009 attempting to read 149572 relations Fri Oct 30 08:13:05 2009 recovered 149572 relations Fri Oct 30 08:13:05 2009 recovered 125294 polynomials Fri Oct 30 08:13:05 2009 attempting to build 61413 cycles Fri Oct 30 08:13:05 2009 found 61413 cycles in 5 passes Fri Oct 30 08:13:05 2009 distribution of cycle lengths: Fri Oct 30 08:13:05 2009 length 1 : 16479 Fri Oct 30 08:13:05 2009 length 2 : 11841 Fri Oct 30 08:13:05 2009 length 3 : 10776 Fri Oct 30 08:13:05 2009 length 4 : 8279 Fri Oct 30 08:13:05 2009 length 5 : 5761 Fri Oct 30 08:13:05 2009 length 6 : 3579 Fri Oct 30 08:13:05 2009 length 7 : 2062 Fri Oct 30 08:13:05 2009 length 9+: 2636 Fri Oct 30 08:13:05 2009 largest cycle: 19 relations Fri Oct 30 08:13:05 2009 matrix is 61176 x 61413 (15.1 MB) with weight 3709126 (60.40/col) Fri Oct 30 08:13:05 2009 sparse part has weight 3709126 (60.40/col) Fri Oct 30 08:13:06 2009 filtering completed in 3 passes Fri Oct 30 08:13:06 2009 matrix is 57171 x 57235 (14.2 MB) with weight 3482985 (60.85/col) Fri Oct 30 08:13:06 2009 sparse part has weight 3482985 (60.85/col) Fri Oct 30 08:13:06 2009 saving the first 48 matrix rows for later Fri Oct 30 08:13:06 2009 matrix is 57123 x 57235 (10.6 MB) with weight 2895121 (50.58/col) Fri Oct 30 08:13:06 2009 sparse part has weight 2423000 (42.33/col) Fri Oct 30 08:13:06 2009 matrix includes 64 packed rows Fri Oct 30 08:13:06 2009 using block size 22894 for processor cache size 1024 kB Fri Oct 30 08:13:07 2009 commencing Lanczos iteration Fri Oct 30 08:13:07 2009 memory use: 9.9 MB Fri Oct 30 08:13:29 2009 lanczos halted after 905 iterations (dim = 57121) Fri Oct 30 08:13:30 2009 recovered 15 nontrivial dependencies Fri Oct 30 08:13:30 2009 prp40 factor: 1154296887283017820556565817700236598461 Fri Oct 30 08:13:30 2009 prp51 factor: 773540093204736296456243349622971513303636130557709 Fri Oct 30 08:13:30 2009 elapsed time 01:06:08
(62·10¹⁴⁸-17)/9 = 6(8)₁₄₇7_<149> = 7² · 13 · 33403 · 2587105617619_<13> · 248476266691661817327986323_<27> · C103
C103 = P44 · P59
P44 = 77534847850900282536204141003399873814651531_<44>
P59 = 64957344590901786161929874304410491618727520507584961391411_<59>

Number: 68887_148 N=5036457829654070447291851666637862041967460202109673946848020460954015526291427291729686600891861400241 ( 103 digits) Divisors found: r1=77534847850900282536204141003399873814651531 (pp44) r2=64957344590901786161929874304410491618727520507584961391411 (pp59) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 12.94 hours. Scaled time: 6.08 units (timescale=0.470). Factorization parameters were as follows: name: 68887_148 n: 5036457829654070447291851666637862041967460202109673946848020460954015526291427291729686600891861400241 skew: 5250.84 # norm 1.51e+14 c5: 158400 c4: -2369595480 c3: -9089246452964 c2: 12488829579152730 c1: 148149926348795334669 c0: 243869513540266992110835 # alpha -5.95 Y1: 46917187199 Y0: -31657450076936910292 # Murphy_E 2.45e-09 # M 4472840802460327703162608013156768940227082287739066635374172230098893954410321033694631482111869343000 type: gnfs rlim: 2300000 alim: 2300000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1150000, 1850001) Primes: RFBsize:169511, AFBsize:170119, largePrimes:4420988 encountered Relations: rels:4544685, finalFF:508022 Max relations in full relation-set: 28 Initial matrix: 339708 x 508022 with sparse part having weight 36322270. Pruned matrix : 211251 x 213013 with weight 16139750. Polynomial selection time: 0.70 hours. Total sieving time: 10.80 hours. Total relation processing time: 0.28 hours. Matrix solve time: 1.00 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000 total time: 12.94 hours. --------- CPU info (if available) ----------
(22·10¹³⁶-7)/3 = 7(3)₁₃₅1_<137> = 19389191 · 4895993365661197097_<19> · C111
C111 = P46 · P66
P46 = 6443188619669826476280091645257651931718381011_<46>
P66 = 119894723769212387435501631561188909687989725490025836640734845023_<66>

Number: 73331_136 N=772504319748246697665149190240682725304722032243784064764023030120508817790677757304825249856253631163551058253 ( 111 digits) SNFS difficulty: 138 digits. Divisors found: r1=6443188619669826476280091645257651931718381011 (pp46) r2=119894723769212387435501631561188909687989725490025836640734845023 (pp66) Version: GGNFS-0.77.1-20060513-k8 Total time: 6.27 hours. Scaled time: 12.36 units (timescale=1.972). Factorization parameters were as follows: name: 73331_136 n: 772504319748246697665149190240682725304722032243784064764023030120508817790677757304825249856253631163551058253 m: 2000000000000000000000000000 deg: 5 c5: 55 c0: -56 skew: 1.00 type: snfs lss: 1 rlim: 1410000 alim: 1410000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1410000/1410000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [705000, 1230001) Primes: RFBsize:107805, AFBsize:107265, largePrimes:3428918 encountered Relations: rels:3561302, finalFF:431806 Max relations in full relation-set: 28 Initial matrix: 215137 x 431806 with sparse part having weight 35153928. Pruned matrix : 155036 x 156175 with weight 10589950. Total sieving time: 5.94 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.18 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,138,5,0,0,0,0,0,0,0,0,1410000,1410000,26,26,48,48,2.3,2.3,75000 total time: 6.27 hours. --------- CPU info (if available) ----------
(22·10¹²⁶+17)/3 = 7(3)₁₂₅9_<127> = 13 · 191 · 840251492083_<12> · 1895876995008967_<16> · C97
C97 = P47 · P50
P47 = 62954221240549700803517895855591515615873618567_<47>
P50 = 29449667885623623024571417153719273982755349467859_<50>

Number: 73339_126 N=1853980907532261085359289430354461486793949958322168440086644145089512112616560650231980192138053 ( 97 digits) SNFS difficulty: 128 digits. Divisors found: r1=62954221240549700803517895855591515615873618567 (pp47) r2=29449667885623623024571417153719273982755349467859 (pp50) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 4.65 hours. Scaled time: 2.18 units (timescale=0.470). Factorization parameters were as follows: name: 73339_126 n: 1853980907532261085359289430354461486793949958322168440086644145089512112616560650231980192138053 m: 20000000000000000000000000 deg: 5 c5: 55 c0: 136 skew: 1.20 type: snfs lss: 1 rlim: 960000 alim: 960000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 960000/960000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [480000, 880001) Primes: RFBsize:75618, AFBsize:75331, largePrimes:2684351 encountered Relations: rels:2649373, finalFF:258875 Max relations in full relation-set: 28 Initial matrix: 151016 x 258875 with sparse part having weight 20919788. Pruned matrix : 123819 x 124638 with weight 7186531. Total sieving time: 4.30 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.19 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,128,5,0,0,0,0,0,0,0,0,960000,960000,26,26,47,47,2.3,2.3,50000 total time: 4.65 hours. --------- CPU info (if available) ----------
(22·10¹³⁰+17)/3 = 7(3)₁₂₉9_<131> = 7 · 2543 · 783371639 · 23314400769738955085791_<23> · C96
C96 = P46 · P50
P46 = 5668358868056523752203461746253003242713937413_<46>
P50 = 39793082832407892372132468962834943667647868416847_<50>

Fri Oct 30 10:44:12 2009 Msieve v. 1.40 Fri Oct 30 10:44:12 2009 random seeds: 4f9e5c6b 8f5e88a9 Fri Oct 30 10:44:12 2009 factoring 225561473960387088874197487909377436905992883142405706677354077914645400486794949390462152796811 (96 digits) Fri Oct 30 10:44:12 2009 no P-1/P+1/ECM available, skipping Fri Oct 30 10:44:12 2009 commencing quadratic sieve (96-digit input) Fri Oct 30 10:44:12 2009 using multiplier of 19 Fri Oct 30 10:44:12 2009 using 32kb Intel Core sieve core Fri Oct 30 10:44:12 2009 sieve interval: 36 blocks of size 32768 Fri Oct 30 10:44:12 2009 processing polynomials in batches of 6 Fri Oct 30 10:44:12 2009 using a sieve bound of 2225473 (82353 primes) Fri Oct 30 10:44:12 2009 using large prime bound of 333820950 (28 bits) Fri Oct 30 10:44:12 2009 using double large prime bound of 2199502175184600 (43-51 bits) Fri Oct 30 10:44:12 2009 using trial factoring cutoff of 51 bits Fri Oct 30 10:44:12 2009 polynomial 'A' values have 12 factors Fri Oct 30 13:12:19 2009 82483 relations (20939 full + 61544 combined from 1214119 partial), need 82449 Fri Oct 30 13:12:20 2009 begin with 1235058 relations Fri Oct 30 13:12:20 2009 reduce to 211848 relations in 10 passes Fri Oct 30 13:12:20 2009 attempting to read 211848 relations Fri Oct 30 13:12:22 2009 recovered 211848 relations Fri Oct 30 13:12:22 2009 recovered 194844 polynomials Fri Oct 30 13:12:22 2009 attempting to build 82483 cycles Fri Oct 30 13:12:22 2009 found 82483 cycles in 6 passes Fri Oct 30 13:12:22 2009 distribution of cycle lengths: Fri Oct 30 13:12:22 2009 length 1 : 20939 Fri Oct 30 13:12:22 2009 length 2 : 14842 Fri Oct 30 13:12:22 2009 length 3 : 13930 Fri Oct 30 13:12:22 2009 length 4 : 10990 Fri Oct 30 13:12:22 2009 length 5 : 8283 Fri Oct 30 13:12:22 2009 length 6 : 5570 Fri Oct 30 13:12:22 2009 length 7 : 3442 Fri Oct 30 13:12:22 2009 length 9+: 4487 Fri Oct 30 13:12:22 2009 largest cycle: 21 relations Fri Oct 30 13:12:22 2009 matrix is 82353 x 82483 (22.5 MB) with weight 5580538 (67.66/col) Fri Oct 30 13:12:22 2009 sparse part has weight 5580538 (67.66/col) Fri Oct 30 13:12:23 2009 filtering completed in 3 passes Fri Oct 30 13:12:23 2009 matrix is 78173 x 78237 (21.6 MB) with weight 5337663 (68.22/col) Fri Oct 30 13:12:23 2009 sparse part has weight 5337663 (68.22/col) Fri Oct 30 13:12:23 2009 saving the first 48 matrix rows for later Fri Oct 30 13:12:23 2009 matrix is 78125 x 78237 (15.9 MB) with weight 4472451 (57.17/col) Fri Oct 30 13:12:23 2009 sparse part has weight 3699137 (47.28/col) Fri Oct 30 13:12:23 2009 matrix includes 64 packed rows Fri Oct 30 13:12:23 2009 using block size 31294 for processor cache size 8192 kB Fri Oct 30 13:12:24 2009 commencing Lanczos iteration Fri Oct 30 13:12:24 2009 memory use: 14.0 MB Fri Oct 30 13:12:45 2009 lanczos halted after 1238 iterations (dim = 78125) Fri Oct 30 13:12:45 2009 recovered 18 nontrivial dependencies Fri Oct 30 13:12:46 2009 prp46 factor: 5668358868056523752203461746253003242713937413 Fri Oct 30 13:12:46 2009 prp50 factor: 39793082832407892372132468962834943667647868416847 Fri Oct 30 13:12:46 2009 elapsed time 02:28:34
(59·10¹⁹⁰+31)/9 = 6(5)₁₈₉9_<191> = 3 · 13 · 431 · 6199 · 19576751 · 104183263 · 36559727551187_<14> · 135004420102133_<15> · 12932888608664243860259_<23> · 490648692732801719123587_<24> · C94
C94 = P31 · P63
P31 = 9865405008537377442324456789611_<31>
P63 = 998332882065300959385122964248060387944996253698508642405943101_<63>

Number: 65559_190 N=9848958214914575038497851680581147805444684312048313010541252541165888436426497955577193923711 ( 94 digits) Divisors found: r1=9865405008537377442324456789611 (pp31) r2=998332882065300959385122964248060387944996253698508642405943101 (pp63) Version: Msieve-1.40 Total time: 5.33 hours. Scaled time: 10.87 units (timescale=2.038). Factorization parameters were as follows: name: 65559_190 n: 9848958214914575038497851680581147805444684312048313010541252541165888436426497955577193923711 m: 4626552704081064038673 deg: 4 c4: 21496128 c3: 80594542214 c2: -148327043924384507 c1: -201872463427757100 c0: 35697740878523611215328 skew: 1635.250 type: gnfs # adj. I(F,S) = 54.239 # E(F1,F2) = 4.784960e-05 # GGNFS version 0.77.1-20060722-pentium4 polyselect. # Options were: # lcd=1, enumLCD=24, maxS1=60.00000000, seed=1256859102. # maxskew=2000.0 # These parameters should be manually set: rlim: 1200000 alim: 1200000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.4 alambda: 2.4 qintsize: 60000 type: gnfs Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved algebraic special-q in [600000, 1260001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 160364 x 160593 Polynomial selection time: 0.17 hours. Total sieving time: 5.00 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.09 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: gnfs,93,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000 total time: 5.33 hours. --------- CPU info (if available) ----------
(67·10¹²⁵-13)/9 = 7(4)₁₂₄3_<126> = 7 · 23 · 383 · 2112973088280065635622951_<25> · C97
C97 = P34 · P64
P34 = 3637308040834686028487388657126347_<34>
P64 = 1570845943462575746091980845703965709073524066171708229509776313_<64>

Number: 74443_125 N=5713650581068975362283662920696280343317363639223493296916903514253804648431669229237353348818611 ( 97 digits) SNFS difficulty: 126 digits. Divisors found: r1=3637308040834686028487388657126347 (pp34) r2=1570845943462575746091980845703965709073524066171708229509776313 (pp64) Version: GGNFS-0.77.1-20060513-k8 Total time: 2.85 hours. Scaled time: 5.61 units (timescale=1.967). Factorization parameters were as follows: name: 74443_125 n: 5713650581068975362283662920696280343317363639223493296916903514253804648431669229237353348818611 m: 10000000000000000000000000 deg: 5 c5: 67 c0: -13 skew: 0.72 type: snfs lss: 1 rlim: 910000 alim: 910000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 910000/910000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [455000, 705001) Primes: RFBsize:72026, AFBsize:71722, largePrimes:2409478 encountered Relations: rels:2267940, finalFF:164897 Max relations in full relation-set: 28 Initial matrix: 143813 x 164897 with sparse part having weight 11603791. Pruned matrix : 135848 x 136631 with weight 7820050. Total sieving time: 2.65 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.09 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,126,5,0,0,0,0,0,0,0,0,910000,910000,26,26,46,46,2.3,2.3,50000 total time: 2.85 hours. --------- CPU info (if available) ----------
(67·10¹²⁸-13)/9 = 7(4)₁₂₇3_<129> = 97 · 3307 · 102539 · 14264757233_<11> · C109
C109 = P41 · P68
P41 = 16848849103457524845559641834441573294541_<41>
P68 = 94167851235718598569337274009848709690744380558238621290057509744751_<68>

Number: 74443_128 N=1586619915867458882658700891790336634603941150882959229493854020939935382701589118280696639658681911051704291 ( 109 digits) SNFS difficulty: 131 digits. Divisors found: r1=16848849103457524845559641834441573294541 (pp41) r2=94167851235718598569337274009848709690744380558238621290057509744751 (pp68) Version: Msieve-1.40 Total time: 3.09 hours. Scaled time: 6.24 units (timescale=2.019). Factorization parameters were as follows: name: 74443_128 n: 1586619915867458882658700891790336634603941150882959229493854020939935382701589118280696639658681911051704291 m: 50000000000000000000000000 deg: 5 c5: 536 c0: -325 skew: 0.90 type: snfs lss: 1 rlim: 1080000 alim: 1080000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1080000/1080000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [540000, 940001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 167097 x 167345 Total sieving time: 2.89 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.10 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,131.000,5,0,0,0,0,0,0,0,0,1080000,1080000,26,26,47,47,2.3,2.3,50000 total time: 3.09 hours. --------- CPU info (if available) ----------
(67·10¹⁵²-13)/9 = 7(4)₁₅₁3_<153> = 173 · 385193 · 59290667 · 1714313748613543313_<19> · 197788961175491971099981_<24> · C96
C96 = P47 · P49
P47 = 97221051417449319448358224662337021824557951429_<47>
P49 = 5715691719482093033732344844964775540735095156253_<49>

Fri Oct 30 14:37:10 2009 Msieve v. 1.40 Fri Oct 30 14:37:10 2009 random seeds: 58df9d7d a63c1257 Fri Oct 30 14:37:10 2009 factoring 555685558546057878893653180212330583409127836210597174985850701280488576149477345118354339635537 (96 digits) Fri Oct 30 14:37:11 2009 no P-1/P+1/ECM available, skipping Fri Oct 30 14:37:11 2009 commencing quadratic sieve (96-digit input) Fri Oct 30 14:37:11 2009 using multiplier of 3 Fri Oct 30 14:37:11 2009 using 32kb Intel Core sieve core Fri Oct 30 14:37:11 2009 sieve interval: 36 blocks of size 32768 Fri Oct 30 14:37:11 2009 processing polynomials in batches of 6 Fri Oct 30 14:37:11 2009 using a sieve bound of 2299949 (84350 primes) Fri Oct 30 14:37:11 2009 using large prime bound of 344992350 (28 bits) Fri Oct 30 14:37:11 2009 using double large prime bound of 2333764230167400 (43-52 bits) Fri Oct 30 14:37:11 2009 using trial factoring cutoff of 52 bits Fri Oct 30 14:37:11 2009 polynomial 'A' values have 12 factors Fri Oct 30 18:38:25 2009 84448 relations (20475 full + 63973 combined from 1281737 partial), need 84446 Fri Oct 30 18:38:26 2009 begin with 1302212 relations Fri Oct 30 18:38:26 2009 reduce to 222956 relations in 11 passes Fri Oct 30 18:38:26 2009 attempting to read 222956 relations Fri Oct 30 18:38:28 2009 recovered 222956 relations Fri Oct 30 18:38:28 2009 recovered 209931 polynomials Fri Oct 30 18:38:28 2009 attempting to build 84448 cycles Fri Oct 30 18:38:28 2009 found 84448 cycles in 5 passes Fri Oct 30 18:38:28 2009 distribution of cycle lengths: Fri Oct 30 18:38:28 2009 length 1 : 20475 Fri Oct 30 18:38:28 2009 length 2 : 14393 Fri Oct 30 18:38:28 2009 length 3 : 13940 Fri Oct 30 18:38:28 2009 length 4 : 11339 Fri Oct 30 18:38:28 2009 length 5 : 8544 Fri Oct 30 18:38:28 2009 length 6 : 6044 Fri Oct 30 18:38:28 2009 length 7 : 3948 Fri Oct 30 18:38:28 2009 length 9+: 5765 Fri Oct 30 18:38:28 2009 largest cycle: 20 relations Fri Oct 30 18:38:28 2009 matrix is 84350 x 84448 (24.0 MB) with weight 5954508 (70.51/col) Fri Oct 30 18:38:28 2009 sparse part has weight 5954508 (70.51/col) Fri Oct 30 18:38:29 2009 filtering completed in 3 passes Fri Oct 30 18:38:29 2009 matrix is 80666 x 80730 (23.1 MB) with weight 5735368 (71.04/col) Fri Oct 30 18:38:29 2009 sparse part has weight 5735368 (71.04/col) Fri Oct 30 18:38:29 2009 saving the first 48 matrix rows for later Fri Oct 30 18:38:29 2009 matrix is 80618 x 80730 (17.1 MB) with weight 4813504 (59.62/col) Fri Oct 30 18:38:29 2009 sparse part has weight 3986473 (49.38/col) Fri Oct 30 18:38:29 2009 matrix includes 64 packed rows Fri Oct 30 18:38:29 2009 using block size 32292 for processor cache size 8192 kB Fri Oct 30 18:38:29 2009 commencing Lanczos iteration Fri Oct 30 18:38:29 2009 memory use: 14.9 MB Fri Oct 30 18:38:53 2009 lanczos halted after 1276 iterations (dim = 80614) Fri Oct 30 18:38:54 2009 recovered 16 nontrivial dependencies Fri Oct 30 18:38:55 2009 prp47 factor: 97221051417449319448358224662337021824557951429 Fri Oct 30 18:38:55 2009 prp49 factor: 5715691719482093033732344844964775540735095156253 Fri Oct 30 18:38:55 2009 elapsed time 04:01:45
Oct 30, 2009 (6th): By Serge Batalov / GMP-ECM / Oct 30, 2009
(59·10¹⁵⁴+31)/9 = 6(5)₁₅₃9_<155> = 3 · 13 · 41 · 561602387 · 1468996097_<10> · 629373674601490057_<18> · C116
C116 = P32 · P85
P32 = 11515653024662605644224396059681_<32>
P85 = 6856686724641505888344919729757159600810076382419241778190435348457495481603278102507_<85>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3333432130 Step 1 took 2768ms Step 2 took 1908ms ********** Factor found in step 2: 11515653024662605644224396059681 Found probable prime factor of 32 digits: 11515653024662605644224396059681 Probable prime cofactor has 85 digits
(59·10¹⁷⁴+31)/9 = 6(5)₁₇₃9_<175> = 41 · 251 · 3754148753_<10> · 182442596131_<12> · 247407888474658786954353161_<27> · C124
C124 = P34 · C91
P34 = 3665302763719338852949381637894473_<34>
C91 = [1025630214377682248913408120542627988922255145298292474518193455947066469922875791085266431_<91>]

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1424803983 Step 1 took 2564ms ********** Factor found in step 1: 3665302763719338852949381637894473 Found probable prime factor of 34 digits: 3665302763719338852949381637894473 Composite cofactor has 91 digits
(59·10¹⁹⁹+31)/9 = 6(5)₁₉₈9_<200> = 3 · 23 · 41 · 151760533 · 458867159 · 30185840183_<11> · C170
C170 = P28 · P142
P28 = 1602687943698543126131675611_<28>
P142 = 6878258551729128554685038747479659603886933282297464944457396121908040776440780280432667254915111985042970315141255881530546102872883667527461_<142>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2091762947 Step 1 took 3492ms Step 2 took 2452ms ********** Factor found in step 2: 1602687943698543126131675611 Found probable prime factor of 28 digits: 1602687943698543126131675611 Probable prime cofactor has 142 digits
(59·10²⁰⁰+31)/9 = 6(5)₁₉₉9_<201> = 647 · 59141 · 357238529 · C185
C185 = P28 · P158
P28 = 2286251887838065901353298057_<28>
P158 = 20976556125252658394173548582655076279566955914498617474180556805568901829064519383634511266481239826594839102020809479854759222807301826314172217673409387589_<158>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=741387217 Step 1 took 4080ms ********** Factor found in step 1: 2286251887838065901353298057 Found probable prime factor of 28 digits: 2286251887838065901353298057 Probable prime cofactor has 158 digits
(67·10¹⁶¹-13)/9 = 7(4)₁₆₀3_<162> = 7 · 73 · 5280887 · 354444281 · 5910599194139687430907_<22> · 65963915942544805370686211_<26> · C97
C97 = P34 · P63
P34 = 2668794540328995477716550306660659_<34>
P63 = 748003215572714369503951702881054047348463244791006660340612553_<63>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3974447949 Step 1 took 2048ms Step 2 took 1480ms ********** Factor found in step 2: 2668794540328995477716550306660659 Found probable prime factor of 34 digits: 2668794540328995477716550306660659 Probable prime cofactor has 63 digits
(22·10¹⁸³+17)/3 = 7(3)₁₈₂9_<184> = 29 · 41 · 79 · 457 · 176257138459_<12> · C165
C165 = P31 · C135
P31 = 8048080087752238884475113802981_<31>
C135 = [120430718000717344755122639668146818766081866163800205532918460738996973886808495543748787636747999455799416767695465023104549925150223_<135>]

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1294281311 Step 1 took 3488ms Step 2 took 2468ms ********** Factor found in step 2: 8048080087752238884475113802981 Found probable prime factor of 31 digits: 8048080087752238884475113802981 Composite cofactor has 135 digits
(67·10¹⁸¹-13)/9 = 7(4)₁₈₀3_<182> = 127 · 15370583931178846189_<20> · C161
C161 = P34 · C128
P34 = 2253776873153776657897948451534279_<34>
C128 = [16921049169503429770691052650078474147642338224813289853061010395893828071230552899451200517984291274406940600654599798013769439_<128>]

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=736395422 Step 1 took 3560ms Step 2 took 2413ms ********** Factor found in step 2: 2253776873153776657897948451534279 Found probable prime factor of 34 digits: 2253776873153776657897948451534279 Composite cofactor has 128 digits
(22·10¹⁹⁷+17)/3 = 7(3)₁₉₆9_<198> = 2999609 · 17526737 · C185
C185 = P32 · C153
P32 = 85768965380696892224398060458083_<32>
C153 = [162631825549783751295866446947190481527542400941976286560382655837239566893610989918569146348381161296601343514990401403459613148506298287882369753536801_<153>]

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4294209017 Step 1 took 4064ms Step 2 took 2681ms ********** Factor found in step 2: 85768965380696892224398060458083 Found probable prime factor of 32 digits: 85768965380696892224398060458083 Composite cofactor has 153 digits
(22·10¹⁷⁹+17)/3 = 7(3)₁₇₈9_<180> = 15559 · 184211 · 8689564994090088209_<19> · 60523080194263634333609_<23> · 61570408566381724845907_<23> · C106
C106 = P33 · P74
P33 = 446056747541793215384851975393451_<33>
P74 = 17714258502083168870661444117316394335176926736315549830701596471827794183_<74>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1545800992 Step 1 took 2365ms Step 2 took 1700ms ********** Factor found in step 2: 446056747541793215384851975393451 Found probable prime factor of 33 digits: 446056747541793215384851975393451 Probable prime cofactor has 74 digits
(67·10¹⁵⁶-13)/9 = 7(4)₁₅₅3_<157> = 3² · 19 · 47 · 139 · 33161 · C147
C147 = P36 · P112
P36 = 134467084183425554399242168453850521_<36>
P112 = 1494444938340149006807751226662925392418214556242644418555585617423575237956535769730952159502701461363114458621_<112>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2881240165 Step 1 took 2980ms ********** Factor found in step 1: 134467084183425554399242168453850521 Found probable prime factor of 36 digits: 134467084183425554399242168453850521 Probable prime cofactor has 112 digits
(67·10¹⁹⁵-13)/9 = 7(4)₁₉₄3_<196> = 3 · 173 · 4373 · 31069 · 125294581708453_<15> · 1784960739592187_<16> · 87066488362644079096453_<23> · 5741354370893543162557514479_<28> · C105
C105 = P36 · P70
P36 = 123426397951350582174645249823462411_<36>
P70 = 7651098400206075515266178289261247157235344735713694647781980737240803_<70>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=26946518 Step 1 took 2156ms Step 2 took 1684ms ********** Factor found in step 2: 123426397951350582174645249823462411 Found probable prime factor of 36 digits: 123426397951350582174645249823462411 Probable prime cofactor has 70 digits
Oct 30, 2009 (5th): By Dmitry Domanov / GGNFS/msieve / Oct 30, 2009
(22·10¹⁴⁷-7)/3 = 7(3)₁₄₆1_<148> = 877 · 2089 · 125294657 · 1955716477250593_<16> · 5297185565183853217_<19> · C100
C100 = P34 · P66
P34 = 5357601451931949330338251285732117_<34>
P66 = 575584852032572576040227977297423130731945405191587010014254749643_<66>

Number: g100 N=3083754238959747050060530712204481731076920353986016215023861867048446187911390233584704185799384231 ( 100 digits) Divisors found: r1=5357601451931949330338251285732117 (pp34) r2=575584852032572576040227977297423130731945405191587010014254749643 (pp66) Version: Msieve-1.40 Total time: 3.29 hours. Scaled time: 6.46 units (timescale=1.963). Factorization parameters were as follows: name: g100 n: 3083754238959747050060530712204481731076920353986016215023861867048446187911390233584704185799384231 skew: 2378.52 # norm 6.26e+013 c5: 716040 c4: 768401206 c3: -3347407358048 c2: -21666142625728748 c1: -5359048822522704315 c0: 22498539625274014910685 # alpha -6.46 Y1: 3195251251 Y0: -5331242520959992304 # Murphy_E 3.76e-009 # M 2889047347447943462753756483416340182973701438603636079111165743841444508017748937466511011496473051 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [900000, 1300001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 228951 x 229176 Polynomial selection time: 0.38 hours. Total sieving time: 2.65 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.16 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: gnfs,99,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000 total time: 3.29 hours. --------- CPU info (if available) ----------
(65·10¹⁵⁷+61)/9 = 7(2)₁₅₆9_<158> = 79 · 153773771 · 85677699739844835667027_<23> · 1389841419191345191370059_<25> · C101
C101 = P50 · P51
P50 = 70655337767515623403718126937284154445695756983599_<50>
P51 = 706615998528579354350895287081083417163425558047983_<51>

Number: g101 N=49926192047967097030608276609867645116088896365617729035992426846122079146222535243827882930586030817 ( 101 digits) Divisors found: r1=70655337767515623403718126937284154445695756983599 (pp50) r2=706615998528579354350895287081083417163425558047983 (pp51) Version: Msieve-1.40 Total time: 4.53 hours. Scaled time: 8.43 units (timescale=1.860). Factorization parameters were as follows: name: g101 n: 49926192047967097030608276609867645116088896365617729035992426846122079146222535243827882930586030817 skew: 1704.10 # norm 3.47e+013 c5: 755040 c4: -778190204 c3: -4882519895824 c2: 9111802450446 c1: -4465344687580793315 c0: 612530740196218749242 # alpha -5.35 Y1: 11385808801 Y0: -9206017737240624105 # Murphy_E 3.21e-009 # M 42391844600785429460091656032734960392745250527381026440482151276186691213655918782772522577390152249 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [900000, 1500001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 182786 x 183011 Polynomial selection time: 0.43 hours. Total sieving time: 3.77 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.09 hours. Time per square root: 0.21 hours. Prototype def-par.txt line would be: gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000 total time: 4.53 hours. --------- CPU info (if available) ----------
(22·10¹⁶²-7)/3 = 7(3)₁₆₁1_<163> = 17 · 6151 · 32670611801_<11> · 2202000923674657459_<19> · 6467789994663449185869367399_<28> · C102
C102 = P45 · P57
P45 = 199209648585588769622820458941437925059772499_<45>
P57 = 756598949668130460359016509976391729974682603903888934227_<57>

Number: g102 N=150721810883613833860276412458540167568640519018256430521087768408836448415786099602290956392194423273 ( 102 digits) Divisors found: r1=199209648585588769622820458941437925059772499 (pp45) r2=756598949668130460359016509976391729974682603903888934227 (pp57) Version: Msieve-1.40 Total time: 4.99 hours. Scaled time: 9.77 units (timescale=1.957). Factorization parameters were as follows: name: g102 n: 150721810883613833860276412458540167568640519018256430521087768408836448415786099602290956392194423273 skew: 5475.89 # norm 1.34e+014 c5: 68040 c4: -664173246 c3: -7626252806023 c2: -37813406180968319 c1: 52258057748767061759 c0: 107057378213323747343421 # alpha -5.71 Y1: 17409096199 Y0: -18581602017512027734 # Murphy_E 2.75e-009 # M 67503055058093048970044476777557095622419620092815774496828876992418422713533293625409912225975661918 type: gnfs rlim: 2300000 alim: 2300000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1150000, 1750001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 262112 x 262337 Polynomial selection time: 0.50 hours. Total sieving time: 4.23 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.19 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: gnfs,101,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000 total time: 4.99 hours. --------- CPU info (if available) ----------
(62·10¹⁴⁷+1)/9 = 6(8)₁₄₆9_<148> = C148
C148 = P38 · P47 · P64
P38 = 14609058570850068072790171345251209857_<38>
P47 = 54119127478220719186968454440445122879267586001_<47>
P64 = 8713169520734770932259156884452356918743245463266750664655868777_<64>

N=6888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889 ( 148 digits) SNFS difficulty: 150 digits. Divisors found: r1=14609058570850068072790171345251209857 (pp38) r2=54119127478220719186968454440445122879267586001 (pp47) r3=8713169520734770932259156884452356918743245463266750664655868777 (pp64) Version: Msieve-1.40 Total time: 14.47 hours. Scaled time: 13.52 units (timescale=0.934). Factorization parameters were as follows: n: 6888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889 m: 500000000000000000000000000000 deg: 5 c5: 248 c0: 125 skew: 0.87 type: snfs lss: 1 rlim: 2300000 alim: 2300000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1150000, 1750001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 304330 x 304556 Total sieving time: 14.04 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.17 hours. Time per square root: 0.18 hours. Prototype def-par.txt line would be: snfs,150.000,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000 total time: 14.47 hours.
(22·10¹¹⁶+17)/3 = 7(3)₁₁₅9_<117> = 643 · C115
C115 = P45 · P70
P45 = 127199283710829473583831003888420738835436659_<45>
P70 = 8966145609054367047114636580013011049277494734917626941664754253624147_<70>

Number: s115 N=1140487299118714359771902540176257128045619491964748574390876101607050285121824779678589942975635044064282011404873 ( 115 digits) SNFS difficulty: 118 digits. Divisors found: r1=127199283710829473583831003888420738835436659 (pp45) r2=8966145609054367047114636580013011049277494734917626941664754253624147 (pp70) Version: Msieve-1.40 Total time: 1.46 hours. Scaled time: 1.36 units (timescale=0.934). Factorization parameters were as follows: n: 1140487299118714359771902540176257128045619491964748574390876101607050285121824779678589942975635044064282011404873 m: 200000000000000000000000 deg: 5 c5: 55 c0: 136 skew: 1.20 type: snfs lss: 1 rlim: 650000 alim: 650000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2Factor base limits: 650000/650000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [325000, 575001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 71229 x 71454 Total sieving time: 1.42 hours. Total relation processing time: 0.01 hours. Matrix solve time: 0.02 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,118.000,5,0,0,0,0,0,0,0,0,650000,650000,25,25,45,45,2.2,2.2,50000 total time: 1.46 hours. --------- CPU info (if available) ----------
(22·10¹⁵⁴+17)/3 = 7(3)₁₅₃9_<155> = 7 · C155
C155 = P39 · P116
P39 = 184686752453367787287809095416797694533_<39>
P116 = 56724103580930346666691668641253433479051981833696382842269072327040745086396602948789182818404047086941094879036969_<116>

Number: s154 N=10476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190477 ( 155 digits) SNFS difficulty: 156 digits. Divisors found: r1=184686752453367787287809095416797694533 (pp39) r2=56724103580930346666691668641253433479051981833696382842269072327040745086396602948789182818404047086941094879036969 (pp116) Version: Msieve-1.40 Total time: 23.76 hours. Scaled time: 22.19 units (timescale=0.934). Factorization parameters were as follows: n: 10476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190476190477 m: 10000000000000000000000000000000 deg: 5 c5: 11 c0: 85 skew: 1.51 type: snfs lss: 1 rlim: 2800000 alim: 2800000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1400000, 2400001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 481528 x 481757 Total sieving time: 23.09 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.43 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,156.000,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000 total time: 23.76 hours. --------- CPU info (if available) ----------
(22·10¹⁵³-7)/3 = 7(3)₁₅₂1_<154> = C154
C154 = P41 · P53 · P62
P41 = 16102595691756429004184189289923007311587_<41>
P53 = 16804048553475014199523698985582044088874738998911019_<53>
P62 = 27101392731833721574475833973613757042141875062514354080413427_<62>

Number: s154 N=7333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331 ( 154 digits) SNFS difficulty: 155 digits. Divisors found: r1=16102595691756429004184189289923007311587 (pp41) r2=16804048553475014199523698985582044088874738998911019 (pp53) r3=27101392731833721574475833973613757042141875062514354080413427 (pp62) Version: Msieve-1.40 Total time: 17.81 hours. Scaled time: 34.95 units (timescale=1.963). Factorization parameters were as follows: n: 7333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331 m: 5000000000000000000000000000000 deg: 5 c5: 176 c0: -175 skew: 1.00 type: snfs lss: 1 rlim: 2800000 alim: 2800000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1400000, 2400001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 499206 x 499433 Total sieving time: 16.85 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.71 hours. Time per square root: 0.18 hours. Prototype def-par.txt line would be: snfs,155.000,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000 total time: 17.81 hours. --------- CPU info (if available) ----------
Oct 30, 2009 (4th): By Jo Yeong Uk / GMP-ECM / Oct 30, 2009
(62·10¹⁴¹-17)/9 = 6(8)₁₄₀7_<142> = 449 · 643 · 739570927 · 2076569140741_<13> · C116
C116 = P29 · P88
P29 = 12449586199568989558573448867_<29>
P88 = 1247988902077611754486563333046373100040151974373538545203846142963842189794646273724189_<88>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 15536945412520690380033798617839461767749986899777529309993270411105848832394342125721382926624823181351370052543863 (116 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=5231726309 Step 1 took 3478ms Step 2 took 1358ms ********** Factor found in step 2: 12449586199568989558573448867 Found probable prime factor of 29 digits: 12449586199568989558573448867 Probable prime cofactor 1247988902077611754486563333046373100040151974373538545203846142963842189794646273724189 has 88 digits
Oct 30, 2009 (3rd): By Lionel Debroux / GGNFS + Msieve / Oct 30, 2009
(22·10¹⁰³+17)/3 = 7(3)₁₀₂9_<104> = 41 · C103
C103 = P37 · P66
P37 = 1968440256387558857469214196952117053_<37>
P66 = 908647280695882845564443412045563169110619998478775609933242429343_<66>

Number: 73339_103 N=1788617886178861788617886178861788617886178861788617886178861788617886178861788617886178861788617886179 ( 103 digits) SNFS difficulty: 105 digits. Divisors found: r1=1968440256387558857469214196952117053 (pp37) r2=908647280695882845564443412045563169110619998478775609933242429343 (pp66) Version: Msieve v. 1.44 Total time: 1.48 hours. Scaled time: 2.20 units (timescale=1.485). Factorization parameters were as follows: n: 1788617886178861788617886178861788617886178861788617886178861788617886178861788617886178861788617886179 m: 100000000000000000000000000 deg: 4 c4: 11 c0: 85 skew: 1.67 type: snfs lss: 1 rlim: 390000 alim: 390000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 Factor base limits: 390000/390000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [195000, 355001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 62433 x 62681 Total sieving time: 1.45 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,105.000,4,0,0,0,0,0,0,0,0,390000,390000,25,25,44,44,2.2,2.2,20000 total time: 1.48 hours. --------- CPU info (if available) ---------- [ 0.029106] CPU0: Intel(R) Core(TM)2 CPU T7200 @ 2.00GHz stepping 06 [ 0.101090] CPU1: Intel(R) Core(TM)2 CPU T7200 @ 2.00GHz stepping 06 [ 0.000000] Memory: 2051108k/2096800k available (7368k kernel code, 452k absent, 44504k reserved, 3461k data, 768k init) [ 0.001009] Calibrating delay loop (skipped), value calculated using timer frequency.. 3990.00 BogoMIPS (lpj=1995001) [ 0.001999] Calibrating delay using timer specific routine.. 3989.82 BogoMIPS (lpj=1994913) [ 0.102026] Total of 2 processors activated (7979.82 BogoMIPS).
(22·10¹⁰⁵+17)/3 = 7(3)₁₀₄9_<106> = 23 · 79 · 941 · C100
C100 = P42 · P58
P42 = 667319846833294484773950178480591643333119_<42>
P58 = 6427215088318733045674430056423147409336405409180529236673_<58>

Number: 73339_105 N=4289008188301496220506488976956523688679611283288795882396175296443573905752164340757021642530273087 ( 100 digits) SNFS difficulty: 106 digits. Divisors found: r1=667319846833294484773950178480591643333119 (pp42) r2=6427215088318733045674430056423147409336405409180529236673 (pp58) Version: Msieve v. 1.44 Total time: 2.09 hours. Scaled time: 3.01 units (timescale=1.441). Factorization parameters were as follows: n: 4289008188301496220506488976956523688679611283288795882396175296443573905752164340757021642530273087 m: 200000000000000000000000000 deg: 4 c4: 55 c0: 68 skew: 1.05 type: snfs lss: 1 rlim: 420000 alim: 420000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 Factor base limits: 420000/420000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [210000, 450001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 68749 x 68997 Total sieving time: 2.06 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.01 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,106.000,4,0,0,0,0,0,0,0,0,420000,420000,25,25,44,44,2.2,2.2,20000 total time: 2.09 hours. --------- CPU info (if available) ---------- [ 0.029106] CPU0: Intel(R) Core(TM)2 CPU T7200 @ 2.00GHz stepping 06 [ 0.101090] CPU1: Intel(R) Core(TM)2 CPU T7200 @ 2.00GHz stepping 06 [ 0.000000] Memory: 2051108k/2096800k available (7368k kernel code, 452k absent, 44504k reserved, 3461k data, 768k init) [ 0.001009] Calibrating delay loop (skipped), value calculated using timer frequency.. 3990.00 BogoMIPS (lpj=1995001) [ 0.001999] Calibrating delay using timer specific routine.. 3989.82 BogoMIPS (lpj=1994913) [ 0.102026] Total of 2 processors activated (7979.82 BogoMIPS).
Oct 30, 2009 (2nd): Factorizations of 655...559 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.
Oct 30, 2009: By Lionel Debroux / GMP-ECM
Factorizations of 733...339 and Factorizations of 744...443 have been extended up to n=200. Composite numbers that appeared newly have passed 150 times ECM runs at level 35. Unknown factors have probably 30 digits or more.
Oct 29, 2009 (9th): By Erik Branger / GGNFS, Msieve / Oct 29, 2009
(22·10¹⁴⁴-7)/3 = 7(3)₁₄₃1_<145> = 35933501 · 33082734446491157_<17> · C121
C121 = P61 · P61
P61 = 1611222895107357825861684897891027348379434665936113039177013_<61>
P61 = 3828642978160722759423548127980286671936987166408740855033191_<61>

Number: 73331_144 N=6168797223604576285866739275513559616412539375347282679742557779151130854164360406427707025619267418222104317849439238483 ( 121 digits) SNFS difficulty: 146 digits. Divisors found: r1=1611222895107357825861684897891027348379434665936113039177013 (pp61) r2=3828642978160722759423548127980286671936987166408740855033191 (pp61) Version: Msieve-1.40 Total time: 6.72 hours. Scaled time: 6.67 units (timescale=0.992). Factorization parameters were as follows: n: 6168797223604576285866739275513559616412539375347282679742557779151130854164360406427707025619267418222104317849439238483 m: 100000000000000000000000000000 deg: 5 c5: 11 c0: -35 skew: 1.26 type: snfs lss: 1 rlim: 1900000 alim: 1900000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1900000/1900000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [950000, 1850001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 270431 x 270656 Total sieving time: 6.48 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.16 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,146.000,5,0,0,0,0,0,0,0,0,1900000,1900000,26,26,49,49,2.3,2.3,100000 total time: 6.72 hours. --------- CPU info (if available) ----------
(65·10¹⁴⁸+7)/9 = 7(2)₁₄₇3_<149> = 701 · C147
C147 = P34 · P47 · P66
P34 = 3755550574749161555183061499920779_<34>
P47 = 46814150630339904680428759046932495299316986541_<47>
P66 = 586006004706828862487443318948487124438444839144237964283793539957_<66>

Number: 72223_148 N=103027421144396893326993184339831986051672214297035980345538120145823426850530987478205737834839118719289903312727849104453954667934696465366936123 ( 147 digits) SNFS difficulty: 150 digits. Divisors found: r1=3755550574749161555183061499920779 (pp34) r2=46814150630339904680428759046932495299316986541 (pp47) r3=586006004706828862487443318948487124438444839144237964283793539957 (pp66) Version: Msieve v. 1.43 Total time: 25.27 hours. Scaled time: 19.91 units (timescale=0.788). Factorization parameters were as follows: n: 103027421144396893326993184339831986051672214297035980345538120145823426850530987478205737834839118719289903312727849104453954667934696465366936123 m: 500000000000000000000000000000 deg: 5 c5: 104 c0: 35 skew: 0.80 type: snfs lss: 1 rlim: 2300000 alim: 2300000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1150000, 1850001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 363568 x 363798 Total sieving time: 23.94 hours. Total relation processing time: 0.33 hours. Matrix solve time: 0.74 hours. Time per square root: 0.26 hours. Prototype def-par.txt line would be: snfs,150.000,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000 total time: 25.27 hours. --------- CPU info (if available) ----------
(65·10¹⁴⁵+7)/9 = 7(2)₁₄₄3_<146> = 73 · 127 · C142
C142 = P33 · P110
P33 = 215020535686146100995565648128067_<33>
P110 = 36229665693495144004165159106176063374327069676193814029155021451148871281621766835872766224697315800096474339_<110>

Number: 72223_145 N=7790122125145315739642133774374093649252747516149522405589712244873500401490909526720118889248432986972518846103141216936923980392861851172713 ( 142 digits) SNFS difficulty: 146 digits. Divisors found: r1=215020535686146100995565648128067 (pp33) r2=36229665693495144004165159106176063374327069676193814029155021451148871281621766835872766224697315800096474339 (pp110) Version: Msieve-1.40 Total time: 8.81 hours. Scaled time: 9.16 units (timescale=1.039). Factorization parameters were as follows: n: 7790122125145315739642133774374093649252747516149522405589712244873500401490909526720118889248432986972518846103141216936923980392861851172713 m: 100000000000000000000000000000 deg: 5 c5: 65 c0: 7 skew: 0.64 type: snfs lss: 1 rlim: 1960000 alim: 1960000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1960000/1960000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [980000, 2180001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 308284 x 308510 Total sieving time: 8.34 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.20 hours. Time per square root: 0.22 hours. Prototype def-par.txt line would be: snfs,146.000,5,0,0,0,0,0,0,0,0,1960000,1960000,26,26,49,49,2.3,2.3,100000 total time: 8.81 hours. --------- CPU info (if available) ----------
(62·10¹³¹-53)/9 = 6(8)₁₃₀3_<132> = 13 · 19 · 199 · 10513 · 81899 · C119
C119 = P52 · P67
P52 = 2213322253356502762971124059611562807329201224533739_<52>
P67 = 7354433687504421692647292079401137480439947289067440673701943894427_<67>

Number: 68883_131 N=16277731741388260497915416758923984903955258653210841577364643431610859290705103072764367923074919035554697010915572553 ( 119 digits) SNFS difficulty: 133 digits. Divisors found: r1=2213322253356502762971124059611562807329201224533739 (pp52) r2=7354433687504421692647292079401137480439947289067440673701943894427 (pp67) Version: Msieve v. 1.43 Total time: 4.98 hours. Scaled time: 3.91 units (timescale=0.785). Factorization parameters were as follows: n: 16277731741388260497915416758923984903955258653210841577364643431610859290705103072764367923074919035554697010915572553 m: 200000000000000000000000000 deg: 5 c5: 155 c0: -424 skew: 1.22 type: snfs lss: 1 rlim: 1180000 alim: 1180000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1180000/1180000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [590000, 1040001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 161442 x 161667 Total sieving time: 4.69 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.14 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,133.000,5,0,0,0,0,0,0,0,0,1180000,1180000,26,26,47,47,2.3,2.3,75000 total time: 4.98 hours. --------- CPU info (if available) ----------
(62·10¹⁴⁰+1)/9 = 6(8)₁₃₉9_<141> = 13 · 12015911326813_<14> · C127
C127 = P53 · P75
P53 = 10098947505940741188253378705758426820362239035432097_<53>
P75 = 436689750002543719167336765795082713550194093289913311609891257071910504673_<75>

Number: 68889_140 N=4410106861658074670653860173486054163974219973878488208662754414022560015885316271061355644080305761472103499186111823892689281 ( 127 digits) SNFS difficulty: 142 digits. Divisors found: r1=10098947505940741188253378705758426820362239035432097 (pp53) r2=436689750002543719167336765795082713550194093289913311609891257071910504673 (pp75) Version: Msieve-1.40 Total time: 5.09 hours. Scaled time: 5.12 units (timescale=1.006). Factorization parameters were as follows: n: 4410106861658074670653860173486054163974219973878488208662754414022560015885316271061355644080305761472103499186111823892689281 m: 20000000000000000000000000000 deg: 5 c5: 31 c0: 16 skew: 0.88 type: snfs lss: 1 rlim: 1690000 alim: 1690000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1690000/1690000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [845000, 1545001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 219150 x 219377 Total sieving time: 4.88 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.10 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,142.000,5,0,0,0,0,0,0,0,0,1690000,1690000,26,26,48,48,2.3,2.3,100000 total time: 5.09 hours. --------- CPU info (if available) ----------
(65·10¹³⁰+61)/9 = 7(2)₁₂₉9_<131> = 5309 · 133853 · 11432210892981839783_<20> · C103
C103 = P44 · P60
P44 = 88242340891347424067333022942264527163159569_<44>
P60 = 100744829127432112190700097504794978919085457423286387865851_<60>

Number: 72229_130 N=8889959554903411701690137669062704823054606208746224362590409854700706089629534587027889575236078978219 ( 103 digits) SNFS difficulty: 131 digits. Divisors found: r1=88242340891347424067333022942264527163159569 (pp44) r2=100744829127432112190700097504794978919085457423286387865851 (pp60) Version: Msieve v. 1.43 Total time: 5.60 hours. Scaled time: 4.35 units (timescale=0.776). Factorization parameters were as follows: n: 8889959554903411701690137669062704823054606208746224362590409854700706089629534587027889575236078978219 m: 100000000000000000000000000 deg: 5 c5: 65 c0: 61 skew: 0.99 type: snfs lss: 1 rlim: 1100000 alim: 1100000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1100000/1100000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [550000, 1100001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 170836 x 171061 Total sieving time: 5.33 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.14 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,131.000,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000 total time: 5.60 hours. --------- CPU info (if available) ----------
Oct 29, 2009 (8th): By Wataru Sakai / GMP-ECM 6.2.1 / Oct 29, 2009
(83·10¹⁸³+7)/9 = 9(2)₁₈₂3_<184> = 197 · 187504159 · 103695324197_<12> · 10933903999027_<14> · 231095300840004022549_<21> · C129
C129 = P42 · P88
P42 = 224437963133592964448686504282443534327677_<42>
P88 = 4245575694068388034155339395025821288916179217836087032692125228590049200357040943403523_<88>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=4111386264 Step 1 took 38383ms Step 2 took 14033ms ********** Factor found in step 2: 224437963133592964448686504282443534327677 Found probable prime factor of 42 digits: 224437963133592964448686504282443534327677 Probable prime cofactor 4245575694068388034155339395025821288916179217836087032692125228590049200357040943403523 has 88 digits
(22·10¹⁷³-7)/3 = 7(3)₁₇₂1_<174> = 97 · 541859 · 65483111511553_<14> · 29019575156728627496451041059487_<32> · C121
C121 = P34 · C88
P34 = 7085999215281227635840096984763449_<34>
C88 = [1036148358624627286217516372248460715568726928814760434392187296717805689495977792371623_<88>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2752642412 Step 1 took 34284ms Step 2 took 13203ms ********** Factor found in step 2: 7085999215281227635840096984763449 Found probable prime factor of 34 digits: 7085999215281227635840096984763449 Composite cofactor 1036148358624627286217516372248460715568726928814760434392187296717805689495977792371623 has 88 digits
Oct 29, 2009 (7th): By Sinkiti Sibata / Msieve, GGNFS / Oct 29, 2009
(65·10¹¹⁹+61)/9 = 7(2)₁₁₈9_<120> = 3² · 7761437 · C113
C113 = P50 · P63
P50 = 61337291745830448794575516401101672468419237064719_<50>
P63 = 168562748737289305529363034257681167433141794253215672631853727_<63>

Number: 72229_119 N=10339182496778227225222199649400866563787983279416803045653390419872880960091142088797076312060113814007240357713 ( 113 digits) SNFS difficulty: 121 digits. Divisors found: r1=61337291745830448794575516401101672468419237064719 (pp50) r2=168562748737289305529363034257681167433141794253215672631853727 (pp63) Version: Msieve-1.40 Total time: 1.93 hours. Scaled time: 3.95 units (timescale=2.045). Factorization parameters were as follows: name: 72229_119 n: 10339182496778227225222199649400866563787983279416803045653390419872880960091142088797076312060113814007240357713 m: 1000000000000000000000000 deg: 5 c5: 13 c0: 122 skew: 1.56 type: snfs lss: 1 rlim: 730000 alim: 730000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 730000/730000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [365000, 665001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 87883 x 88110 Total sieving time: 1.87 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.03 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,121.000,5,0,0,0,0,0,0,0,0,730000,730000,25,25,46,46,2.2,2.2,50000 total time: 1.93 hours. --------- CPU info (if available) ----------
(64·10¹⁸³+17)/9 = 7(1)₁₈₂3_<184> = 3 · 59 · C182
C182 = P33 · P46 · P104
P33 = 384410432843509184562551441772217_<33>
P46 = 5960154262873601562601591019221235861490470119_<46>
P104 = 17535232633606003339861798618760092993549136117476670102764910728473797048681628830125019112178672954103_<104>

Number: 71113_183 N=40175768989328311362209667294413057124921531701192718141870684243565599497802887633396107972379158819836785938480853735091023226616446955430006277463904582548650345260514752040175769 ( 182 digits) SNFS difficulty: 185 digits. Divisors found: r1=384410432843509184562551441772217 (pp33) r2=5960154262873601562601591019221235861490470119 (pp46) r3=17535232633606003339861798618760092993549136117476670102764910728473797048681628830125019112178672954103 (pp104) Version: Msieve v. 1.42 Total time: 12.89 hours. Scaled time: 10.99 units (timescale=0.853). Factorization parameters were as follows: name: 71113_183 n: 40175768989328311362209667294413057124921531701192718141870684243565599497802887633396107972379158819836785938480853735091023226616446955430006277463904582548650345260514752040175769 m: 4000000000000000000000000000000000000 deg: 5 c5: 125 c0: 34 skew: 0.77 type: snfs lss: 1 rlim: 8500000 alim: 8500000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 Factor base limits: 8500000/8500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [4250000, 7450001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1649596 x 1649831 Total sieving time: 0.00 hours. Total relation processing time: 0.20 hours. Matrix solve time: 11.71 hours. Time per square root: 0.97 hours. Prototype def-par.txt line would be: snfs,185.000,5,0,0,0,0,0,0,0,0,8500000,8500000,28,28,54,54,2.5,2.5,100000 total time: 12.89 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 5600+ stepping 02 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 5600+ stepping 02 Memory: 3886124k/4718592k available (3786k kernel code, 656964k absent, 175504k reserved, 2294k data, 1304k init) Calibrating delay loop (skipped), value calculated using timer frequency.. 5827.16 BogoMIPS (lpj=2913583) Calibrating delay using timer specific routine.. 5826.53 BogoMIPS (lpj=2913268) Total of 2 processors activated (11653.70 BogoMIPS). Total time: 125hours 39min
(62·10¹²⁸-17)/9 = 6(8)₁₂₇7_<129> = 3 · 1657 · 105522593823052741_<18> · 4736156499474908470847_<22> · C87
C87 = P41 · P47
P41 = 19238524155145887995567897573406759382183_<41>
P47 = 14413258025958972317973107989704103083120550217_<47>

Thu Oct 29 08:01:12 2009 Msieve v. 1.42 Thu Oct 29 08:01:12 2009 random seeds: 0947fb50 3b7d3568 Thu Oct 29 08:01:12 2009 factoring 277289812686762027301312045381903076962595440431498977011201304744729183842977946583711 (87 digits) Thu Oct 29 08:01:13 2009 searching for 15-digit factors Thu Oct 29 08:01:13 2009 commencing quadratic sieve (87-digit input) Thu Oct 29 08:01:13 2009 using multiplier of 35 Thu Oct 29 08:01:13 2009 using 32kb Intel Core sieve core Thu Oct 29 08:01:13 2009 sieve interval: 20 blocks of size 32768 Thu Oct 29 08:01:13 2009 processing polynomials in batches of 11 Thu Oct 29 08:01:13 2009 using a sieve bound of 1484803 (56667 primes) Thu Oct 29 08:01:13 2009 using large prime bound of 118784240 (26 bits) Thu Oct 29 08:01:13 2009 using double large prime bound of 342425267860000 (42-49 bits) Thu Oct 29 08:01:13 2009 using trial factoring cutoff of 49 bits Thu Oct 29 08:01:13 2009 polynomial 'A' values have 11 factors Thu Oct 29 08:50:06 2009 56767 relations (15620 full + 41147 combined from 598038 partial), need 56763 Thu Oct 29 08:50:07 2009 begin with 613658 relations Thu Oct 29 08:50:08 2009 reduce to 136464 relations in 11 passes Thu Oct 29 08:50:08 2009 attempting to read 136464 relations Thu Oct 29 08:50:09 2009 recovered 136464 relations Thu Oct 29 08:50:09 2009 recovered 117722 polynomials Thu Oct 29 08:50:10 2009 attempting to build 56767 cycles Thu Oct 29 08:50:10 2009 found 56767 cycles in 5 passes Thu Oct 29 08:50:10 2009 distribution of cycle lengths: Thu Oct 29 08:50:10 2009 length 1 : 15620 Thu Oct 29 08:50:10 2009 length 2 : 11099 Thu Oct 29 08:50:10 2009 length 3 : 10028 Thu Oct 29 08:50:10 2009 length 4 : 7451 Thu Oct 29 08:50:10 2009 length 5 : 5227 Thu Oct 29 08:50:10 2009 length 6 : 3205 Thu Oct 29 08:50:10 2009 length 7 : 1902 Thu Oct 29 08:50:10 2009 length 9+: 2235 Thu Oct 29 08:50:10 2009 largest cycle: 22 relations Thu Oct 29 08:50:10 2009 matrix is 56667 x 56767 (13.5 MB) with weight 3322806 (58.53/col) Thu Oct 29 08:50:10 2009 sparse part has weight 3322806 (58.53/col) Thu Oct 29 08:50:11 2009 filtering completed in 4 passes Thu Oct 29 08:50:11 2009 matrix is 52465 x 52529 (12.7 MB) with weight 3116575 (59.33/col) Thu Oct 29 08:50:11 2009 sparse part has weight 3116575 (59.33/col) Thu Oct 29 08:50:11 2009 saving the first 48 matrix rows for later Thu Oct 29 08:50:11 2009 matrix is 52417 x 52529 (8.7 MB) with weight 2519016 (47.95/col) Thu Oct 29 08:50:11 2009 sparse part has weight 1975140 (37.60/col) Thu Oct 29 08:50:11 2009 matrix includes 64 packed rows Thu Oct 29 08:50:11 2009 using block size 21011 for processor cache size 1024 kB Thu Oct 29 08:50:11 2009 commencing Lanczos iteration Thu Oct 29 08:50:11 2009 memory use: 8.6 MB Thu Oct 29 08:50:29 2009 lanczos halted after 831 iterations (dim = 52415) Thu Oct 29 08:50:29 2009 recovered 18 nontrivial dependencies Thu Oct 29 08:50:29 2009 prp41 factor: 19238524155145887995567897573406759382183 Thu Oct 29 08:50:29 2009 prp47 factor: 14413258025958972317973107989704103083120550217 Thu Oct 29 08:50:29 2009 elapsed time 00:49:17
(62·10¹³⁰-17)/9 = 6(8)₁₂₉7_<131> = 7 · 13 · 151² · 619 · 1091 · 4691 · 3632610707018230033248932603_<28> · C88
C88 = P40 · P49
P40 = 2216843675469889748033783817831646405793_<40>
P49 = 1301424962816481848646950520141595158687854696197_<49>

Thu Oct 29 09:38:44 2009 Msieve v. 1.42 Thu Oct 29 09:38:44 2009 random seeds: 844858f0 9939bf40 Thu Oct 29 09:38:44 2009 factoring 2885055697918354219788012698586494272919721129686201143026490798695353880043070995869221 (88 digits) Thu Oct 29 09:38:45 2009 searching for 15-digit factors Thu Oct 29 09:38:45 2009 commencing quadratic sieve (88-digit input) Thu Oct 29 09:38:46 2009 using multiplier of 5 Thu Oct 29 09:38:46 2009 using 32kb Intel Core sieve core Thu Oct 29 09:38:46 2009 sieve interval: 25 blocks of size 32768 Thu Oct 29 09:38:46 2009 processing polynomials in batches of 9 Thu Oct 29 09:38:46 2009 using a sieve bound of 1517707 (57351 primes) Thu Oct 29 09:38:46 2009 using large prime bound of 121416560 (26 bits) Thu Oct 29 09:38:46 2009 using double large prime bound of 356205104400640 (42-49 bits) Thu Oct 29 09:38:46 2009 using trial factoring cutoff of 49 bits Thu Oct 29 09:38:46 2009 polynomial 'A' values have 11 factors Thu Oct 29 10:19:57 2009 57823 relations (16380 full + 41443 combined from 602864 partial), need 57447 Thu Oct 29 10:19:58 2009 begin with 619244 relations Thu Oct 29 10:19:59 2009 reduce to 137627 relations in 10 passes Thu Oct 29 10:19:59 2009 attempting to read 137627 relations Thu Oct 29 10:20:01 2009 recovered 137627 relations Thu Oct 29 10:20:01 2009 recovered 111021 polynomials Thu Oct 29 10:20:01 2009 attempting to build 57823 cycles Thu Oct 29 10:20:01 2009 found 57823 cycles in 5 passes Thu Oct 29 10:20:01 2009 distribution of cycle lengths: Thu Oct 29 10:20:01 2009 length 1 : 16380 Thu Oct 29 10:20:01 2009 length 2 : 11364 Thu Oct 29 10:20:01 2009 length 3 : 10278 Thu Oct 29 10:20:01 2009 length 4 : 7544 Thu Oct 29 10:20:01 2009 length 5 : 5180 Thu Oct 29 10:20:01 2009 length 6 : 3069 Thu Oct 29 10:20:01 2009 length 7 : 1919 Thu Oct 29 10:20:01 2009 length 9+: 2089 Thu Oct 29 10:20:01 2009 largest cycle: 18 relations Thu Oct 29 10:20:01 2009 matrix is 57351 x 57823 (13.7 MB) with weight 3355406 (58.03/col) Thu Oct 29 10:20:01 2009 sparse part has weight 3355406 (58.03/col) Thu Oct 29 10:20:02 2009 filtering completed in 3 passes Thu Oct 29 10:20:02 2009 matrix is 52428 x 52492 (12.5 MB) with weight 3061277 (58.32/col) Thu Oct 29 10:20:02 2009 sparse part has weight 3061277 (58.32/col) Thu Oct 29 10:20:02 2009 saving the first 48 matrix rows for later Thu Oct 29 10:20:02 2009 matrix is 52380 x 52492 (8.7 MB) with weight 2464760 (46.95/col) Thu Oct 29 10:20:02 2009 sparse part has weight 1969615 (37.52/col) Thu Oct 29 10:20:02 2009 matrix includes 64 packed rows Thu Oct 29 10:20:02 2009 using block size 20996 for processor cache size 1024 kB Thu Oct 29 10:20:03 2009 commencing Lanczos iteration Thu Oct 29 10:20:03 2009 memory use: 8.5 MB Thu Oct 29 10:20:20 2009 lanczos halted after 830 iterations (dim = 52377) Thu Oct 29 10:20:20 2009 recovered 16 nontrivial dependencies Thu Oct 29 10:20:21 2009 prp40 factor: 2216843675469889748033783817831646405793 Thu Oct 29 10:20:21 2009 prp49 factor: 1301424962816481848646950520141595158687854696197 Thu Oct 29 10:20:21 2009 elapsed time 00:41:37
(62·10¹⁴⁹-17)/9 = 6(8)₁₄₈7_<150> = 3⁴ · 53 · 563 · 3259 · 12479 · 27827 · 1543019 · 317866189 · 30231364087_<11> · 1303276091026529_<16> · C92
C92 = P44 · P48
P44 = 14990515629278420189522772956896539661364399_<44>
P48 = 869406757400744216491505254904358858761686953217_<48>

Thu Oct 29 10:31:36 2009 Msieve v. 1.42 Thu Oct 29 10:31:36 2009 random seeds: 10de91b8 65f02773 Thu Oct 29 10:31:36 2009 factoring 13032855585016127987715163764187861752979788193972047216203105388131327964051192003502321583 (92 digits) Thu Oct 29 10:31:37 2009 searching for 15-digit factors Thu Oct 29 10:31:37 2009 commencing quadratic sieve (92-digit input) Thu Oct 29 10:31:37 2009 using multiplier of 3 Thu Oct 29 10:31:37 2009 using 32kb Intel Core sieve core Thu Oct 29 10:31:37 2009 sieve interval: 36 blocks of size 32768 Thu Oct 29 10:31:37 2009 processing polynomials in batches of 6 Thu Oct 29 10:31:37 2009 using a sieve bound of 1748623 (65882 primes) Thu Oct 29 10:31:37 2009 using large prime bound of 176610923 (27 bits) Thu Oct 29 10:31:37 2009 using double large prime bound of 699248562996980 (42-50 bits) Thu Oct 29 10:31:37 2009 using trial factoring cutoff of 50 bits Thu Oct 29 10:31:37 2009 polynomial 'A' values have 12 factors Thu Oct 29 12:23:28 2009 66409 relations (16846 full + 49563 combined from 801134 partial), need 65978 Thu Oct 29 12:23:29 2009 begin with 817980 relations Thu Oct 29 12:23:30 2009 reduce to 167485 relations in 11 passes Thu Oct 29 12:23:30 2009 attempting to read 167485 relations Thu Oct 29 12:23:32 2009 recovered 167485 relations Thu Oct 29 12:23:32 2009 recovered 148683 polynomials Thu Oct 29 12:23:32 2009 attempting to build 66409 cycles Thu Oct 29 12:23:32 2009 found 66409 cycles in 6 passes Thu Oct 29 12:23:32 2009 distribution of cycle lengths: Thu Oct 29 12:23:32 2009 length 1 : 16846 Thu Oct 29 12:23:32 2009 length 2 : 12029 Thu Oct 29 12:23:32 2009 length 3 : 11566 Thu Oct 29 12:23:32 2009 length 4 : 9050 Thu Oct 29 12:23:32 2009 length 5 : 6594 Thu Oct 29 12:23:32 2009 length 6 : 4335 Thu Oct 29 12:23:32 2009 length 7 : 2615 Thu Oct 29 12:23:33 2009 length 9+: 3374 Thu Oct 29 12:23:33 2009 largest cycle: 19 relations Thu Oct 29 12:23:33 2009 matrix is 65882 x 66409 (16.6 MB) with weight 4091728 (61.61/col) Thu Oct 29 12:23:33 2009 sparse part has weight 4091728 (61.61/col) Thu Oct 29 12:23:34 2009 filtering completed in 3 passes Thu Oct 29 12:23:34 2009 matrix is 62231 x 62295 (15.6 MB) with weight 3839753 (61.64/col) Thu Oct 29 12:23:34 2009 sparse part has weight 3839753 (61.64/col) Thu Oct 29 12:23:34 2009 saving the first 48 matrix rows for later Thu Oct 29 12:23:34 2009 matrix is 62183 x 62295 (9.7 MB) with weight 3001449 (48.18/col) Thu Oct 29 12:23:34 2009 sparse part has weight 2164215 (34.74/col) Thu Oct 29 12:23:34 2009 matrix includes 64 packed rows Thu Oct 29 12:23:34 2009 using block size 24918 for processor cache size 1024 kB Thu Oct 29 12:23:35 2009 commencing Lanczos iteration Thu Oct 29 12:23:35 2009 memory use: 10.0 MB Thu Oct 29 12:23:59 2009 lanczos halted after 984 iterations (dim = 62181) Thu Oct 29 12:23:59 2009 recovered 16 nontrivial dependencies Thu Oct 29 12:24:00 2009 prp44 factor: 14990515629278420189522772956896539661364399 Thu Oct 29 12:24:00 2009 prp48 factor: 869406757400744216491505254904358858761686953217 Thu Oct 29 12:24:00 2009 elapsed time 01:52:24
(62·10¹³⁶-17)/9 = 6(8)₁₃₅7_<137> = 7 · 13 · 53 · 69581581 · 1013310464338031_<16> · C111
C111 = P44 · P67
P44 = 21445140596559027674445600227216279078028913_<44>
P67 = 9446397147569998958870814273587432081956274848493168972552660851483_<67>

Number: 68887_136 N=202579314960572784853853841483578465366236882142762231912399875722301397628634517434793217876549853255872927979 ( 111 digits) SNFS difficulty: 138 digits. Divisors found: r1=21445140596559027674445600227216279078028913 (pp44) r2=9446397147569998958870814273587432081956274848493168972552660851483 (pp67) Version: GGNFS-0.77.1-20060513-k8 Total time: 7.69 hours. Scaled time: 15.12 units (timescale=1.967). Factorization parameters were as follows: name: 68887_136 n: 202579314960572784853853841483578465366236882142762231912399875722301397628634517434793217876549853255872927979 m: 2000000000000000000000000000 deg: 5 c5: 155 c0: -136 skew: 0.97 type: snfs lss: 1 rlim: 1430000 alim: 1430000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1430000/1430000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [715000, 1390001) Primes: RFBsize:109205, AFBsize:109105, largePrimes:3313683 encountered Relations: rels:3256308, finalFF:265958 Max relations in full relation-set: 28 Initial matrix: 218377 x 265958 with sparse part having weight 21751660. Pruned matrix : 202781 x 203936 with weight 13649675. Total sieving time: 7.13 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.38 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,138,5,0,0,0,0,0,0,0,0,1430000,1430000,26,26,48,48,2.3,2.3,75000 total time: 7.69 hours. --------- CPU info (if available) ----------
(62·10¹²⁶+1)/9 = 6(8)₁₂₅9_<127> = 7 · 47 · 83 · 1541963399_<10> · 660931435820087_<15> · C99
C99 = P41 · P59
P41 = 24438968728948515381731252918147334447671_<41>
P59 = 10128889662287420283252120128975774558249253186011221512749_<59>

Number: 68889_126 N=247539617715612152894729759876354338742558857147054971673720876347783084339220280796770906999857579 ( 99 digits) SNFS difficulty: 128 digits. Divisors found: r1=24438968728948515381731252918147334447671 (pp41) r2=10128889662287420283252120128975774558249253186011221512749 (pp59) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 4.21 hours. Scaled time: 1.98 units (timescale=0.470). Factorization parameters were as follows: name: 68889_126 n: 247539617715612152894729759876354338742558857147054971673720876347783084339220280796770906999857579 m: 20000000000000000000000000 deg: 5 c5: 155 c0: 8 skew: 0.55 type: snfs lss: 1 rlim: 980000 alim: 980000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 980000/980000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [490000, 840001) Primes: RFBsize:77067, AFBsize:76704, largePrimes:2697581 encountered Relations: rels:2682573, finalFF:279654 Max relations in full relation-set: 28 Initial matrix: 153838 x 279654 with sparse part having weight 21371172. Pruned matrix : 119190 x 120023 with weight 6566874. Total sieving time: 3.90 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.17 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,128,5,0,0,0,0,0,0,0,0,980000,980000,26,26,47,47,2.3,2.3,50000 total time: 4.21 hours. --------- CPU info (if available) ----------
(22·10¹²⁵-7)/3 = 7(3)₁₂₄1_<126> = 139 · 1753 · 29813712015624763_<17> · C105
C105 = P46 · P59
P46 = 5835514109274418429331289019347933750642074023_<46>
P59 = 17298543348572175255854507216815323864835034117825029046357_<59>

Number: 73331_125 N=100945893780488072805794054903888609442778207215050028770210697409559135193502458841115087258636292484211 ( 105 digits) SNFS difficulty: 126 digits. Divisors found: r1=5835514109274418429331289019347933750642074023 (pp46) r2=17298543348572175255854507216815323864835034117825029046357 (pp59) Version: Msieve v. 1.42 Total time: 0.06 hours. Scaled time: 0.06 units (timescale=1.024). Factorization parameters were as follows: name: 73331_125 n: 100945893780488072805794054903888609442778207215050028770210697409559135193502458841115087258636292484211 m: 10000000000000000000000000 deg: 5 c5: 22 c0: -7 skew: 0.80 type: snfs lss: 1 rlim: 890000 alim: 890000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 890000/890000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [445000, 695001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 102874 x 103106 Total sieving time: 0.00 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.02 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,126.000,5,0,0,0,0,0,0,0,0,890000,890000,26,26,46,46,2.3,2.3,50000 total time: 0.06 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q6600 @ 2.40GHz stepping 0b CPU1: Intel(R) Core(TM)2 Quad CPU Q6600 @ 2.40GHz stepping 0b CPU2: Intel(R) Core(TM)2 Quad CPU Q6600 @ 2.40GHz stepping 0b CPU3: Intel(R) Core(TM)2 Quad CPU Q6600 @ 2.40GHz stepping 0b Memory: 3057976k/3145344k available (3786k kernel code, 496k absent, 86872k reserved, 2294k data, 1304k init) Calibrating delay loop (skipped), value calculated using timer frequency.. 4787.88 BogoMIPS (lpj=2393941) Calibrating delay using timer specific routine.. 4787.76 BogoMIPS (lpj=2393880) Calibrating delay using timer specific routine.. 4787.77 BogoMIPS (lpj=2393886) Calibrating delay using timer specific routine.. 4787.78 BogoMIPS (lpj=2393891) Total of 4 processors activated (19151.19 BogoMIPS). total time: 57 min
(62·10¹²⁷-53)/9 = 6(8)₁₂₆3_<128> = 3² · 7 · 4373075016167159_<16> · C111
C111 = P40 · P71
P40 = 5453325435685665821475301936816985008441_<40>
P71 = 45852211565333095184206412202116635585191607632222241319520518384375539_<71>

Number: 68883_127 N=250047031611671426524712294764192025608047985060941485564187383018891286802343657348586214528075249412428924699 ( 111 digits) SNFS difficulty: 129 digits. Divisors found: r1=5453325435685665821475301936816985008441 (pp40) r2=45852211565333095184206412202116635585191607632222241319520518384375539 (pp71) Version: GGNFS-0.77.1-20060513-k8 Total time: 5.22 hours. Scaled time: 10.27 units (timescale=1.967). Factorization parameters were as follows: name: 68883_127 n: 250047031611671426524712294764192025608047985060941485564187383018891286802343657348586214528075249412428924699 m: 20000000000000000000000000 deg: 5 c5: 775 c0: -212 skew: 0.77 type: snfs lss: 1 rlim: 1000000 alim: 1000000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [500000, 1050001) Primes: RFBsize:78498, AFBsize:78237, largePrimes:2790052 encountered Relations: rels:2715447, finalFF:211136 Max relations in full relation-set: 28 Initial matrix: 156802 x 211136 with sparse part having weight 18694044. Pruned matrix : 143833 x 144681 with weight 10166225. Total sieving time: 4.95 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.13 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,129,5,0,0,0,0,0,0,0,0,1000000,1000000,26,26,47,47,2.3,2.3,50000 total time: 5.22 hours. --------- CPU info (if available) ----------
(62·10¹³⁰+1)/9 = 6(8)₁₂₉9_<131> = 3 · 1021 · 4517 · 97829 · C119
C119 = P36 · P84
P36 = 172646517491005006256239973571080363_<36>
P84 = 294799441210256853477729159395431700808480725079520017412819392555476174232512350517_<84>

Number: 68889_130 N=50896096883245111904087491066818110988048098986769458408393871306471379148082206150305806791176779739197015576231597671 ( 119 digits) SNFS difficulty: 132 digits. Divisors found: r1=172646517491005006256239973571080363 (pp36) r2=294799441210256853477729159395431700808480725079520017412819392555476174232512350517 (pp84) Version: Msieve v. 1.42 Total time: 0.11 hours. Scaled time: 0.11 units (timescale=1.025). Factorization parameters were as follows: name: 68889_130 n: 50896096883245111904087491066818110988048098986769458408393871306471379148082206150305806791176779739197015576231597671 m: 200000000000000000000000000 deg: 5 c5: 31 c0: 16 skew: 0.88 type: snfs lss: 1 rlim: 1150000 alim: 1150000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1150000/1150000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [575000, 875001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 165872 x 166120 Total sieving time: 0.00 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.06 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,132.000,5,0,0,0,0,0,0,0,0,1150000,1150000,26,26,47,47,2.3,2.3,50000 total time: 0.11 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q6600 @ 2.40GHz stepping 0b CPU1: Intel(R) Core(TM)2 Quad CPU Q6600 @ 2.40GHz stepping 0b CPU2: Intel(R) Core(TM)2 Quad CPU Q6600 @ 2.40GHz stepping 0b CPU3: Intel(R) Core(TM)2 Quad CPU Q6600 @ 2.40GHz stepping 0b Memory: 3057976k/3145344k available (3786k kernel code, 496k absent, 86872k reserved, 2294k data, 1304k init) Calibrating delay loop (skipped), value calculated using timer frequency.. 4787.88 BogoMIPS (lpj=2393941) Calibrating delay using timer specific routine.. 4787.76 BogoMIPS (lpj=2393880) Calibrating delay using timer specific routine.. 4787.77 BogoMIPS (lpj=2393886) Calibrating delay using timer specific routine.. 4787.78 BogoMIPS (lpj=2393891) Total of 4 processors activated (19151.19 BogoMIPS). total time: 1 hour 17 min
(62·10¹³⁰-53)/9 = 6(8)₁₂₉3_<131> = 3 · 827 · 209767934901885224303739917497_<30> · C99
C99 = P38 · P61
P38 = 27526445632823402801555781212943586751_<38>
P61 = 4808760820477327944086801289662261340494201135301405931889669_<61>

Number: 68883_130 N=132368093286120427073132380496392850742543712691797795425763461226071196035292063716102728062175419 ( 99 digits) SNFS difficulty: 131 digits. Divisors found: r1=27526445632823402801555781212943586751 (pp38) r2=4808760820477327944086801289662261340494201135301405931889669 (pp61) Version: Msieve v. 1.42 Total time: 0.12 hours. Scaled time: 0.13 units (timescale=1.025). Factorization parameters were as follows: name: 68883_130 n: 132368093286120427073132380496392850742543712691797795425763461226071196035292063716102728062175419 m: 100000000000000000000000000 deg: 5 c5: 62 c0: -53 skew: 0.97 type: snfs lss: 1 rlim: 1100000 alim: 1100000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1100000/1100000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [550000, 1050001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 180005 x 180230 Total sieving time: 0.00 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.07 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,131.000,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000 total time: 0.12 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q6600 @ 2.40GHz stepping 0b CPU1: Intel(R) Core(TM)2 Quad CPU Q6600 @ 2.40GHz stepping 0b CPU2: Intel(R) Core(TM)2 Quad CPU Q6600 @ 2.40GHz stepping 0b CPU3: Intel(R) Core(TM)2 Quad CPU Q6600 @ 2.40GHz stepping 0b Memory: 3057976k/3145344k available (3786k kernel code, 496k absent, 86872k reserved, 2294k data, 1304k init) Calibrating delay loop (skipped), value calculated using timer frequency.. 4787.88 BogoMIPS (lpj=2393941) Calibrating delay using timer specific routine.. 4787.76 BogoMIPS (lpj=2393880) Calibrating delay using timer specific routine.. 4787.77 BogoMIPS (lpj=2393886) Calibrating delay using timer specific routine.. 4787.78 BogoMIPS (lpj=2393891) Total of 4 processors activated (19151.19 BogoMIPS). total time: 1 hour 55 min
(62·10¹³⁹-17)/9 = 6(8)₁₃₈7_<140> = 23 · 757 · 18719 · 30161 · 130303 · 696107 · 2665811 · 5686673 · C103
C103 = P39 · P64
P39 = 926007323380718041367848667604976818917_<39>
P64 = 5503825234459097628568763534609341243640504139868724244565262153_<64>

Number: 68887_139 N=5096582473716721911320817165106487433415795470035694878499516371602090541767465977942766273924114548301 ( 103 digits) SNFS difficulty: 141 digits. Divisors found: r1=926007323380718041367848667604976818917 (pp39) r2=5503825234459097628568763534609341243640504139868724244565262153 (pp64) Version: Msieve-1.40 Total time: 6.59 hours. Scaled time: 13.64 units (timescale=2.071). Factorization parameters were as follows: name: 68887_139 n: 5096582473716721911320817165106487433415795470035694878499516371602090541767465977942766273924114548301 m: 10000000000000000000000000000 deg: 5 c5: 31 c0: -85 skew: 1.22 type: snfs lss: 1 rlim: 1600000 alim: 1600000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1600000/1600000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [800000, 1600001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 227013 x 227254 Total sieving time: 6.28 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.18 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,141.000,5,0,0,0,0,0,0,0,0,1600000,1600000,26,26,48,48,2.3,2.3,100000 total time: 6.59 hours. --------- CPU info (if available) ----------
Oct 29, 2009 (6th): By Robert Backstrom / GGNFS, Msieve / Oct 29, 2009
(22·10¹²⁷-7)/3 = 7(3)₁₂₆1_<128> = 479 · 44075527 · C118
C118 = P46 · P72
P46 = 6577399073481143560931762320945836405658976407_<46>
P72 = 528097615006827450101667740710985593710548414937408630323507149175477101_<72>

Number: n N=3473508763653508525973618996598802094452506079093510872225215128682143135403106733322106848803942284172130817527756107 ( 118 digits) SNFS difficulty: 128 digits. Divisors found: r1=6577399073481143560931762320945836405658976407 (pp46) r2=528097615006827450101667740710985593710548414937408630323507149175477101 (pp72) Version: GGNFS-0.77.1-20051202-athlon Total time: 1.95 hours. Scaled time: 3.55 units (timescale=1.823). Factorization parameters were as follows: name: KA_7_3_126_1 n: 3473508763653508525973618996598802094452506079093510872225215128682143135403106733322106848803942284172130817527756107 m: 20000000000000000000000000 deg: 5 c5: 275 c0: -28 skew: 0.63 type: snfs lss: 1 rlim: 990000 alim: 990000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 qintsize: 10000 Factor base limits: 990000/990000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [495000, 835001) Primes: RFBsize:77777, AFBsize:77453, largePrimes:2595907 encountered Relations: rels:2454373, finalFF:189776 Max relations in full relation-set: 48 Initial matrix: 155297 x 189776 with sparse part having weight 16134020. Pruned matrix : 143607 x 144447 with weight 8818753. Total sieving time: 1.77 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.11 hours. Total square root time: 0.02 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,128,5,0,0,0,0,0,0,0,0,990000,990000,26,26,47,47,2.3,2.3,50000 total time: 1.95 hours. --------- CPU info (if available) ----------
(62·10¹²⁶-17)/9 = 6(8)₁₂₅7_<127> = 126222973133549_<15> · C113
C113 = P44 · P70
P44 = 17478016109900362123148044512875872521564383_<44>
P70 = 3122616420509176390118982265005374742402752146903093305407083770722861_<70>

Number: n N=54577140102698788478968629476910731542323421602049717663968754282023809748791855193804422746495616416174461459763 ( 113 digits) SNFS difficulty: 128 digits. Divisors found: r1=17478016109900362123148044512875872521564383 (pp44) r2=3122616420509176390118982265005374742402752146903093305407083770722861 (pp70) Version: GGNFS-0.77.1-20051202-athlon Total time: 2.44 hours. Scaled time: 4.44 units (timescale=1.823). Factorization parameters were as follows: name: KA_6_8_125_7 n: 54577140102698788478968629476910731542323421602049717663968754282023809748791855193804422746495616416174461459763 m: 20000000000000000000000000 deg: 5 c5: 155 c0: -136 skew: 0.97 type: snfs lss: 1 rlim: 980000 alim: 980000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 qintsize: 10000 Factor base limits: 980000/980000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [490000, 850001) Primes: RFBsize:77067, AFBsize:77074, largePrimes:2525068 encountered Relations: rels:2371743, finalFF:176884 Max relations in full relation-set: 48 Initial matrix: 154208 x 176884 with sparse part having weight 15357027. Pruned matrix : 146855 x 147690 with weight 9842125. Total sieving time: 2.24 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.12 hours. Total square root time: 0.02 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,128,5,0,0,0,0,0,0,0,0,980000,980000,26,26,47,47,2.3,2.3,50000 total time: 2.44 hours. --------- CPU info (if available) ----------
(62·10¹²⁸+1)/9 = 6(8)₁₂₇9_<129> = 13 · 97 · 197 · 1571 · C121
C121 = P54 · P67
P54 = 221839062921055719484107373612660853699302142746356139_<54>
P67 = 7957078823320286782689262399302302972074139970168996053248181231993_<67>

Number: n N=1765190909754349106047805048835653555356153326809056765104083714705035874397650631344173890587328534974454782088558755027 ( 121 digits) SNFS difficulty: 131 digits. Divisors found: Thu Oct 29 22:10:41 2009 prp54 factor: 221839062921055719484107373612660853699302142746356139 Thu Oct 29 22:10:41 2009 prp67 factor: 7957078823320286782689262399302302972074139970168996053248181231993 Thu Oct 29 22:10:41 2009 elapsed time 00:08:18 (Msieve 1.43 - dependency 2) Version: GGNFS-0.77.1-20051202-athlon Total time: 1.84 hours. Scaled time: 3.36 units (timescale=1.829). Factorization parameters were as follows: name: KA_6_8_127_9 n: 1765190909754349106047805048835653555356153326809056765104083714705035874397650631344173890587328534974454782088558755027 m: 100000000000000000000000000 deg: 5 c5: 31 c0: 50 skew: 1.10 type: snfs lss: 1 rlim: 1090000 alim: 1090000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 qintsize: 10000 Factor base limits: 1090000/1090000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved special-q in [545000, 885331) Primes: RFBsize:84976, AFBsize:85149, largePrimes:2650390 encountered Relations: rels:2480173, finalFF:181106 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 234173 hash collisions in 2642513 relations Msieve: matrix is 158517 x 158742 (42.6 MB) Total sieving time: 1.79 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,1090000,1090000,26,26,47,47,2.3,2.3,50000 total time: 1.84 hours. --------- CPU info (if available) ----------
Oct 29, 2009 (5th): By matsui / Msieve / Oct 29, 2009
(64·10³³³-1)/9 = 7(1)₃₃₃_<334> = 13 · 4999 · 228777281 · 1541677987_<10> · 1103253089147723_<16> · 897821565552123255197697079_<27> · 1138685703753966317205547366328393186964066889_<46> · 3426549570671671064841267094850481127005282543233354557266456990784769879505493_<79> · C146
C146 = P56 · P91
P56 = 12174361251367883129391909180738935636343765462088551283_<56>
P91 = 6593745087362144980904245668229480104648255993069991196974660634291764657660612015236166117_<91>

N=80274634692979035236916096891593763332243932346695290164007809815885473899897686446683991310308022576677193511877133845257360068833629111661478111 ( 146 digits) Divisors found: r1=12174361251367883129391909180738935636343765462088551283 (pp56) r2=6593745087362144980904245668229480104648255993069991196974660634291764657660612015236166117 (pp91) Version: Msieve v. 1.43 Total time: 6730.09 hours. Scaled time: 12289.14 units (timescale=1.826). Factorization parameters were as follows: name: 71111_333 n: 80274634692979035236916096891593763332243932346695290164007809815885473899897686446683991310308022576677193511877133845257360068833629111661478111 skew: 377073.07 # norm 6.21e+19 c5: 1288500 c4: 68290971667 c3: 619913143244182622 c2: -26447842285036047361452 c1: -55420844824743942680919908090 c0: 1642140321092668673121090476858417 # alpha -5.93 Y1: 7265089991871023 Y0: -9097012245689260132720497456 # Murphy_E 8.85e-12 # M 51307725631548334216899866953555587407604198005490433969505896061629967361718503918766814953119299580128428318493399064108307143252143563690561581 type: gnfs rlim: 16800000 alim: 16800000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.6 alambda: 2.6 qintsize: 800000 Factor base limits: 16800000/16800000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved algebraic special-q in [8400000, 23600001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 3285994 x 3286224 Total sieving time: 6713.90 hours. Total relation processing time: 0.29 hours. Matrix solve time: 14.23 hours. Time per square root: 1.66 hours. Prototype def-par.txt line would be: gnfs,145,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,16800000,16800000,29,29,58,58,2.6,2.6,100000 total time: 6730.09 hours.
c146 is the second largest composite number which was factored by gnfs in our tables so far. Congratulations!
Oct 29, 2009 (4th): By juno1369 / GGNFS, Msieve v1.41 / Oct 29, 2009
(62·10¹⁴⁹-71)/9 = 6(8)₁₄₈1_<150> = 3 · 2417 · 74029477891_<11> · 3497744479903_<13> · 382748316025440940507_<21> · C102
C102 = P35 · P68
P35 = 43565025495414996045361762082014639_<35>
P68 = 22004284299797228251633148946891172189744868497880149030614978474539_<68>

Number: 68881_149 N=958617206529026163078164168986373017228530684647348271505022568050178553786224842053248585300086776421 ( 102 digits) Divisors found: r1=43565025495414996045361762082014639 (pp35) r2=22004284299797228251633148946891172189744868497880149030614978474539 (pp68) Version: Msieve-1.40 Total time: 8.42 hours. Scaled time: 14.82 units (timescale=1.761). Factorization parameters were as follows: name: 68881_149 n: 958617206529026163078164168986373017228530684647348271505022568050178553786224842053248585300086776421 skew: 22580.98 # norm 2.26e+014 c5: 6720 c4: 338199084 c3: -10505707699312 c2: -4051122316080619 c1: 2503178937575702048042 c0: -9365976316249819726224600 # alpha -6.53 Y1: 38483326871 Y0: -42741647054392727347 # Murphy_E 2.68e-009 # M 52154113368020348603538907067962726876078627937292628552976680809307400113998793692763656046280578354 type: gnfs rlim: 2300000 alim: 2300000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 2300000/2300000 Large primes per side: 2 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1150000, 1750001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 280615 x 280863 Total sieving time: 7.77 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.47 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: gnfs,101,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000 total time: 8.42 hours. --------- CPU info (if available) ----------
Oct 29, 2009 (3rd): By Dmitry Domanov / GGNFS/msieve / Oct 29, 2009
(65·10¹³⁴+61)/9 = 7(2)₁₃₃9_<135> = 3 · 17 · 137 · 14707723 · C124
C124 = P58 · P66
P58 = 8170620663352175538141363624278865919798181514357283034749_<58>
P66 = 860160735400974356984124869352479240710535091232943755301407369921_<66>

Number: s124 N=7028047078471404241385538249417286890637656454374573587608436511688677005460215314566301659645079212232217122710089340384829 ( 124 digits) SNFS difficulty: 136 digits. Divisors found: r1=8170620663352175538141363624278865919798181514357283034749 (pp58) r2=860160735400974356984124869352479240710535091232943755301407369921 (pp66) Version: Msieve-1.40 Total time: 3.37 hours. Scaled time: 6.60 units (timescale=1.957). Factorization parameters were as follows: n: 7028047078471404241385538249417286890637656454374573587608436511688677005460215314566301659645079212232217122710089340384829 m: 1000000000000000000000000000 deg: 5 c5: 13 c0: 122 skew: 1.56 type: snfs lss: 1 rlim: 1300000 alim: 1300000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [650000, 1325001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 196084 x 196310 Total sieving time: 3.24 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.10 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,136.000,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,48,48,2.3,2.3,75000 total time: 3.37 hours. --------- CPU info (if available) ----------
(62·10¹³⁵-17)/9 = 6(8)₁₃₄7_<136> = C136
C136 = P34 · P103
P34 = 3006133944868273649904641611835927_<34>
P103 = 2291610758279353520262479427436718759759968530711012838648548023370471952701819314481826902624062304481_<103>

Number: 136-2 N=6888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888887 ( 136 digits) SNFS difficulty: 136 digits. Divisors found: r1=3006133944868273649904641611835927 (pp34) r2=2291610758279353520262479427436718759759968530711012838648548023370471952701819314481826902624062304481 (pp103) Version: Msieve-1.40 Total time: 4.00 hours. Scaled time: 7.87 units (timescale=1.969). Factorization parameters were as follows: n: 6888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888887 m: 1000000000000000000000000000 deg: 5 c5: 62 c0: -17 skew: 0.77 type: snfs lss: 1 rlim: 1330000 alim: 1330000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3Factor base limits: 1330000/1330000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [665000, 1415001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 166629 x 166854 Total sieving time: 3.88 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.07 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,136.000,5,0,0,0,0,0,0,0,0,1330000,1330000,26,26,48,48,2.3,2.3,75000 total time: 4.00 hours. --------- CPU info (if available) ----------
Oct 29, 2009 (2nd): By Ignacio Santos / GGNFS, Msieve / Oct 29, 2009
(64·10¹⁶⁷+17)/9 = 7(1)₁₆₆3_<168> = 13 · 19 · 31 · C164
C164 = P66 · P99
P66 = 147801285874676743702605376197388769702296463745069614255372510569_<66>
P99 = 628348532318111008341516309337363050902767140223828818956120842657819837747040849338498348275327161_<99>

Number: 71113_167 N=92870721054082683963838462989566554931580398473437522673515882344405264608999753312147200092870721054082683963838462989566554931580398473437522673515882344405264609 ( 164 digits) SNFS difficulty: 169 digits. Divisors found: r1=147801285874676743702605376197388769702296463745069614255372510569 (pp66) r2=628348532318111008341516309337363050902767140223828818956120842657819837747040849338498348275327161 (pp99) Version: Msieve-1.40 Total time: 37.66 hours. Scaled time: 65.68 units (timescale=1.744). Factorization parameters were as follows: n: 92870721054082683963838462989566554931580398473437522673515882344405264608999753312147200092870721054082683963838462989566554931580398473437522673515882344405264609 m: 4000000000000000000000000000000000 deg: 5 c5: 25 c0: 68 skew: 1.22 type: snfs lss: 1 rlim: 4700000 alim: 4700000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 4700000/4700000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2350000, 4250001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 799987 x 800213 Total sieving time: 36.03 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.81 hours. Time per square root: 0.72 hours. Prototype def-par.txt line would be: snfs,169.000,5,0,0,0,0,0,0,0,0,4700000,4700000,27,27,52,52,2.4,2.4,100000 total time: 37.66 hours.
Oct 29, 2009: Factorizations of 688...883, Factorizations of 688...887 and Factorizations of 688...889 have been extended up to n=150. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.
Oct 28, 2009 (8th): By Dmitry Domanov / GGNFS/msieve, ECMNET, GMP-ECM / Oct 28, 2009
(62·10¹⁴²-71)/9 = 6(8)₁₄₁1_<143> = 17 · 127 · C140
C140 = P32 · P39 · P70
P32 = 88605204287423670249671527649293_<32>
P39 = 282298075240783523797463502563785239997_<39>
P70 = 1275643702644799867268139877864205097833015033358005502736075772881079_<70>

Number: s140 N=31907776233853121301013843857753074983274149554835057382533065719726210694251453862384848952704441356595131490916576604395038855437187998559 ( 140 digits) SNFS difficulty: 144 digits. Divisors found: r1=88605204287423670249671527649293 (pp32) r2=282298075240783523797463502563785239997 (pp39) r3=1275643702644799867268139877864205097833015033358005502736075772881079 (pp70) Version: Msieve-1.40 Total time: 7.72 hours. Scaled time: 15.16 units (timescale=1.963). Factorization parameters were as follows: n: 31907776233853121301013843857753074983274149554835057382533065719726210694251453862384848952704441356595131490916576604395038855437187998559 m: 20000000000000000000000000000 deg: 5 c5: 775 c0: -284 skew: 0.82 type: snfs lss: 1 rlim: 1790000 alim: 1790000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3Factor base limits: 1790000/1790000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [895000, 2295001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 313997 x 314222 Total sieving time: 7.26 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.26 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,144.000,5,0,0,0,0,0,0,0,0,1790000,1790000,26,26,49,49,2.3,2.3,100000 total time: 7.72 hours. --------- CPU info (if available) ----------
(61·10¹⁴⁴+11)/9 = 6(7)₁₄₃9_<145> = 139 · C143
C143 = P32 · P36 · P76
P32 = 35451613663413251648447982109961_<32>
P36 = 902835582445713727649667691606922077_<36>
P76 = 1523448755300188337671604898103869412215946977128520856830739463707719389413_<76>

Number: s143 N=48760991207034372501998401278976818545163868904876099120703437250199840127897681854516386890487609912070343725019984012789768185451638689048761 ( 143 digits) SNFS difficulty: 146 digits. Divisors found: r1=35451613663413251648447982109961 (pp32) r2=902835582445713727649667691606922077 (pp36) r3=1523448755300188337671604898103869412215946977128520856830739463707719389413 (pp76) Version: Msieve-1.40 Total time: 8.06 hours. Scaled time: 15.04 units (timescale=1.866). Factorization parameters were as follows: n: 48760991207034372501998401278976818545163868904876099120703437250199840127897681854516386890487609912070343725019984012789768185451638689048761 m: 100000000000000000000000000000 deg: 5 c5: 61 c0: 110 skew: 1.13 type: snfs lss: 1 rlim: 1960000 alim: 1960000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3Factor base limits: 1960000/1960000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [980000, 2480001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 325579 x 325804 Total sieving time: 7.78 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.13 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,146.000,5,0,0,0,0,0,0,0,0,1960000,1960000,26,26,49,49,2.3,2.3,100000 total time: 8.06 hours. --------- CPU info (if available) ----------
(59·10¹⁶⁶+13)/9 = 6(5)₁₆₅7_<167> = 17 · 67 · C164
C164 = P64 · P101
P64 = 1520300600803178723554489839762734450050310979284651413036412657_<64>
P101 = 37857881804580042766073071926977642450283485731120277261311868008262073402242471720348178440977797559_<101>

Number: 164-1 N=57555360452638766949565896010145351673007511462296361330601892498292849478099697590478977660716027704614183982050531655448248951321822261242805579943420154131304263 ( 164 digits) SNFS difficulty: 168 digits. Divisors found: r1=1520300600803178723554489839762734450050310979284651413036412657 (pp64) r2=37857881804580042766073071926977642450283485731120277261311868008262073402242471720348178440977797559 (pp101) Version: Msieve-1.40 Total time: 54.33 hours. Scaled time: 101.39 units (timescale=1.866). Factorization parameters were as follows: n: 57555360452638766949565896010145351673007511462296361330601892498292849478099697590478977660716027704614183982050531655448248951321822261242805579943420154131304263 m: 2000000000000000000000000000000000 deg: 5 c5: 295 c0: 208 skew: 0.93 type: snfs lss: 1 rlim: 4600000 alim: 4600000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4Factor base limits: 4600000/4600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2300000, 5400001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 963749 x 963974 Total sieving time: 52.94 hours. Total relation processing time: 0.11 hours. Matrix solve time: 1.17 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: snfs,168.000,5,0,0,0,0,0,0,0,0,4600000,4600000,27,27,52,52,2.4,2.4,100000 total time: 54.33 hours. --------- CPU info (if available) ----------
(59·10¹⁶⁵+13)/9 = 6(5)₁₆₄7_<166> = 23² · C164
C164 = P81 · P84
P81 = 110196508485120959229584433888099581893885727408622561715778078112344496125474827_<81>
P84 = 112456871072618870945836117361013701928460846350502379302614333335364545406654278879_<84>

Number: 164-2 N=12392354547363999159840369670237345095568157950010501995379122033186305398025624868725057760974585171182524679689140936777987817685360218441503885738290275152278933 ( 164 digits) SNFS difficulty: 166 digits. Divisors found: r1=110196508485120959229584433888099581893885727408622561715778078112344496125474827 (pp81) r2=112456871072618870945836117361013701928460846350502379302614333335364545406654278879 (pp84) Version: Msieve-1.40 Total time: 30.84 hours. Scaled time: 58.75 units (timescale=1.905). Factorization parameters were as follows: n: 12392354547363999159840369670237345095568157950010501995379122033186305398025624868725057760974585171182524679689140936777987817685360218441503885738290275152278933 m: 1000000000000000000000000000000000 deg: 5 c5: 59 c0: 13 skew: 0.74 type: snfs lss: 1 rlim: 4200000 alim: 4200000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4Factor base limits: 4200000/4200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [2100000, 3800001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 716975 x 717202 Total sieving time: 30.05 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.63 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,166.000,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000 total time: 30.84 hours. --------- CPU info (if available) ----------
(65·10¹⁷⁶+7)/9 = 7(2)₁₇₅3_<177> = 3² · C176
C176 = P37 · P140
P37 = 4442942910712936991397591050639207179_<37>
P140 = 18061657597884841998286548530250959539096033255123941595949495422393933276866461274947045522461378351677425535396899275108324213821248779493_<140>

Factor=4442942910712936991397591050639207179 Method=ECM B1=11000000 Sigma=1661063128
(65·10¹³¹+61)/9 = 7(2)₁₃₀9_<132> = 3 · 79 · C130
C130 = P52 · P79
P52 = 1280509510648682082491308652467981505699141252049001_<52>
P79 = 2379795794779564354598086165038364450138527040490957073655723750806221001915617_<79>

Number: s130-1 N=3047351148616971401781528363806844819503047351148616971401781528363806844819503047351148616971401781528363806844819503047351148617 ( 130 digits) SNFS difficulty: 132 digits. Divisors found: r1=1280509510648682082491308652467981505699141252049001 (pp52) r2=2379795794779564354598086165038364450138527040490957073655723750806221001915617 (pp79) Version: Msieve-1.40 Total time: 3.55 hours. Scaled time: 6.62 units (timescale=1.866). Factorization parameters were as follows: n: 3047351148616971401781528363806844819503047351148616971401781528363806844819503047351148616971401781528363806844819503047351148617 m: 100000000000000000000000000 deg: 5 c5: 650 c0: 61 skew: 0.62 type: snfs lss: 1 rlim: 1140000 alim: 1140000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3Factor base limits: 1140000/1140000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [570000, 1320001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 149370 x 149595 Total sieving time: 3.44 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.05 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,132.000,5,0,0,0,0,0,0,0,0,1140000,1140000,26,26,47,47,2.3,2.3,50000 total time: 3.55 hours. --------- CPU info (if available) ----------
(65·10¹⁵²+61)/9 = 7(2)₁₅₁9_<153> = 3 · C153
C153 = P35 · P118
P35 = 31146531695975924298765364037305309_<35>
P118 = 7729295290102686139699794454856781365379879804351612416391812646752847109285668325511683064669740001403032177197768627_<118>

Factor=31146531695975924298765364037305309 Method=ECM B1=11000000 Sigma=190775455
(22·10¹⁴³-7)/3 = 7(3)₁₄₂1_<144> = C144
C144 = P43 · P44 · P58
P43 = 3107752485792958896855128352023536341050509_<43>
P44 = 59206074072516662497430087693127541112104321_<44>
P58 = 3985554382642451971682452172996902377956999045276349984479_<58>

Number: s144 N=733333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331 ( 144 digits) SNFS difficulty: 145 digits. Divisors found: r1=3107752485792958896855128352023536341050509 (pp43) r2=59206074072516662497430087693127541112104321 (pp44) r3=3985554382642451971682452172996902377956999045276349984479 (pp58) Version: Msieve-1.40 Total time: 6.51 hours. Scaled time: 12.04 units (timescale=1.850). Factorization parameters were as follows: n: 733333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331 m: 50000000000000000000000000000 deg: 5 c5: 176 c0: -175 skew: 1.00 type: snfs lss: 1 rlim: 1880000 alim: 1880000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3Factor base limits: 1880000/1880000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [940000, 2140001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 331290 x 331538 Total sieving time: 6.24 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.14 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,145.000,5,0,0,0,0,0,0,0,0,1880000,1880000,26,26,49,49,2.3,2.3,100000 total time: 6.51 hours. --------- CPU info (if available) ----------
(65·10¹³⁷-11)/9 = 7(2)₁₃₆1_<138> = C138
C138 = P40 · P99
P40 = 3856127651773716445077580043028022865033_<40>
P99 = 187292093893732785337096962993710590056537036033026265546665061444636987452833698017865574966552037_<99>

Number: s138-2 N=722222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221 ( 138 digits) SNFS difficulty: 140 digits. Divisors found: r1=3856127651773716445077580043028022865033 (pp40) r2=187292093893732785337096962993710590056537036033026265546665061444636987452833698017865574966552037 (pp99) Version: Msieve-1.40 Total time: 4.39 hours. Scaled time: 8.15 units (timescale=1.855). Factorization parameters were as follows: n: 722222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221 m: 5000000000000000000000000000 deg: 5 c5: 52 c0: -275 skew: 1.40 type: snfs lss: 1 rlim: 1520000 alim: 1520000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3Factor base limits: 1520000/1520000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [760000, 1585001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 262716 x 262964 Total sieving time: 4.26 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.08 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,140.000,5,0,0,0,0,0,0,0,0,1520000,1520000,26,26,48,48,2.3,2.3,75000 total time: 4.39 hours. --------- CPU info (if available) ----------
(65·10¹⁸⁵+61)/9 = 7(2)₁₈₄9_<186> = 3 · C186
C186 = P38 · C148
P38 = 35141952992942757477971514122621284567_<38>
C148 = [6850522530409352594617032385273079677147742201520609487175172835765408849862204938465321362129623843494992872240521378843361310626504793995366334929_<148>]

Factor=35141952992942757477971514122621284567 Method=ECM B1=11000000 Sigma=2647286449
(22·10¹⁵⁰-7)/3 = 7(3)₁₄₉1_<151> = C151
C151 = P63 · P89
P63 = 557437416104319050904396406476585854891860424980271017156626667_<63>
P89 = 13155437940608153459755208722920934403344534831120327715310189648982331381764859489159993_<89>

Number: s151-1 N=7333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331 ( 151 digits) SNFS difficulty: 151 digits. Divisors found: r1=557437416104319050904396406476585854891860424980271017156626667 (pp63) r2=13155437940608153459755208722920934403344534831120327715310189648982331381764859489159993 (pp89) Version: Msieve-1.40 Total time: 10.22 hours. Scaled time: 19.13 units (timescale=1.872). Factorization parameters were as follows: n: 7333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331 m: 1000000000000000000000000000000 deg: 5 c5: 22 c0: -7 skew: 0.80 type: snfs lss: 1 rlim: 2300000 alim: 2300000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1150000, 1750001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 352545 x 352780 Total sieving time: 9.85 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.15 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,151.000,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000 total time: 10.22 hours. --------- CPU info (if available) ----------
(65·10¹⁶³-11)/9 = 7(2)₁₆₂1_<164> = C164
C164 = P42 · P47 · P77
P42 = 382159282100879841810432048201209139152111_<42>
P47 = 12134760941028933954849302273360311799514764407_<47>
P77 = 15573822111719989074008727773441965485234326451554657360445839721618992013973_<77>

Number: 164-3 N=72222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221 ( 164 digits) SNFS difficulty: 165 digits. Divisors found: r1=382159282100879841810432048201209139152111 (pp42) r2=12134760941028933954849302273360311799514764407 (pp47) r3=15573822111719989074008727773441965485234326451554657360445839721618992013973 (pp77) Version: Msieve-1.40 Total time: 30.58 hours. Scaled time: 55.93 units (timescale=1.829). Factorization parameters were as follows: n: 72222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221 m: 500000000000000000000000000000000 deg: 5 c5: 104 c0: -55 skew: 0.88 type: snfs lss: 1 rlim: 4000000 alim: 4000000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [2000000, 3700001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 743661 x 743886 Total sieving time: 29.67 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.68 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: snfs,165.000,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,51,51,2.4,2.4,100000 total time: 30.58 hours. --------- CPU info (if available) ----------
Oct 28, 2009 (7th): By Sinkiti Sibata / Msieve, GGNFS / Oct 28, 2009
(65·10¹⁴⁸-11)/9 = 7(2)₁₄₇1_<149> = 821 · 15121 · 434867 · 2659663 · 4831786039_<10> · 5683466138107710514513519_<25> · C96
C96 = P39 · P57
P39 = 939723580029040882857358260430399230301_<39>
P57 = 194913992192781453472395092670134360915528563343150609321_<57>

Tue Oct 27 22:38:26 2009 Msieve v. 1.42 Tue Oct 27 22:38:26 2009 random seeds: a4cc6856 2144dfb9 Tue Oct 27 22:38:26 2009 factoring 183165274541153112029213156380438260588196891503607577322934423409998681788864687052077556235621 (96 digits) Tue Oct 27 22:38:28 2009 no P-1/P+1/ECM available, skipping Tue Oct 27 22:38:28 2009 commencing quadratic sieve (96-digit input) Tue Oct 27 22:38:28 2009 using multiplier of 5 Tue Oct 27 22:38:28 2009 using 64kb Pentium 4 sieve core Tue Oct 27 22:38:28 2009 sieve interval: 18 blocks of size 65536 Tue Oct 27 22:38:28 2009 processing polynomials in batches of 6 Tue Oct 27 22:38:28 2009 using a sieve bound of 2231357 (82234 primes) Tue Oct 27 22:38:28 2009 using large prime bound of 334703550 (28 bits) Tue Oct 27 22:38:28 2009 using double large prime bound of 2209980934643550 (43-51 bits) Tue Oct 27 22:38:28 2009 using trial factoring cutoff of 51 bits Tue Oct 27 22:38:28 2009 polynomial 'A' values have 12 factors Wed Oct 28 06:29:56 2009 82388 relations (19397 full + 62991 combined from 1246766 partial), need 82330 Wed Oct 28 06:30:01 2009 begin with 1266163 relations Wed Oct 28 06:30:02 2009 reduce to 217857 relations in 11 passes Wed Oct 28 06:30:03 2009 attempting to read 217857 relations Wed Oct 28 06:30:10 2009 recovered 217857 relations Wed Oct 28 06:30:10 2009 recovered 205011 polynomials Wed Oct 28 06:30:10 2009 attempting to build 82388 cycles Wed Oct 28 06:30:10 2009 found 82388 cycles in 6 passes Wed Oct 28 06:30:10 2009 distribution of cycle lengths: Wed Oct 28 06:30:10 2009 length 1 : 19397 Wed Oct 28 06:30:10 2009 length 2 : 13993 Wed Oct 28 06:30:10 2009 length 3 : 13942 Wed Oct 28 06:30:10 2009 length 4 : 11324 Wed Oct 28 06:30:10 2009 length 5 : 8561 Wed Oct 28 06:30:10 2009 length 6 : 5904 Wed Oct 28 06:30:10 2009 length 7 : 3771 Wed Oct 28 06:30:10 2009 length 9+: 5496 Wed Oct 28 06:30:10 2009 largest cycle: 21 relations Wed Oct 28 06:30:11 2009 matrix is 82234 x 82388 (22.9 MB) with weight 5663813 (68.75/col) Wed Oct 28 06:30:11 2009 sparse part has weight 5663813 (68.75/col) Wed Oct 28 06:30:13 2009 filtering completed in 3 passes Wed Oct 28 06:30:13 2009 matrix is 78854 x 78918 (22.0 MB) with weight 5462402 (69.22/col) Wed Oct 28 06:30:13 2009 sparse part has weight 5462402 (69.22/col) Wed Oct 28 06:30:13 2009 saving the first 48 matrix rows for later Wed Oct 28 06:30:14 2009 matrix is 78806 x 78918 (15.6 MB) with weight 4513875 (57.20/col) Wed Oct 28 06:30:14 2009 sparse part has weight 3618396 (45.85/col) Wed Oct 28 06:30:14 2009 matrix includes 64 packed rows Wed Oct 28 06:30:14 2009 using block size 21845 for processor cache size 512 kB Wed Oct 28 06:30:15 2009 commencing Lanczos iteration Wed Oct 28 06:30:15 2009 memory use: 14.7 MB Wed Oct 28 06:31:23 2009 lanczos halted after 1248 iterations (dim = 78806) Wed Oct 28 06:31:24 2009 recovered 18 nontrivial dependencies Wed Oct 28 06:31:26 2009 prp39 factor: 939723580029040882857358260430399230301 Wed Oct 28 06:31:26 2009 prp57 factor: 194913992192781453472395092670134360915528563343150609321 Wed Oct 28 06:31:26 2009 elapsed time 07:53:00
(62·10¹⁴¹-71)/9 = 6(8)₁₄₀1_<142> = 7 · 965308026157_<12> · 39824757917563793_<17> · C113
C113 = P47 · P66
P47 = 67396829659826934567187683042527026494165158749_<47>
P66 = 379832927230764651413352296349336303801716583716324523571650614767_<66>

Number: 68881_141 N=25599535095765284772907421390742729405999308114306671311586277227479931833907608502472969991698711464297998646483 ( 113 digits) SNFS difficulty: 143 digits. Divisors found: r1=67396829659826934567187683042527026494165158749 (pp47) r2=379832927230764651413352296349336303801716583716324523571650614767 (pp66) Version: GGNFS-0.77.1-20060513-k8 Total time: 15.56 hours. Scaled time: 30.54 units (timescale=1.963). Factorization parameters were as follows: name: 68881_141 n: 25599535095765284772907421390742729405999308114306671311586277227479931833907608502472969991698711464297998646483 m: 20000000000000000000000000000 deg: 5 c5: 155 c0: -568 skew: 1.30 type: snfs lss: 1 rlim: 1740000 alim: 1740000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1740000/1740000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [870000, 2170001) Primes: RFBsize:130902, AFBsize:130802, largePrimes:3951723 encountered Relations: rels:4084666, finalFF:353287 Max relations in full relation-set: 28 Initial matrix: 261771 x 353287 with sparse part having weight 36947158. Pruned matrix : 232903 x 234275 with weight 21833316. Total sieving time: 14.65 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.68 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,143,5,0,0,0,0,0,0,0,0,1740000,1740000,26,26,48,48,2.3,2.3,100000 total time: 15.56 hours. --------- CPU info (if available) ----------
(22·10¹²⁰-7)/3 = 7(3)₁₁₉1_<121> = 23 · 5569172379466719569647_<22> · C98
C98 = P38 · P61
P38 = 12467268040968644200593760852105178561_<38>
P61 = 4592103128437975144998245779741025244221395688765409799392491_<61>

Number: 73331_120 N=57250980574006896711440906216273061639096909115796536426296321791734696445274584207837732877585451 ( 98 digits) SNFS difficulty: 121 digits. Divisors found: r1=12467268040968644200593760852105178561 (pp38) r2=4592103128437975144998245779741025244221395688765409799392491 (pp61) Version: GGNFS-0.77.1-20060513-k8 Total time: 1.72 hours. Scaled time: 3.40 units (timescale=1.981). Factorization parameters were as follows: name: 73331_120 n: 57250980574006896711440906216273061639096909115796536426296321791734696445274584207837732877585451 m: 1000000000000000000000000 deg: 5 c5: 22 c0: -7 skew: 0.80 type: snfs lss: 1 rlim: 740000 alim: 740000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 740000/740000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [370000, 520001) Primes: RFBsize:59531, AFBsize:59739, largePrimes:1304416 encountered Relations: rels:1281725, finalFF:153417 Max relations in full relation-set: 28 Initial matrix: 119336 x 153417 with sparse part having weight 6853124. Pruned matrix : 101139 x 101799 with weight 3462450. Total sieving time: 1.62 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.03 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,121,5,0,0,0,0,0,0,0,0,740000,740000,25,25,46,46,2.2,2.2,50000 total time: 1.72 hours. --------- CPU info (if available) ----------
(65·10¹¹⁴-11)/9 = 7(2)₁₁₃1_<115> = 3² · 233 · 409 · 558040613659747_<15> · C95
C95 = P39 · P56
P39 = 160981721112651612109794172448162077483_<39>
P56 = 93736068617683451547390765327106178850798232594071318277_<56>

Wed Oct 28 07:53:02 2009 Msieve v. 1.42 Wed Oct 28 07:53:02 2009 random seeds: 2df2b7a0 fd14a991 Wed Oct 28 07:53:02 2009 factoring 15089793656408292305935405066824835096685463605339172081455823016898078435395327872084828056791 (95 digits) Wed Oct 28 07:53:04 2009 no P-1/P+1/ECM available, skipping Wed Oct 28 07:53:04 2009 commencing quadratic sieve (95-digit input) Wed Oct 28 07:53:04 2009 using multiplier of 1 Wed Oct 28 07:53:04 2009 using 64kb Pentium 4 sieve core Wed Oct 28 07:53:04 2009 sieve interval: 18 blocks of size 65536 Wed Oct 28 07:53:04 2009 processing polynomials in batches of 6 Wed Oct 28 07:53:04 2009 using a sieve bound of 2083057 (77647 primes) Wed Oct 28 07:53:04 2009 using large prime bound of 295794094 (28 bits) Wed Oct 28 07:53:04 2009 using double large prime bound of 1769216945767030 (42-51 bits) Wed Oct 28 07:53:04 2009 using trial factoring cutoff of 51 bits Wed Oct 28 07:53:04 2009 polynomial 'A' values have 12 factors Wed Oct 28 12:47:27 2009 77846 relations (19670 full + 58176 combined from 1126255 partial), need 77743 Wed Oct 28 12:47:32 2009 begin with 1145925 relations Wed Oct 28 12:47:33 2009 reduce to 200673 relations in 12 passes Wed Oct 28 12:47:33 2009 attempting to read 200673 relations Wed Oct 28 12:47:39 2009 recovered 200673 relations Wed Oct 28 12:47:40 2009 recovered 182034 polynomials Wed Oct 28 12:47:40 2009 attempting to build 77846 cycles Wed Oct 28 12:47:40 2009 found 77846 cycles in 5 passes Wed Oct 28 12:47:40 2009 distribution of cycle lengths: Wed Oct 28 12:47:40 2009 length 1 : 19670 Wed Oct 28 12:47:40 2009 length 2 : 13856 Wed Oct 28 12:47:40 2009 length 3 : 13168 Wed Oct 28 12:47:40 2009 length 4 : 10392 Wed Oct 28 12:47:40 2009 length 5 : 7815 Wed Oct 28 12:47:40 2009 length 6 : 5267 Wed Oct 28 12:47:40 2009 length 7 : 3239 Wed Oct 28 12:47:40 2009 length 9+: 4439 Wed Oct 28 12:47:40 2009 largest cycle: 22 relations Wed Oct 28 12:47:40 2009 matrix is 77647 x 77846 (20.2 MB) with weight 4991551 (64.12/col) Wed Oct 28 12:47:40 2009 sparse part has weight 4991551 (64.12/col) Wed Oct 28 12:47:42 2009 filtering completed in 3 passes Wed Oct 28 12:47:42 2009 matrix is 73601 x 73665 (19.3 MB) with weight 4757494 (64.58/col) Wed Oct 28 12:47:42 2009 sparse part has weight 4757494 (64.58/col) Wed Oct 28 12:47:43 2009 saving the first 48 matrix rows for later Wed Oct 28 12:47:43 2009 matrix is 73553 x 73665 (12.1 MB) with weight 3744511 (50.83/col) Wed Oct 28 12:47:43 2009 sparse part has weight 2717431 (36.89/col) Wed Oct 28 12:47:43 2009 matrix includes 64 packed rows Wed Oct 28 12:47:43 2009 using block size 21845 for processor cache size 512 kB Wed Oct 28 12:47:44 2009 commencing Lanczos iteration Wed Oct 28 12:47:44 2009 memory use: 12.3 MB Wed Oct 28 12:48:38 2009 lanczos halted after 1165 iterations (dim = 73552) Wed Oct 28 12:48:38 2009 recovered 17 nontrivial dependencies Wed Oct 28 12:48:40 2009 prp39 factor: 160981721112651612109794172448162077483 Wed Oct 28 12:48:40 2009 prp56 factor: 93736068617683451547390765327106178850798232594071318277 Wed Oct 28 12:48:40 2009 elapsed time 04:55:38
(22·10¹³⁰-7)/3 = 7(3)₁₂₉1_<131> = 17 · 7433 · 3557979273660185577548488019_<28> · C99
C99 = P39 · P61
P39 = 134460901537550527043746602103014314371_<39>
P61 = 1213078594105218010976731081776468633605124806837098291598179_<61>

Number: 73331_130 N=163111641399291940164106253116807208918321091467924877033762537156128353415965974233879839517130409 ( 99 digits) SNFS difficulty: 131 digits. Divisors found: r1=134460901537550527043746602103014314371 (pp39) r2=1213078594105218010976731081776468633605124806837098291598179 (pp61) Version: GGNFS-0.77.1-20060513-k8 Total time: 4.02 hours. Scaled time: 7.72 units (timescale=1.919). Factorization parameters were as follows: name: 73331_130 n: 163111641399291940164106253116807208918321091467924877033762537156128353415965974233879839517130409 m: 100000000000000000000000000 deg: 5 c5: 22 c0: -7 skew: 0.80 type: snfs lss: 1 rlim: 1080000 alim: 1080000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1080000/1080000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [540000, 890001) Primes: RFBsize:84270, AFBsize:84284, largePrimes:3048064 encountered Relations: rels:3176662, finalFF:414631 Max relations in full relation-set: 28 Initial matrix: 168620 x 414631 with sparse part having weight 33226394. Pruned matrix : 113770 x 114677 with weight 7927149. Total sieving time: 3.83 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.07 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,1080000,1080000,26,26,47,47,2.3,2.3,50000 total time: 4.02 hours. --------- CPU info (if available) ----------
(65·10¹⁴⁹+7)/9 = 7(2)₁₄₈3_<150> = 3² · C149
C149 = P36 · P114
P36 = 105819244784386683109998203139936629_<36>
P114 = 758339503780763218629421606198547022990365677947048506292345087129713241005798463428316768844290881088734441938843_<114>

Number: 72223_149 N=80246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580247 ( 149 digits) SNFS difficulty: 151 digits. Divisors found: r1=105819244784386683109998203139936629 (pp36) r2=758339503780763218629421606198547022990365677947048506292345087129713241005798463428316768844290881088734441938843 (pp114) Version: Msieve-1.40 Total time: 17.34 hours. Scaled time: 34.91 units (timescale=2.013). Factorization parameters were as follows: name: 72223_149 n: 80246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580247 m: 1000000000000000000000000000000 deg: 5 c5: 13 c0: 14 skew: 1.01 type: snfs lss: 1 rlim: 2300000 alim: 2300000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1150000, 1850001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 373221 x 373469 Total sieving time: 16.65 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.49 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,151.000,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000 total time: 17.34 hours. --------- CPU info (if available) ----------
(22·10¹¹⁸-7)/3 = 7(3)₁₁₇1_<119> = 235522201 · C111
C111 = P33 · P78
P33 = 677750033164238962514135169268793_<33>
P78 = 459409558976066599817050888415589308499006600496142633440871915604917908812067_<78>

Number: 73331_118 N=311364843831997533571509606151028341202251813761426819093514387347854877312960120194076028243865355747644925131 ( 111 digits) SNFS difficulty: 120 digits. Divisors found: r1=677750033164238962514135169268793 (pp33) r2=459409558976066599817050888415589308499006600496142633440871915604917908812067 (pp78) Version: GGNFS-0.77.1-20060513-k8 Total time: 2.39 hours. Scaled time: 4.76 units (timescale=1.989). Factorization parameters were as follows: name: 73331_118 n: 311364843831997533571509606151028341202251813761426819093514387347854877312960120194076028243865355747644925131 m: 500000000000000000000000 deg: 5 c5: 176 c0: -175 skew: 1.00 type: snfs lss: 1 rlim: 720000 alim: 720000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 720000/720000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [360000, 610001) Primes: RFBsize:58029, AFBsize:57998, largePrimes:1411373 encountered Relations: rels:1434070, finalFF:193473 Max relations in full relation-set: 28 Initial matrix: 116094 x 193473 with sparse part having weight 9266838. Pruned matrix : 90589 x 91233 with weight 3277602. Total sieving time: 2.29 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.03 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,120,5,0,0,0,0,0,0,0,0,720000,720000,25,25,46,46,2.2,2.2,50000 total time: 2.39 hours. --------- CPU info (if available) ----------
(22·10¹²²-7)/3 = 7(3)₁₂₁1_<123> = 1530693038761_<13> · C111
C111 = P37 · P75
P37 = 1563778519534554459376784440862037907_<37>
P75 = 306364243034504327427694743241261865971138614286892595581588786721014964953_<75>

Number: 73331_122 N=479085822410821615351658824263053170082524325756116963166672692714955311750266379072262180668088864623762473371 ( 111 digits) SNFS difficulty: 123 digits. Divisors found: r1=1563778519534554459376784440862037907 (pp37) r2=306364243034504327427694743241261865971138614286892595581588786721014964953 (pp75) Version: GGNFS-0.77.1-20060513-k8 Total time: 3.26 hours. Scaled time: 6.24 units (timescale=1.914). Factorization parameters were as follows: name: 73331_122 n: 479085822410821615351658824263053170082524325756116963166672692714955311750266379072262180668088864623762473371 m: 2000000000000000000000000 deg: 5 c5: 275 c0: -28 skew: 0.63 type: snfs lss: 1 rlim: 810000 alim: 810000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 810000/810000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [405000, 755001) Primes: RFBsize:64683, AFBsize:64458, largePrimes:1606389 encountered Relations: rels:1722493, finalFF:278867 Max relations in full relation-set: 28 Initial matrix: 129208 x 278867 with sparse part having weight 14688172. Pruned matrix : 91624 x 92334 with weight 4159609. Total sieving time: 3.15 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.03 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,123,5,0,0,0,0,0,0,0,0,810000,810000,25,25,46,46,2.2,2.2,50000 total time: 3.26 hours. --------- CPU info (if available) ----------
(65·10¹²³+61)/9 = 7(2)₁₂₂9_<124> = 205592060411_<12> · C113
C113 = P53 · P60
P53 = 43832229960417833389559695476524062451127923298934897_<53>
P60 = 801439867065015004955353448349678622394919140325219877510687_<60>

Number: 72229_123 N=35128896552640436304237638852300777831238242048760563711369157626269703401120520531589052046752787199110834744239 ( 113 digits) SNFS difficulty: 125 digits. Divisors found: r1=43832229960417833389559695476524062451127923298934897 (pp53) r2=801439867065015004955353448349678622394919140325219877510687 (pp60) Version: Msieve-1.40 Total time: 2.23 hours. Scaled time: 4.63 units (timescale=2.078). Factorization parameters were as follows: name: 72229_123 n: 35128896552640436304237638852300777831238242048760563711369157626269703401120520531589052046752787199110834744239 m: 5000000000000000000000000 deg: 5 c5: 104 c0: 305 skew: 1.24 type: snfs lss: 1 rlim: 860000 alim: 860000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 860000/860000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [430000, 730001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 138461 x 138703 Total sieving time: 2.08 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.07 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,125.000,5,0,0,0,0,0,0,0,0,860000,860000,26,26,46,46,2.3,2.3,50000 total time: 2.23 hours. --------- CPU info (if available) ----------
(65·10¹²¹+61)/9 = 7(2)₁₂₀9_<122> = 179 · 7207 · 7309 · 801733 · 9292867 · C100
C100 = P41 · P59
P41 = 20970409353518247468689112397010047726039_<41>
P59 = 49025151298473527075633438557521717012039531437304980040413_<59>

Number: 72229_121 N=1028077491347156507372296855523252062931863952111775925648980556755371523816490127643897432972414107 ( 100 digits) SNFS difficulty: 122 digits. Divisors found: r1=20970409353518247468689112397010047726039 (pp41) r2=49025151298473527075633438557521717012039531437304980040413 (pp59) Version: GGNFS-0.77.1-20060513-k8 Total time: 3.16 hours. Scaled time: 6.05 units (timescale=1.916). Factorization parameters were as follows: name: 72229_121 n: 1028077491347156507372296855523252062931863952111775925648980556755371523816490127643897432972414107 m: 1000000000000000000000000 deg: 5 c5: 650 c0: 61 skew: 0.62 type: snfs lss: 1 rlim: 780000 alim: 780000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 780000/780000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [390000, 740001) Primes: RFBsize:62468, AFBsize:62166, largePrimes:1452590 encountered Relations: rels:1463616, finalFF:183399 Max relations in full relation-set: 28 Initial matrix: 124701 x 183399 with sparse part having weight 9655301. Pruned matrix : 106872 x 107559 with weight 4217800. Total sieving time: 3.03 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.04 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,122,5,0,0,0,0,0,0,0,0,780000,780000,25,25,46,46,2.2,2.2,50000 total time: 3.16 hours. --------- CPU info (if available) ----------
Oct 28, 2009 (6th): By Robert Backstrom / GGNFS, Msieve / Oct 28, 2009
(65·10¹¹⁶+61)/9 = 7(2)₁₁₅9_<117> = 3 · C117
C117 = P47 · P70
P47 = 34527480997338766455831224411614972334483833577_<47>
P70 = 6972438584769506590625189732568805545326881025591814765362809896626159_<70>

Number: n N=240740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740743 ( 117 digits) SNFS difficulty: 117 digits. Divisors found: Wed Oct 28 16:56:37 2009 prp47 factor: 34527480997338766455831224411614972334483833577 Wed Oct 28 16:56:37 2009 prp70 factor: 6972438584769506590625189732568805545326881025591814765362809896626159 Wed Oct 28 16:56:37 2009 elapsed time 00:02:19 (Msieve 1.43 - dependency 1) Version: GGNFS-0.77.1-20051202-athlon Total time: 1.05 hours. Scaled time: 1.92 units (timescale=1.829). Factorization parameters were as follows: name: KA_7_2_115_9 n: 240740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740743 m: 100000000000000000000000 deg: 5 c5: 650 c0: 61 skew: 0.62 type: snfs lss: 1 rlim: 640000 alim: 640000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 qintsize: 10000 Factor base limits: 640000/640000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved special-q in [320000, 561061) Primes: RFBsize:52074, AFBsize:51702, largePrimes:1210995 encountered Relations: rels:1144261, finalFF:109583 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 87777 hash collisions in 1223142 relations Msieve: matrix is 79909 x 80151 (21.9 MB) Total sieving time: 1.03 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,117,5,0,0,0,0,0,0,0,0,640000,640000,25,25,45,45,2.2,2.2,50000 total time: 1.05 hours. --------- CPU info (if available) ----------
(22·10¹²⁴-7)/3 = 7(3)₁₂₃1_<125> = 75534607 · C117
C117 = P37 · P81
P37 = 8115001058452151810981501720352816797_<37>
P81 = 119637373860289775776679722919530050967368885966201837192042266522620691868053089_<81>

Number: n N=970857415506687329866339720723420634641460878102315847533744808301356930781851202765023101706656570455623517486935933 ( 117 digits) SNFS difficulty: 126 digits. Divisors found: r1=8115001058452151810981501720352816797 (pp37) r2=119637373860289775776679722919530050967368885966201837192042266522620691868053089 (pp81) Version: GGNFS-0.77.1-20051202-athlon Total time: 1.22 hours. Scaled time: 2.22 units (timescale=1.823). Factorization parameters were as follows: name: KA_7_3_123_1 n: 970857415506687329866339720723420634641460878102315847533744808301356930781851202765023101706656570455623517486935933 m: 10000000000000000000000000 deg: 5 c5: 11 c0: -35 skew: 1.26 type: snfs lss: 1 rlim: 880000 alim: 880000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 qintsize: 10000 Factor base limits: 880000/880000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [440000, 640001) Primes: RFBsize:69823, AFBsize:69714, largePrimes:2298551 encountered Relations: rels:2160546, finalFF:174436 Max relations in full relation-set: 48 Initial matrix: 139602 x 174436 with sparse part having weight 12948806. Pruned matrix : 125159 x 125921 with weight 6476055. Total sieving time: 1.10 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.06 hours. Total square root time: 0.02 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,126,5,0,0,0,0,0,0,0,0,880000,880000,26,26,46,46,2.3,2.3,50000 total time: 1.22 hours. --------- CPU info (if available) ----------
Oct 28, 2009 (5th): By Wataru Sakai / GMP-ECM 6.2.1 / Oct 28, 2009
(65·10¹⁸⁵-11)/9 = 7(2)₁₈₄1_<186> = 3673 · 145459 · 51028247 · 523181223872965338269_<21> · 1045359163418150399691709_<25> · C125
C125 = P32 · P93
P32 = 61950651458183075429960343799297_<32>
P93 = 781871016839220677109463407665525311825701689960463807826403466950410272126295951203562513177_<93>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2064621114 Step 1 took 34199ms Step 2 took 13550ms ********** Factor found in step 2: 61950651458183075429960343799297 Found probable prime factor of 32 digits: 61950651458183075429960343799297 Probable prime cofactor 781871016839220677109463407665525311825701689960463807826403466950410272126295951203562513177 has 93 digits
(65·10¹⁹⁴+7)/9 = 7(2)₁₉₃3_<195> = 3⁴ · 7884797231020992193_<19> · 2877176822753658311521667_<25> · C150
C150 = P37 · C113
P37 = 7624190601160779016659090250310483321_<37>
C113 = [51550751522675018522266287786788814275048077732851829746459474778039978537603238494488272159493076802130222223133_<113>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1441488083 Step 1 took 47275ms Step 2 took 16303ms ********** Factor found in step 2: 7624190601160779016659090250310483321 Found probable prime factor of 37 digits: 7624190601160779016659090250310483321 Composite cofactor 51550751522675018522266287786788814275048077732851829746459474778039978537603238494488272159493076802130222223133 has 113 digits
(65·10¹⁸⁴+7)/9 = 7(2)₁₈₃3_<185> = 60719 · 171726193 · 51058810193_<11> · 228486884552752127332609_<24> · C138
C138 = P38 · P101
P38 = 21849812748236144008464710337280850879_<38>
P101 = 27172525737692482212391401687104134737901694575685983842308802500321577962738259082419630105067070303_<101>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3570817345 Step 1 took 42646ms Step 2 took 14810ms ********** Factor found in step 2: 21849812748236144008464710337280850879 Found probable prime factor of 38 digits: 21849812748236144008464710337280850879 Probable prime cofactor 27172525737692482212391401687104134737901694575685983842308802500321577962738259082419630105067070303 has 101 digits
Oct 28, 2009 (4th): By Serge Batalov / Msieve / Oct 28, 2009
(65·10¹⁰²+61)/9 = 7(2)₁₀₁9_<103> = 7 · 17 · 137 · 38468687 · C92
C92 = P42 · P50
P42 = 175788552003242654918707023394121127082163_<42>
P50 = 65509663177054239063561837808654735019636969220503_<50>

SNFS difficulty: 104 digits. Divisors found: r1=175788552003242654918707023394121127082163 (pp42) r2=65509663177054239063561837808654735019636969220503 (pp50) Version: Msieve v. 1.44 SVN130 Total time: 0.26 hours. Scaled time: 0.63 units (timescale=2.400). Factorization parameters were as follows: n: 11515848832114509541969286728301648150391951381143915818708913267971130126036386168945187989 m: 50000000000000000000000000 deg: 4 c4: 52 c0: 305 skew: 1.56 type: snfs lss: 1 rlim: 390000 alim: 390000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 Factor base limits: 390000/390000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [195000, 275001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 31248 x 31496 Total sieving time: 0.25 hours. Total relation processing time: 0.01 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,104.000,4,0,0,0,0,0,0,0,0,390000,390000,25,25,44,44,2.2,2.2,10000 total time: 0.26 hours.
(22·10¹⁰⁹-7)/3 = 7(3)₁₀₈1_<110> = C110
C110 = P36 · P75
P36 = 366976113897403798134036390219247147_<36>
P75 = 199831352930603192222342071083610479760495108319628605228753948824443242873_<75>

SNFS difficulty: 111 digits. Divisors found: r1=366976113897403798134036390219247147 (pp36) r2=199831352930603192222342071083610479760495108319628605228753948824443242873 (pp75) Version: Msieve v. 1.44 SVN130 Total time: 0.46 hours. Scaled time: 1.12 units (timescale=2.400). Factorization parameters were as follows: n: 73333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331 m: 10000000000000000000000 deg: 5 c5: 11 c0: -35 skew: 1.26 type: snfs lss: 1 rlim: 500000 alim: 500000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 Factor base limits: 500000/500000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [250000, 400001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 37502 x 37737 Total sieving time: 0.44 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.01 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,111.000,5,0,0,0,0,0,0,0,0,500000,500000,25,25,44,44,2.2,2.2,50000 total time: 0.46 hours.
(65·10¹¹²-11)/9 = 7(2)₁₁₁1_<113> = 349 · 1609 · C108
C108 = P41 · P67
P41 = 70607932059021754016721120546462990586001_<41>
P67 = 1821528136121762022116250471027322875569923541409150218970043515481_<67>

SNFS difficulty: 115 digits. Divisors found: r1=70607932059021754016721120546462990586001 (pp41) r2=1821528136121762022116250471027322875569923541409150218970043515481 (pp67) Version: Msieve v. 1.44 SVN130 Total time: 0.72 hours. Scaled time: 1.73 units (timescale=2.400). Factorization parameters were as follows: n: 128614334878881902162481853012019108528535266743162515688475502629767411858122954908407796086523018305381481 m: 50000000000000000000000 deg: 5 c5: 52 c0: -275 skew: 1.40 type: snfs lss: 1 rlim: 580000 alim: 580000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 Factor base limits: 580000/580000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [362500, 612501) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 64101 x 64332 Total sieving time: 0.68 hours. Total relation processing time: 0.01 hours. Matrix solve time: 0.01 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,115.000,5,0,0,0,0,0,0,0,0,580000,580000,25,25,45,45,2.2,2.2,50000 total time: 0.72 hours.
(65·10¹²³+7)/9 = 7(2)₁₂₂3_<124> = 31 · 433341079 · C114
C114 = P47 · P68
P47 = 31760089599647095470964140303933168837398685341_<47>
P68 = 16927685203118105408193075223017693529147950521552388939439515578947_<68>

SNFS difficulty: 125 digits. Divisors found: r1=31760089599647095470964140303933168837398685341 (pp47) r2=16927685203118105408193075223017693529147950521552388939439515578947 (pp68) Version: Msieve v. 1.44 SVN130 Total time: 1.07 hours. Scaled time: 2.57 units (timescale=2.400). Factorization parameters were as follows: n: 537624798765651370372182957215632388524131277277257415040186469316725900027661524584873859219275425292106297115927 m: 5000000000000000000000000 deg: 5 c5: 104 c0: 35 skew: 0.80 type: snfs lss: 1 rlim: 860000 alim: 860000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 860000/860000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [537500, 837501) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 114687 x 114917 Total sieving time: 0.98 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.05 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,125.000,5,0,0,0,0,0,0,0,0,860000,860000,26,26,46,46,2.3,2.3,50000 total time: 1.07 hours.
(65·10¹²⁴+7)/9 = 7(2)₁₂₃3_<125> = 23627 · 122179984837067_<15> · C107
C107 = P52 · P55
P52 = 2779713843164198342229108373215405036999849001718309_<52>
P55 = 9000406178344471728392191196472373929710255397699359483_<55>

SNFS difficulty: 126 digits. Divisors found: r1=2779713843164198342229108373215405036999849001718309 (pp52) r2=9000406178344471728392191196472373929710255397699359483 (pp55) Version: Msieve v. 1.44 SVN130 Total time: 1.10 hours. Scaled time: 2.64 units (timescale=2.400). Factorization parameters were as follows: n: 25018553648044706659806696982403245276792059272573860134171871212230208677668993529533362509883455693874247 m: 10000000000000000000000000 deg: 5 c5: 13 c0: 14 skew: 1.01 type: snfs lss: 1 rlim: 890000 alim: 890000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 890000/890000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [556250, 856251) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 121199 x 121429 Total sieving time: 1.01 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.05 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,126.000,5,0,0,0,0,0,0,0,0,890000,890000,26,26,46,46,2.3,2.3,50000 total time: 1.10 hours.
Oct 28, 2009 (3rd): By Jo Yeong Uk / GMP-ECM v6.2.3, YAFU v1.10, Msieve / Oct 28, 2009
(65·10¹⁴⁵-11)/9 = 7(2)₁₄₄1_<146> = 47 · 607 · 351457 · 10203519393642125535430984893281_<32> · C105
C105 = P41 · P65
P41 = 70454049702556330053008041614724445605807_<41>
P65 = 10019732907879640889882400544847060911821000275230632388769933171_<65>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 705930760298091485229453256487302969635908437931309773233506439012655251426409443017893127773611999523997 (105 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1037193634 Step 1 took 3494ms Step 2 took 3588ms ********** Factor found in step 2: 70454049702556330053008041614724445605807 Found probable prime factor of 41 digits: 70454049702556330053008041614724445605807 Probable prime cofactor 10019732907879640889882400544847060911821000275230632388769933171 has 65 digits
(65·10¹³⁷+7)/9 = 7(2)₁₃₆3_<138> = 3 · 23 · 73 · 30871 · 1386083 · 720941959457_<12> · C112
C112 = P30 · P31 · P53
P30 = 190061403203275865525088244967_<30>
P31 = 1244841026681448907106941991207_<31>
P53 = 19644945785038727533820766473773169516200342274306591_<53>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 4647920156400974489982688051665613882176378983480078042769794813814236946086858104526358893394750640417706768879 (112 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=6061696595 Step 1 took 3495ms Step 2 took 3822ms ********** Factor found in step 2: 190061403203275865525088244967 Found probable prime factor of 30 digits: 190061403203275865525088244967 Composite cofactor 24454834480149011868325660087316764591350057434391682905368504067395322836744145337 has 83 digits 10/27/09 21:28:44 v1.10 @ 조영욱-PC, starting SIQS on c83: 24454834480149011868325660087316764591350057434391682905368504067395322836744145337 10/27/09 21:28:44 v1.10 @ 조영욱-PC, random seeds: 2880975533, 481832920 10/27/09 21:28:45 v1.10 @ 조영욱-PC, ==== sieve params ==== 10/27/09 21:28:45 v1.10 @ 조영욱-PC, n = 83 digits, 274 bits 10/27/09 21:28:45 v1.10 @ 조영욱-PC, factor base: 49771 primes (max prime = 1295131) 10/27/09 21:28:45 v1.10 @ 조영욱-PC, single large prime cutoff: 123037445 (95 * pmax) 10/27/09 21:28:45 v1.10 @ 조영욱-PC, double large prime range from 42 to 49 bits 10/27/09 21:28:45 v1.10 @ 조영욱-PC, double large prime cutoff: 364810346638489 10/27/09 21:28:45 v1.10 @ 조영욱-PC, using 14 large prime slices of factor base 10/27/09 21:28:45 v1.10 @ 조영욱-PC, buckets hold 1024 elements 10/27/09 21:28:45 v1.10 @ 조영욱-PC, sieve interval: 7 blocks of size 65536 10/27/09 21:28:45 v1.10 @ 조영욱-PC, polynomial A has ~ 10 factors 10/27/09 21:28:45 v1.10 @ 조영욱-PC, using multiplier of 1 10/27/09 21:28:45 v1.10 @ 조영욱-PC, using small prime variation correction of 18 bits 10/27/09 21:28:45 v1.10 @ 조영욱-PC, using SSE2 for trial division and x128 sieve scanning 10/27/09 21:28:45 v1.10 @ 조영욱-PC, trial factoring cutoff at 94 bits 10/27/09 21:28:45 v1.10 @ 조영욱-PC, ==== sieving started ==== 10/27/09 21:40:57 v1.10 @ 조영욱-PC, sieve time = 340.0500, relation time = 136.3560, poly_time = 255.6500 10/27/09 21:40:57 v1.10 @ 조영욱-PC, 49848 relations found: 21802 full + 28046 from 290299 partial, using 172944 polys (244 A polys) 10/27/09 21:40:57 v1.10 @ 조영욱-PC, on average, sieving found 1.80 rels/poly and 426.07 rels/sec 10/27/09 21:40:57 v1.10 @ 조영욱-PC, trial division touched 6239436 sieve locations out of 158676811776 10/27/09 21:40:57 v1.10 @ 조영욱-PC, ==== post processing stage (msieve-1.38) ==== 10/27/09 21:40:57 v1.10 @ 조영욱-PC, begin with 312101 relations 10/27/09 21:40:57 v1.10 @ 조영욱-PC, reduce to 79841 relations in 7 passes 10/27/09 21:40:58 v1.10 @ 조영욱-PC, recovered 79841 relations 10/27/09 21:40:58 v1.10 @ 조영욱-PC, recovered 63984 polynomials 10/27/09 21:40:58 v1.10 @ 조영욱-PC, attempting to build 49848 cycles 10/27/09 21:40:58 v1.10 @ 조영욱-PC, found 49848 cycles in 3 passes 10/27/09 21:40:58 v1.10 @ 조영욱-PC, distribution of cycle lengths: 10/27/09 21:40:58 v1.10 @ 조영욱-PC, length 1 : 21802 10/27/09 21:40:58 v1.10 @ 조영욱-PC, length 2 : 20836 10/27/09 21:40:58 v1.10 @ 조영욱-PC, length 3 : 5377 10/27/09 21:40:58 v1.10 @ 조영욱-PC, length 4 : 1388 10/27/09 21:40:58 v1.10 @ 조영욱-PC, length 5 : 329 10/27/09 21:40:58 v1.10 @ 조영욱-PC, length 6 : 97 10/27/09 21:40:58 v1.10 @ 조영욱-PC, length 7 : 16 10/27/09 21:40:58 v1.10 @ 조영욱-PC, length 9+: 3 10/27/09 21:40:58 v1.10 @ 조영욱-PC, largest cycle: 9 relations 10/27/09 21:40:58 v1.10 @ 조영욱-PC, matrix is 49771 x 49848 (8.2 MB) with weight 1749155 (35.09/col) 10/27/09 21:40:58 v1.10 @ 조영욱-PC, sparse part has weight 1749155 (35.09/col) 10/27/09 21:40:58 v1.10 @ 조영욱-PC, filtering completed in 3 passes 10/27/09 21:40:58 v1.10 @ 조영욱-PC, matrix is 38980 x 39042 (6.8 MB) with weight 1458401 (37.35/col) 10/27/09 21:40:58 v1.10 @ 조영욱-PC, sparse part has weight 1458401 (37.35/col) 10/27/09 21:40:58 v1.10 @ 조영욱-PC, saving the first 48 matrix rows for later 10/27/09 21:40:58 v1.10 @ 조영욱-PC, matrix is 38932 x 39042 (4.7 MB) with weight 1118471 (28.65/col) 10/27/09 21:40:58 v1.10 @ 조영욱-PC, sparse part has weight 846197 (21.67/col) 10/27/09 21:40:58 v1.10 @ 조영욱-PC, matrix includes 64 packed rows 10/27/09 21:40:58 v1.10 @ 조영욱-PC, using block size 15616 for processor cache size 4096 kB 10/27/09 21:40:58 v1.10 @ 조영욱-PC, commencing Lanczos iteration 10/27/09 21:40:58 v1.10 @ 조영욱-PC, memory use: 4.6 MB 10/27/09 21:41:03 v1.10 @ 조영욱-PC, lanczos halted after 617 iterations (dim = 38926) 10/27/09 21:41:03 v1.10 @ 조영욱-PC, recovered 13 nontrivial dependencies 10/27/09 21:41:03 v1.10 @ 조영욱-PC, prp31 = 1244841026681448907106941991207 10/27/09 21:41:03 v1.10 @ 조영욱-PC, prp53 = 19644945785038727533820766473773169516200342274306591 10/27/09 21:41:03 v1.10 @ 조영욱-PC, Lanczos elapsed time = 6.0210 seconds. 10/27/09 21:41:03 v1.10 @ 조영욱-PC, Sqrt elapsed time = 0.5150 seconds. 10/27/09 21:41:03 v1.10 @ 조영욱-PC, SIQS elapsed time = 739.0400 seconds. 10/27/09 21:41:03 v1.10 @ 조영욱-PC, 10/27/09 21:41:03 v1.10 @ 조영욱-PC,
(22·10¹⁰⁸-7)/3 = 7(3)₁₀₇1_<109> = 197 · 2311 · 315155716987_<12> · 2708183643299_<13> · C80
C80 = P33 · P48
P33 = 133878894470440665305883428582177_<33>
P48 = 140967772262343217162849205986846194637148762593_<48>

10/28/09 01:14:46 v1.10 @ 조영욱-PC, starting SIQS on c80: 18872609506443360331949072625824394175999049219789808838348481048176363964104961 10/28/09 01:14:46 v1.10 @ 조영욱-PC, random seeds: 2953276341, 473520796 10/28/09 01:14:47 v1.10 @ 조영욱-PC, ==== sieve params ==== 10/28/09 01:14:47 v1.10 @ 조영욱-PC, n = 80 digits, 264 bits 10/28/09 01:14:47 v1.10 @ 조영욱-PC, factor base: 41901 primes (max prime = 1074701) 10/28/09 01:14:47 v1.10 @ 조영욱-PC, single large prime cutoff: 91349585 (85 * pmax) 10/28/09 01:14:47 v1.10 @ 조영욱-PC, using 13 large prime slices of factor base 10/28/09 01:14:47 v1.10 @ 조영욱-PC, buckets hold 1024 elements 10/28/09 01:14:47 v1.10 @ 조영욱-PC, sieve interval: 5 blocks of size 65536 10/28/09 01:14:47 v1.10 @ 조영욱-PC, polynomial A has ~ 10 factors 10/28/09 01:14:47 v1.10 @ 조영욱-PC, using multiplier of 1 10/28/09 01:14:47 v1.10 @ 조영욱-PC, using small prime variation correction of 17 bits 10/28/09 01:14:47 v1.10 @ 조영욱-PC, using SSE2 for trial division and x64 sieve scanning 10/28/09 01:14:47 v1.10 @ 조영욱-PC, trial factoring cutoff at 95 bits 10/28/09 01:14:47 v1.10 @ 조영욱-PC, ==== sieving started ==== 10/28/09 01:21:38 v1.10 @ 조영욱-PC, sieve time = 193.1750, relation time = 50.4470, poly_time = 167.9450 10/28/09 01:21:38 v1.10 @ 조영욱-PC, 42077 relations found: 21186 full + 20891 from 219340 partial, using 140092 polys (274 A polys) 10/28/09 01:21:38 v1.10 @ 조영욱-PC, on average, sieving found 1.72 rels/poly and 583.88 rels/sec 10/28/09 01:21:38 v1.10 @ 조영욱-PC, trial division touched 2486400 sieve locations out of 91810693120 10/28/09 01:21:38 v1.10 @ 조영욱-PC, ==== post processing stage (msieve-1.38) ==== 10/28/09 01:21:38 v1.10 @ 조영욱-PC, begin with 240526 relations 10/28/09 01:21:38 v1.10 @ 조영욱-PC, reduce to 60274 relations in 2 passes 10/28/09 01:21:39 v1.10 @ 조영욱-PC, recovered 60274 relations 10/28/09 01:21:39 v1.10 @ 조영욱-PC, recovered 49064 polynomials 10/28/09 01:21:39 v1.10 @ 조영욱-PC, attempting to build 42077 cycles 10/28/09 01:21:39 v1.10 @ 조영욱-PC, found 42077 cycles in 1 passes 10/28/09 01:21:39 v1.10 @ 조영욱-PC, distribution of cycle lengths: 10/28/09 01:21:39 v1.10 @ 조영욱-PC, length 1 : 21186 10/28/09 01:21:39 v1.10 @ 조영욱-PC, length 2 : 20891 10/28/09 01:21:39 v1.10 @ 조영욱-PC, largest cycle: 2 relations 10/28/09 01:21:39 v1.10 @ 조영욱-PC, matrix is 41901 x 42077 (6.1 MB) with weight 1266037 (30.09/col) 10/28/09 01:21:39 v1.10 @ 조영욱-PC, sparse part has weight 1266037 (30.09/col) 10/28/09 01:21:39 v1.10 @ 조영욱-PC, filtering completed in 4 passes 10/28/09 01:21:39 v1.10 @ 조영욱-PC, matrix is 30689 x 30753 (4.9 MB) with weight 1028952 (33.46/col) 10/28/09 01:21:39 v1.10 @ 조영욱-PC, sparse part has weight 1028952 (33.46/col) 10/28/09 01:21:39 v1.10 @ 조영욱-PC, saving the first 48 matrix rows for later 10/28/09 01:21:39 v1.10 @ 조영욱-PC, matrix is 30641 x 30753 (3.6 MB) with weight 811519 (26.39/col) 10/28/09 01:21:39 v1.10 @ 조영욱-PC, sparse part has weight 632898 (20.58/col) 10/28/09 01:21:39 v1.10 @ 조영욱-PC, matrix includes 64 packed rows 10/28/09 01:21:39 v1.10 @ 조영욱-PC, using block size 12301 for processor cache size 4096 kB 10/28/09 01:21:39 v1.10 @ 조영욱-PC, commencing Lanczos iteration 10/28/09 01:21:39 v1.10 @ 조영욱-PC, memory use: 3.5 MB 10/28/09 01:21:42 v1.10 @ 조영욱-PC, lanczos halted after 486 iterations (dim = 30639) 10/28/09 01:21:42 v1.10 @ 조영욱-PC, recovered 15 nontrivial dependencies 10/28/09 01:21:42 v1.10 @ 조영욱-PC, prp48 = 140967772262343217162849205986846194637148762593 10/28/09 01:21:43 v1.10 @ 조영욱-PC, prp33 = 133878894470440665305883428582177 10/28/09 01:21:43 v1.10 @ 조영욱-PC, Lanczos elapsed time = 3.7600 seconds. 10/28/09 01:21:43 v1.10 @ 조영욱-PC, Sqrt elapsed time = 0.7330 seconds. 10/28/09 01:21:43 v1.10 @ 조영욱-PC, SIQS elapsed time = 416.4350 seconds. 10/28/09 01:21:43 v1.10 @ 조영욱-PC, 10/28/09 01:21:43 v1.10 @ 조영욱-PC,
(65·10¹⁸⁴-11)/9 = 7(2)₁₈₃1_<185> = 691 · 219621875269_<12> · 2157276602733659502141754392473_<31> · 1366875469678489414121668461325082477_<37> · C105
C105 = P34 · P71
P34 = 4503477033199215094729890033147187_<34>
P71 = 35837232906713279419812768310828169169378234147431171772663813102526637_<71>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 161392155328794403131606385552815547402281189086153913445436817927538091137682507550470946122430609120119 (105 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4945725169 Step 1 took 3478ms Step 2 took 3698ms ********** Factor found in step 2: 4503477033199215094729890033147187 Found probable prime factor of 34 digits: 4503477033199215094729890033147187 Probable prime cofactor 35837232906713279419812768310828169169378234147431171772663813102526637 has 71 digits
(59·10¹⁵³+13)/9 = 6(5)₁₅₂7_<154> = 61 · 14431 · 448464904859558179943943527591218691_<36> · C113
C113 = P34 · P79
P34 = 1945389686705257859216885747713751_<34>
P79 = 8535877402069090294321958359979736349858550365095150663138218416934201553637547_<79>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 16605607864965677941097681100617903499359254644723048816511846628405008244182350794304630346346316241452961808797 (113 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2517939697 Step 1 took 3448ms Step 2 took 3775ms ********** Factor found in step 2: 1945389686705257859216885747713751 Found probable prime factor of 34 digits: 1945389686705257859216885747713751 Probable prime cofactor 8535877402069090294321958359979736349858550365095150663138218416934201553637547 has 79 digits
Oct 28, 2009 (2nd): By Erik Branger / GGNFS, Msieve, YAFU / Oct 28, 2009
(65·10¹³⁸+7)/9 = 7(2)₁₃₇3_<139> = 31 · 229 · 33461 · 1259007165190111865378078821_<28> · C104
C104 = P51 · P54
P51 = 241431719926832113054176853658594117687436004218661_<51>
P54 = 100025844120941294664361239378525121327867816498537297_<54>

Number: 72223_138 N=24149411583252065135541995261870948312801057540026010846855723972400408737150851077914404918027851899317 ( 104 digits) SNFS difficulty: 140 digits. Divisors found: r1=241431719926832113054176853658594117687436004218661 (pp51) r2=100025844120941294664361239378525121327867816498537297 (pp54) Version: Msieve-1.40 Total time: 5.45 hours. Scaled time: 5.30 units (timescale=0.971). Factorization parameters were as follows: n: 24149411583252065135541995261870948312801057540026010846855723972400408737150851077914404918027851899317 m: 5000000000000000000000000000 deg: 5 c5: 104 c0: 35 skew: 0.80 type: snfs lss: 1 rlim: 1540000 alim: 1540000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1540000/1540000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [770000, 1570001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 229296 x 229521 Total sieving time: 5.25 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.13 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,140.000,5,0,0,0,0,0,0,0,0,1540000,1540000,26,26,48,48,2.3,2.3,100000 total time: 5.45 hours. --------- CPU info (if available) ----------
(65·10¹⁰⁴+61)/9 = 7(2)₁₀₃9_<105> = 3 · 743 · 4139 · 158017 · 318523367 · C85
C85 = P38 · P47
P38 = 40936918812214106518239018554059251721_<38>
P47 = 37993131474820395090146307173650064397787555261_<47>

10/27/09 17:32:06 v1.12 @ ERIK-DATOR, starting SIQS on c85: 1555321738606498913184153860786756010560527305346283314428864765623009053835596854181 10/27/09 17:32:06 v1.12 @ ERIK-DATOR, random seeds: 3962589134, 1153892920 10/27/09 17:32:06 v1.12 @ ERIK-DATOR, ==== sieve params ==== 10/27/09 17:32:06 v1.12 @ ERIK-DATOR, n = 85 digits, 280 bits 10/27/09 17:32:06 v1.12 @ ERIK-DATOR, factor base: 54371 primes (max prime = 1426717) 10/27/09 17:32:06 v1.12 @ ERIK-DATOR, single large prime cutoff: 135538115 (95 * pmax) 10/27/09 17:32:06 v1.12 @ ERIK-DATOR, double large prime range from 42 to 49 bits 10/27/09 17:32:06 v1.12 @ ERIK-DATOR, double large prime cutoff: 434220771349436 10/27/09 17:32:06 v1.12 @ ERIK-DATOR, using 0 large prime slices of factor base 10/27/09 17:32:06 v1.12 @ ERIK-DATOR, buckets hold 1024 elements 10/27/09 17:32:06 v1.12 @ ERIK-DATOR, sieve interval: 14 blocks of size 32768 10/27/09 17:32:06 v1.12 @ ERIK-DATOR, polynomial A has ~ -1878638032 factors 10/27/09 17:32:06 v1.12 @ ERIK-DATOR, using multiplier of 1 10/27/09 17:32:06 v1.12 @ ERIK-DATOR, using small prime variation correction of 19 bits 10/27/09 17:32:06 v1.12 @ ERIK-DATOR, using SSE2 for trial division and x128 sieve scanning 10/27/09 17:32:06 v1.12 @ ERIK-DATOR, trial factoring cutoff at 91 bits 10/27/09 17:32:06 v1.12 @ ERIK-DATOR, ==== sieving started ( 2 threads) ==== 10/27/09 17:45:18 v1.12 @ ERIK-DATOR, sieve time = 169.0812, relation time = 175.8406, poly_time = 323.7462 10/27/09 17:45:18 v1.12 @ ERIK-DATOR, 54712 relations found: 17242 full + 37470 from 548555 partial, using 22772460 polys (501 A polys) 10/27/09 17:45:18 v1.12 @ ERIK-DATOR, on average, sieving found 0.02 rels/poly and 714.15 rels/sec 10/27/09 17:45:18 v1.12 @ ERIK-DATOR, trial division touched 13327686 sieve locations out of 20893823139840 10/27/09 17:45:18 v1.12 @ ERIK-DATOR, ==== post processing stage (msieve-1.38) ==== 10/27/09 17:45:19 v1.12 @ ERIK-DATOR, begin with 565797 relations 10/27/09 17:45:19 v1.12 @ ERIK-DATOR, reduce to 119482 relations in 11 passes 10/27/09 17:45:24 v1.12 @ ERIK-DATOR, recovered 119482 relations 10/27/09 17:45:24 v1.12 @ ERIK-DATOR, recovered 87233 polynomials 10/27/09 17:45:24 v1.12 @ ERIK-DATOR, attempting to build 54712 cycles 10/27/09 17:45:24 v1.12 @ ERIK-DATOR, found 54712 cycles in 5 passes 10/27/09 17:45:24 v1.12 @ ERIK-DATOR, distribution of cycle lengths: 10/27/09 17:45:24 v1.12 @ ERIK-DATOR, length 1 : 17242 10/27/09 17:45:24 v1.12 @ ERIK-DATOR, length 2 : 12987 10/27/09 17:45:24 v1.12 @ ERIK-DATOR, length 3 : 10242 10/27/09 17:45:24 v1.12 @ ERIK-DATOR, length 4 : 6560 10/27/09 17:45:24 v1.12 @ ERIK-DATOR, length 5 : 3769 10/27/09 17:45:24 v1.12 @ ERIK-DATOR, length 6 : 1911 10/27/09 17:45:24 v1.12 @ ERIK-DATOR, length 7 : 1038 10/27/09 17:45:24 v1.12 @ ERIK-DATOR, length 9+: 963 10/27/09 17:45:24 v1.12 @ ERIK-DATOR, largest cycle: 16 relations 10/27/09 17:45:25 v1.12 @ ERIK-DATOR, matrix is 54371 x 54712 (11.1 MB) with weight 2693387 (49.23/col) 10/27/09 17:45:25 v1.12 @ ERIK-DATOR, sparse part has weight 2693387 (49.23/col) 10/27/09 17:45:25 v1.12 @ ERIK-DATOR, filtering completed in 3 passes 10/27/09 17:45:25 v1.12 @ ERIK-DATOR, matrix is 48327 x 48390 (10.0 MB) with weight 2415324 (49.91/col) 10/27/09 17:45:25 v1.12 @ ERIK-DATOR, sparse part has weight 2415324 (49.91/col) 10/27/09 17:45:25 v1.12 @ ERIK-DATOR, saving the first 48 matrix rows for later 10/27/09 17:45:25 v1.12 @ ERIK-DATOR, matrix is 48279 x 48390 (8.4 MB) with weight 2085580 (43.10/col) 10/27/09 17:45:25 v1.12 @ ERIK-DATOR, sparse part has weight 1899415 (39.25/col) 10/27/09 17:45:25 v1.12 @ ERIK-DATOR, matrix includes 64 packed rows 10/27/09 17:45:25 v1.12 @ ERIK-DATOR, using block size 19356 for processor cache size 2048 kB 10/27/09 17:45:26 v1.12 @ ERIK-DATOR, commencing Lanczos iteration 10/27/09 17:45:26 v1.12 @ ERIK-DATOR, memory use: 7.5 MB 10/27/09 17:45:42 v1.12 @ ERIK-DATOR, lanczos halted after 764 iterations (dim = 48277) 10/27/09 17:45:42 v1.12 @ ERIK-DATOR, recovered 15 nontrivial dependencies 10/27/09 17:45:43 v1.12 @ ERIK-DATOR, prp38 = 40936918812214106518239018554059251721 10/27/09 17:45:50 v1.12 @ ERIK-DATOR, Lanczos elapsed time = 23.2130 seconds. 10/27/09 17:45:50 v1.12 @ ERIK-DATOR, Sqrt elapsed time = 8.6580 seconds. 10/27/09 17:45:50 v1.12 @ ERIK-DATOR, SIQS elapsed time = 824.1340 seconds.
(65·10¹⁰⁷+61)/9 = 7(2)₁₀₆9_<108> = 3 · 23 · C107
C107 = P47 · P60
P47 = 79042814270215615286909496928517614545370473299_<47>
P60 = 132421761857768186465514068388207008726242724827202973362059_<60>

Number: 72229_107 N=10466988727858293075684380032206119162640901771336553945249597423510466988727858293075684380032206119162641 ( 107 digits) SNFS difficulty: 110 digits. Divisors found: r1=79042814270215615286909496928517614545370473299 (pp47) r2=132421761857768186465514068388207008726242724827202973362059 (pp60) Version: Msieve-1.40 Total time: 0.81 hours. Scaled time: 0.81 units (timescale=1.005). Factorization parameters were as follows: n: 10466988727858293075684380032206119162640901771336553945249597423510466988727858293075684380032206119162641 m: 5000000000000000000000 deg: 5 c5: 52 c0: 1525 skew: 1.97 type: snfs lss: 1 rlim: 480000 alim: 480000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 Factor base limits: 480000/480000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [240000, 390001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 46369 x 46594 Total sieving time: 0.79 hours. Total relation processing time: 0.01 hours. Matrix solve time: 0.01 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,110.000,5,0,0,0,0,0,0,0,0,480000,480000,25,25,44,44,2.2,2.2,50000 total time: 0.81 hours. --------- CPU info (if available) ----------
(65·10¹³⁵-11)/9 = 7(2)₁₃₄1_<136> = 3 · 19 · 8053 · 180391 · 10080019 · C118
C118 = P47 · P72
P47 = 47143046448625917952027767536030904815495237561_<47>
P72 = 183545791821273701961220689454604108763314382917801245535477001041814229_<72>

Number: 72221_135 N=8652907789280129252198822257687729096160252806243514414209614921213401995731190366456215067084773588979155172785055469 ( 118 digits) SNFS difficulty: 136 digits. Divisors found: r1=47143046448625917952027767536030904815495237561 (pp47) r2=183545791821273701961220689454604108763314382917801245535477001041814229 (pp72) Version: Msieve v. 1.43 Total time: 6.58 hours. Scaled time: 5.15 units (timescale=0.782). Factorization parameters were as follows: n: 8652907789280129252198822257687729096160252806243514414209614921213401995731190366456215067084773588979155172785055469 m: 1000000000000000000000000000 deg: 5 c5: 65 c0: -11 skew: 0.70 type: snfs lss: 1 rlim: 1330000 alim: 1330000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1330000/1330000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [665000, 1190001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 201818 x 202043 Total sieving time: 5.65 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.21 hours. Time per square root: 0.61 hours. Prototype def-par.txt line would be: snfs,136.000,5,0,0,0,0,0,0,0,0,1330000,1330000,26,26,48,48,2.3,2.3,75000 total time: 6.58 hours. --------- CPU info (if available) ----------
(65·10¹¹¹+61)/9 = 7(2)₁₁₀9_<112> = C112
C112 = P32 · P32 · P50
P32 = 14428621383131545651735579585663_<32>
P32 = 18758370112130867494247173697377_<32>
P50 = 26683998610560713798271832980145381354268977407179_<50>

Number: 72229_111 N=7222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222229 ( 112 digits) SNFS difficulty: 112 digits. Divisors found: r1=14428621383131545651735579585663 (pp32) r2=18758370112130867494247173697377 (pp32) r3=26683998610560713798271832980145381354268977407179 (pp50) Version: Msieve-1.40 Total time: 1.11 hours. Scaled time: 1.06 units (timescale=0.954). Factorization parameters were as follows: n: 7222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222229 m: 10000000000000000000000 deg: 5 c5: 650 c0: 61 skew: 0.62 type: snfs lss: 1 rlim: 530000 alim: 530000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 Factor base limits: 530000/530000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [265000, 465001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 57157 x 57383 Total sieving time: 1.07 hours. Total relation processing time: 0.01 hours. Matrix solve time: 0.01 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,112.000,5,0,0,0,0,0,0,0,0,530000,530000,25,25,45,45,2.2,2.2,50000 total time: 1.11 hours. --------- CPU info (if available) ----------
(22·10¹¹⁷-7)/3 = 7(3)₁₁₆1_<118> = 131 · 2340703 · 874029479 · C101
C101 = P32 · P69
P32 = 73599418399459784738905045672909_<32>
P69 = 371777716502150259894247513418601899164271481551734543209609930979997_<69>

Number: 73331_117 N=27362623708437501481435967480647416522582967037243405954798475215929239453117920160504986430683801273 ( 101 digits) SNFS difficulty: 118 digits. Divisors found: r1=73599418399459784738905045672909 (pp32) r2=371777716502150259894247513418601899164271481551734543209609930979997 (pp69) Version: Msieve-1.40 Total time: 1.12 hours. Scaled time: 1.10 units (timescale=0.985). Factorization parameters were as follows: n: 27362623708437501481435967480647416522582967037243405954798475215929239453117920160504986430683801273 m: 200000000000000000000000 deg: 5 c5: 275 c0: -28 skew: 0.63 type: snfs lss: 1 rlim: 670000 alim: 670000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 Factor base limits: 670000/670000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [335000, 535001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 79136 x 79384 Total sieving time: 1.08 hours. Total relation processing time: 0.01 hours. Matrix solve time: 0.02 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,118.000,5,0,0,0,0,0,0,0,0,670000,670000,25,25,45,45,2.2,2.2,50000 total time: 1.12 hours. --------- CPU info (if available) ----------
(65·10¹¹⁵+61)/9 = 7(2)₁₁₄9_<116> = 205397 · C111
C111 = P42 · P70
P42 = 328435207543886906309884067988371073769559_<42>
P70 = 1070599521074343091789542842721123619754026479476702613661538459978023_<70>

Number: 72229_115 N=351622575900437797154886498937288384067061457675731496673379953077319640609269961207915511045547024650906401857 ( 111 digits) SNFS difficulty: 116 digits. Divisors found: r1=328435207543886906309884067988371073769559 (pp42) r2=1070599521074343091789542842721123619754026479476702613661538459978023 (pp70) Version: Msieve v. 1.43 Total time: 2.15 hours. Scaled time: 1.69 units (timescale=0.786). Factorization parameters were as follows: n: 351622575900437797154886498937288384067061457675731496673379953077319640609269961207915511045547024650906401857 m: 100000000000000000000000 deg: 5 c5: 65 c0: 61 skew: 0.99 type: snfs lss: 1 rlim: 620000 alim: 620000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 Factor base limits: 620000/620000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [310000, 560001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 71961 x 72186 Total sieving time: 2.09 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.03 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,116.000,5,0,0,0,0,0,0,0,0,620000,620000,25,25,45,45,2.2,2.2,50000 total time: 2.15 hours. --------- CPU info (if available) ----------
(65·10¹¹⁷+61)/9 = 7(2)₁₁₆9_<118> = 47 · 55405520323687_<14> · C103
C103 = P38 · P65
P38 = 42093341119931891329454249457027079313_<38>
P65 = 65888034547824796575698532984997713657408166425194274082537404797_<65>

Number: 72229_117 N=2773447513943446569817561422303395282509228786333955391050715933373497446320373021357915263447705664461 ( 103 digits) SNFS difficulty: 120 digits. Divisors found: r1=42093341119931891329454249457027079313 (pp38) r2=65888034547824796575698532984997713657408166425194274082537404797 (pp65) Version: Msieve-1.40 Total time: 1.41 hours. Scaled time: 1.34 units (timescale=0.948). Factorization parameters were as follows: n: 2773447513943446569817561422303395282509228786333955391050715933373497446320373021357915263447705664461 m: 500000000000000000000000 deg: 5 c5: 52 c0: 1525 skew: 1.97 type: snfs lss: 1 rlim: 710000 alim: 710000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 710000/710000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [355000, 605001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 90219 x 90444 Total sieving time: 1.34 hours. Total relation processing time: 0.01 hours. Matrix solve time: 0.02 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,120.000,5,0,0,0,0,0,0,0,0,710000,710000,25,25,46,46,2.2,2.2,50000 total time: 1.41 hours. --------- CPU info (if available) ----------
Oct 28, 2009: By Lionel Debroux / GMP-ECM
Factorizations of 722...229 and Factorizations of 733...331 have been extended up to n=200. Composite numbers that appeared newly have passed 150 times ECM runs at level 35. Unknown factors have probably 30 digits or more.
Oct 27, 2009 (8th): By Robert Backstrom / Msieve, GGNFS / Oct 27, 2009
(73·10²²⁸-1)/9 = 8(1)₂₂₈_<229> = C229
C229 = P95 · P134
P95 = 82040674460345276418092109635781689113066914859498489130035782209201051170000071099537504824993_<95>
P134 = 98866948187166021079702228415749082839158698719028540432556084739146464048408908049274520025910320723752161628884636948875147203809127_<134>

Sieving ~ 240 CPU days + 203 hrs Lanczos with Msieve 1.42 Sun Oct 18 23:45:19 2009 Sun Oct 18 23:45:19 2009 Sun Oct 18 23:45:19 2009 Msieve v. 1.42 Sun Oct 18 23:45:19 2009 random seeds: 6d66a88d 9990fcd1 Sun Oct 18 23:45:19 2009 factoring 8111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 (229 digits) Sun Oct 18 23:45:21 2009 no P-1/P+1/ECM available, skipping Sun Oct 18 23:45:21 2009 commencing number field sieve (229-digit input) Sun Oct 18 23:45:21 2009 R0: -100000000000000000000000000000000000000 Sun Oct 18 23:45:21 2009 R1: 1 Sun Oct 18 23:45:21 2009 A0: -1 Sun Oct 18 23:45:21 2009 A1: 0 Sun Oct 18 23:45:21 2009 A2: 0 Sun Oct 18 23:45:21 2009 A3: 0 Sun Oct 18 23:45:21 2009 A4: 0 Sun Oct 18 23:45:21 2009 A5: 0 Sun Oct 18 23:45:21 2009 A6: 73 Sun Oct 18 23:45:21 2009 skew 1.00, size 2.476818e-11, alpha 1.224717, combined = 1.221636e-12 Sun Oct 18 23:45:21 2009 Sun Oct 18 23:45:21 2009 commencing relation filtering Sun Oct 18 23:45:21 2009 estimated available RAM is 7924.4 MB Sun Oct 18 23:45:21 2009 commencing duplicate removal, pass 1 Sun Oct 18 23:45:36 2009 error -11 reading relation 2694508 Sun Oct 18 23:45:37 2009 error -15 reading relation 2872732 Sun Oct 18 23:46:12 2009 error -11 reading relation 9214336 Sun Oct 18 23:46:56 2009 error -11 reading relation 17266893 Sun Oct 18 23:47:08 2009 error -11 reading relation 19445707 Sun Oct 18 23:47:49 2009 error -11 reading relation 26762938 Sun Oct 18 23:48:17 2009 error -11 reading relation 31897864 Sun Oct 18 23:48:20 2009 error -11 reading relation 32438426 Sun Oct 18 23:48:24 2009 error -11 reading relation 33197093 Sun Oct 18 23:48:36 2009 error -11 reading relation 35426385 Sun Oct 18 23:49:25 2009 error -11 reading relation 43496383 Sun Oct 18 23:50:28 2009 error -11 reading relation 55107936 Sun Oct 18 23:51:15 2009 error -11 reading relation 60505135 Sun Oct 18 23:51:38 2009 error -6 reading relation 64394186 Sun Oct 18 23:51:50 2009 error -11 reading relation 66647536 Sun Oct 18 23:52:00 2009 error -11 reading relation 68358255 Sun Oct 18 23:52:09 2009 error -6 reading relation 70104845 Sun Oct 18 23:52:57 2009 error -11 reading relation 78093580 Sun Oct 18 23:53:09 2009 error -11 reading relation 80154003 Sun Oct 18 23:53:26 2009 error -11 reading relation 83269566 Sun Oct 18 23:53:38 2009 error -11 reading relation 85439373 Sun Oct 18 23:53:57 2009 error -11 reading relation 88668784 Sun Oct 18 23:54:02 2009 error -11 reading relation 89540526 Sun Oct 18 23:54:06 2009 found 15179751 hash collisions in 90256777 relations Sun Oct 18 23:54:22 2009 commencing duplicate removal, pass 2 Sun Oct 18 23:55:57 2009 found 14787900 duplicates and 75468877 unique relations Sun Oct 18 23:55:57 2009 memory use: 426.4 MB Sun Oct 18 23:55:57 2009 reading ideals above 83951616 Sun Oct 18 23:55:57 2009 commencing singleton removal, initial pass Mon Oct 19 00:04:47 2009 memory use: 1193.5 MB Mon Oct 19 00:04:47 2009 reading all ideals from disk Mon Oct 19 00:04:55 2009 memory use: 1253.5 MB Mon Oct 19 00:05:02 2009 commencing in-memory singleton removal Mon Oct 19 00:05:09 2009 begin with 75468877 relations and 71429593 unique ideals Mon Oct 19 00:06:20 2009 reduce to 33368308 relations and 23102541 ideals in 19 passes Mon Oct 19 00:06:20 2009 max relations containing the same ideal: 28 Mon Oct 19 00:06:25 2009 reading ideals above 720000 Mon Oct 19 00:06:25 2009 commencing singleton removal, initial pass Mon Oct 19 00:11:51 2009 memory use: 596.8 MB Mon Oct 19 00:11:52 2009 reading all ideals from disk Mon Oct 19 00:11:59 2009 memory use: 1246.6 MB Mon Oct 19 00:12:08 2009 keeping 32677867 ideals with weight <= 200, target excess is 174639 Mon Oct 19 00:12:16 2009 commencing in-memory singleton removal Mon Oct 19 00:12:24 2009 begin with 33368308 relations and 32677867 unique ideals Mon Oct 19 00:14:33 2009 reduce to 33118187 relations and 32426869 ideals in 16 passes Mon Oct 19 00:14:33 2009 max relations containing the same ideal: 200 Mon Oct 19 00:15:09 2009 removing 2785840 relations and 2541472 ideals in 244368 cliques Mon Oct 19 00:15:10 2009 commencing in-memory singleton removal Mon Oct 19 00:15:18 2009 begin with 30332347 relations and 32426869 unique ideals Mon Oct 19 00:16:45 2009 reduce to 30140693 relations and 29691582 ideals in 12 passes Mon Oct 19 00:16:45 2009 max relations containing the same ideal: 196 Mon Oct 19 00:17:17 2009 removing 2018847 relations and 1774479 ideals in 244368 cliques Mon Oct 19 00:17:18 2009 commencing in-memory singleton removal Mon Oct 19 00:17:25 2009 begin with 28121846 relations and 29691582 unique ideals Mon Oct 19 00:18:19 2009 reduce to 28011472 relations and 27805669 ideals in 8 passes Mon Oct 19 00:18:19 2009 max relations containing the same ideal: 187 Mon Oct 19 00:18:58 2009 relations with 0 large ideals: 6501 Mon Oct 19 00:18:58 2009 relations with 1 large ideals: 1045 Mon Oct 19 00:18:58 2009 relations with 2 large ideals: 6849 Mon Oct 19 00:18:58 2009 relations with 3 large ideals: 76396 Mon Oct 19 00:18:58 2009 relations with 4 large ideals: 501001 Mon Oct 19 00:18:58 2009 relations with 5 large ideals: 1974881 Mon Oct 19 00:18:58 2009 relations with 6 large ideals: 4825536 Mon Oct 19 00:18:58 2009 relations with 7+ large ideals: 20619263 Mon Oct 19 00:18:58 2009 commencing 2-way merge Mon Oct 19 00:19:39 2009 reduce to 16924970 relation sets and 16719168 unique ideals Mon Oct 19 00:19:39 2009 ignored 1 oversize relation sets Mon Oct 19 00:19:39 2009 commencing full merge Mon Oct 19 00:27:27 2009 memory use: 2107.1 MB Mon Oct 19 00:27:30 2009 found 8999888 cycles, need 8981368 Mon Oct 19 00:27:36 2009 weight of 8981368 cycles is about 629038424 (70.04/cycle) Mon Oct 19 00:27:36 2009 distribution of cycle lengths: Mon Oct 19 00:27:36 2009 1 relations: 1407270 Mon Oct 19 00:27:36 2009 2 relations: 1249187 Mon Oct 19 00:27:36 2009 3 relations: 1131311 Mon Oct 19 00:27:36 2009 4 relations: 950440 Mon Oct 19 00:27:36 2009 5 relations: 792936 Mon Oct 19 00:27:36 2009 6 relations: 650379 Mon Oct 19 00:27:36 2009 7 relations: 540476 Mon Oct 19 00:27:36 2009 8 relations: 441114 Mon Oct 19 00:27:36 2009 9 relations: 358546 Mon Oct 19 00:27:36 2009 10+ relations: 1459709 Mon Oct 19 00:27:36 2009 heaviest cycle: 28 relations Mon Oct 19 00:27:38 2009 commencing cycle optimization Mon Oct 19 00:28:01 2009 start with 49064201 relations Mon Oct 19 00:29:42 2009 pruned 1034355 relations Mon Oct 19 00:29:42 2009 memory use: 1642.5 MB Mon Oct 19 00:29:43 2009 distribution of cycle lengths: Mon Oct 19 00:29:43 2009 1 relations: 1407270 Mon Oct 19 00:29:43 2009 2 relations: 1273515 Mon Oct 19 00:29:43 2009 3 relations: 1165835 Mon Oct 19 00:29:43 2009 4 relations: 965226 Mon Oct 19 00:29:43 2009 5 relations: 804038 Mon Oct 19 00:29:43 2009 6 relations: 654272 Mon Oct 19 00:29:43 2009 7 relations: 539463 Mon Oct 19 00:29:43 2009 8 relations: 435494 Mon Oct 19 00:29:43 2009 9 relations: 353137 Mon Oct 19 00:29:43 2009 10+ relations: 1383118 Mon Oct 19 00:29:43 2009 heaviest cycle: 28 relations Mon Oct 19 00:30:03 2009 RelProcTime: 2682 Mon Oct 19 00:30:03 2009 Mon Oct 19 00:30:03 2009 commencing linear algebra Mon Oct 19 00:30:10 2009 read 8981368 cycles Mon Oct 19 00:30:29 2009 cycles contain 27737847 unique relations Mon Oct 19 00:33:24 2009 read 27737847 relations Mon Oct 19 00:34:16 2009 using 20 quadratic characters above 1073741672 Mon Oct 19 00:36:34 2009 building initial matrix Mon Oct 19 00:42:04 2009 memory use: 3378.6 MB Mon Oct 19 00:42:10 2009 read 8981368 cycles Mon Oct 19 00:42:15 2009 matrix is 8981191 x 8981368 (2704.3 MB) with weight 782303917 (87.10/col) Mon Oct 19 00:42:15 2009 sparse part has weight 610125085 (67.93/col) Mon Oct 19 00:44:22 2009 filtering completed in 2 passes Mon Oct 19 00:44:24 2009 matrix is 8977172 x 8977349 (2704.0 MB) with weight 782193362 (87.13/col) Mon Oct 19 00:44:24 2009 sparse part has weight 610095193 (67.96/col) Mon Oct 19 00:45:05 2009 read 8977349 cycles Mon Oct 19 00:45:10 2009 matrix is 8977172 x 8977349 (2704.0 MB) with weight 782193362 (87.13/col) Mon Oct 19 00:45:10 2009 sparse part has weight 610095193 (67.96/col) Mon Oct 19 00:45:10 2009 saving the first 48 matrix rows for later Mon Oct 19 00:45:14 2009 matrix is 8977124 x 8977349 (2578.3 MB) with weight 627869172 (69.94/col) Mon Oct 19 00:45:14 2009 sparse part has weight 586117479 (65.29/col) Mon Oct 19 00:45:14 2009 matrix includes 64 packed rows Mon Oct 19 00:45:14 2009 using block size 65536 for processor cache size 6144 kB Mon Oct 19 00:45:49 2009 commencing Lanczos iteration (4 threads) Mon Oct 19 00:45:49 2009 memory use: 2813.4 MB Tue Oct 27 11:21:10 2009 lanczos halted after 141967 iterations (dim = 8977122) Tue Oct 27 11:21:29 2009 recovered 30 nontrivial dependencies Tue Oct 27 11:21:30 2009 BLanczosTime: 730287 Tue Oct 27 11:21:30 2009 Tue Oct 27 11:21:30 2009 commencing square root phase Tue Oct 27 11:21:30 2009 reading relations for dependency 1 Tue Oct 27 11:21:32 2009 read 4490596 cycles Tue Oct 27 11:21:42 2009 cycles contain 16870428 unique relations Tue Oct 27 11:23:42 2009 read 16870428 relations Tue Oct 27 11:25:27 2009 multiplying 13873600 relations Tue Oct 27 12:05:42 2009 multiply complete, coefficients have about 419.03 million bits Tue Oct 27 12:05:46 2009 initial square root is modulo 33011653 Tue Oct 27 13:04:31 2009 sqrtTime: 6181 Tue Oct 27 13:04:31 2009 prp95 factor: 82040674460345276418092109635781689113066914859498489130035782209201051170000071099537504824993 Tue Oct 27 13:04:31 2009 prp134 factor: 98866948187166021079702228415749082839158698719028540432556084739146464048408908049274520025910320723752161628884636948875147203809127 Tue Oct 27 13:04:31 2009 elapsed time 205:19:12
c229 is the largest composite number which was factored by SNFS in our tables so far. Congratulations!
(14·10¹⁷³-17)/3 = 4(6)₁₇₂1_<174> = 13 · 859 · 5998697 · 13845991 · 409103341929942277576340139824293_<33> · C124
C124 = P55 · P69
P55 = 4187044847170696975495032484814703095237037002928822757_<55>
P69 = 293730235942494492861511218837078094643977016140350496314412187630029_<69>

Number: n N=1229861670861254617548494925913918290044304120418280776400992158432398260682671962391119989681635502520909226281982831769953 ( 124 digits) Divisors found: Wed Oct 28 01:20:11 2009 prp55 factor: 4187044847170696975495032484814703095237037002928822757 Wed Oct 28 01:20:11 2009 prp69 factor: 293730235942494492861511218837078094643977016140350496314412187630029 Wed Oct 28 01:20:11 2009 elapsed time 02:55:22 (Msieve 1.43 - dependency 1) Version: GGNFS-0.77.1-20051202-athlon Total time: 24.12 hours. Scaled time: 44.11 units (timescale=1.829). Factorization parameters were as follows: name: KA_4_6_172_1 n: 1229861670861254617548494925913918290044304120418280776400992158432398260682671962391119989681635502520909226281982831769953 Y0: -679980794164857001434425 Y1: 20228359617079 c0: 574058941022120395736367581472 c1: 15189963738966010296654600 c2: -20437377482172436876 c3: -1303581716936282 c4: 1749624141 c5: 8460 skew: 186678.04 type: gnfs rlim: 5000000 alim: 5000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.4 alambda: 2.4 qintsize: 50000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [2500000, 5100269) Primes: RFBsize:348513, AFBsize:349151, largePrimes:15654479 encountered Relations: rels:14625624, finalFF:735763 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1637074 hash collisions in 15982632 relations Msieve: matrix is 846990 x 847215 (231.9 MB) Total sieving time: 23.66 hours. Total relation processing time: 0.46 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,123,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,28,28,56,56,2.4,2.4,60000 total time: 24.12 hours. --------- CPU info (if available) ----------
Oct 27, 2009 (7th): By Sinkiti Sibata / Msieve, GGNFS / Oct 27, 2009
(65·10¹⁵⁷-11)/9 = 7(2)₁₅₆1_<158> = 467 · 881 · 34893421 · 76139466457_<11> · 45062034422087_<14> · 16026975876783402520793945195297_<32> · C89
C89 = P37 · P53
P37 = 2781337945606846567176996666297459217_<37>
P53 = 32893382824650786898544395629261720525621863468742293_<53>

ue Oct 27 07:50:11 2009 Msieve v. 1.42 Tue Oct 27 07:50:11 2009 random seeds: f5d8dff7 b54d31b6 Tue Oct 27 07:50:11 2009 factoring 91487613809573751425008504937197311213425423081348495271434108401057020019688124450564581 (89 digits) Tue Oct 27 07:50:13 2009 no P-1/P+1/ECM available, skipping Tue Oct 27 07:50:13 2009 commencing quadratic sieve (89-digit input) Tue Oct 27 07:50:13 2009 using multiplier of 5 Tue Oct 27 07:50:13 2009 using 64kb Pentium 4 sieve core Tue Oct 27 07:50:13 2009 sieve interval: 17 blocks of size 65536 Tue Oct 27 07:50:13 2009 processing polynomials in batches of 6 Tue Oct 27 07:50:13 2009 using a sieve bound of 1561823 (59333 primes) Tue Oct 27 07:50:13 2009 using large prime bound of 124945840 (26 bits) Tue Oct 27 07:50:13 2009 using double large prime bound of 375058674136800 (42-49 bits) Tue Oct 27 07:50:13 2009 using trial factoring cutoff of 49 bits Tue Oct 27 07:50:13 2009 polynomial 'A' values have 11 factors Tue Oct 27 09:57:07 2009 59872 relations (15645 full + 44227 combined from 638789 partial), need 59429 Tue Oct 27 09:57:09 2009 begin with 654434 relations Tue Oct 27 09:57:10 2009 reduce to 147759 relations in 9 passes Tue Oct 27 09:57:10 2009 attempting to read 147759 relations Tue Oct 27 09:57:14 2009 recovered 147759 relations Tue Oct 27 09:57:14 2009 recovered 127871 polynomials Tue Oct 27 09:57:14 2009 attempting to build 59872 cycles Tue Oct 27 09:57:14 2009 found 59872 cycles in 6 passes Tue Oct 27 09:57:14 2009 distribution of cycle lengths: Tue Oct 27 09:57:14 2009 length 1 : 15645 Tue Oct 27 09:57:14 2009 length 2 : 11335 Tue Oct 27 09:57:14 2009 length 3 : 10329 Tue Oct 27 09:57:14 2009 length 4 : 8029 Tue Oct 27 09:57:14 2009 length 5 : 5649 Tue Oct 27 09:57:14 2009 length 6 : 3678 Tue Oct 27 09:57:14 2009 length 7 : 2279 Tue Oct 27 09:57:14 2009 length 9+: 2928 Tue Oct 27 09:57:14 2009 largest cycle: 18 relations Tue Oct 27 09:57:14 2009 matrix is 59333 x 59872 (15.0 MB) with weight 3697274 (61.75/col) Tue Oct 27 09:57:14 2009 sparse part has weight 3697274 (61.75/col) Tue Oct 27 09:57:16 2009 filtering completed in 3 passes Tue Oct 27 09:57:16 2009 matrix is 55708 x 55771 (14.0 MB) with weight 3439964 (61.68/col) Tue Oct 27 09:57:16 2009 sparse part has weight 3439964 (61.68/col) Tue Oct 27 09:57:16 2009 saving the first 48 matrix rows for later Tue Oct 27 09:57:16 2009 matrix is 55660 x 55771 (10.7 MB) with weight 2917754 (52.32/col) Tue Oct 27 09:57:16 2009 sparse part has weight 2471995 (44.32/col) Tue Oct 27 09:57:16 2009 matrix includes 64 packed rows Tue Oct 27 09:57:16 2009 using block size 21845 for processor cache size 512 kB Tue Oct 27 09:57:17 2009 commencing Lanczos iteration Tue Oct 27 09:57:17 2009 memory use: 9.9 MB Tue Oct 27 09:57:50 2009 lanczos halted after 881 iterations (dim = 55654) Tue Oct 27 09:57:50 2009 recovered 15 nontrivial dependencies Tue Oct 27 09:57:54 2009 prp37 factor: 2781337945606846567176996666297459217 Tue Oct 27 09:57:54 2009 prp53 factor: 32893382824650786898544395629261720525621863468742293 Tue Oct 27 09:57:54 2009 elapsed time 02:07:43
(62·10¹⁴³-71)/9 = 6(8)₁₄₂1_<144> = 3³ · 213480877273187_<15> · C129
C129 = P51 · P79
P51 = 103755478159889828751485057885748821715212892879557_<51>
P79 = 1151901651383832725319629282005586242558015694434569307514321563885225997402317_<79>

Number: 68881_143 N=119516106632496283665894694538282365100792261988213590436675492772858536245889750978063107224994882728409718860150351667953733569 ( 129 digits) SNFS difficulty: 146 digits. Divisors found: r1=103755478159889828751485057885748821715212892879557 (pp51) r2=1151901651383832725319629282005586242558015694434569307514321563885225997402317 (pp79) Version: GGNFS-0.77.1-20060513-k8 Total time: 21.93 hours. Scaled time: 43.67 units (timescale=1.991). Factorization parameters were as follows: name: 68881_143 n: 119516106632496283665894694538282365100792261988213590436675492772858536245889750978063107224994882728409718860150351667953733569 m: 50000000000000000000000000000 deg: 5 c5: 496 c0: -1775 skew: 1.29 type: snfs lss: 1 rlim: 1910000 alim: 1910000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1910000/1910000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [955000, 2855001) Primes: RFBsize:142718, AFBsize:142742, largePrimes:4317703 encountered Relations: rels:4561580, finalFF:361745 Max relations in full relation-set: 28 Initial matrix: 285527 x 361745 with sparse part having weight 41726282. Pruned matrix : 260885 x 262376 with weight 28387579. Total sieving time: 20.68 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.99 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1910000,1910000,26,26,49,49,2.3,2.3,100000 total time: 21.93 hours. --------- CPU info (if available) ----------
(61·10¹⁴²+11)/9 = 6(7)₁₄₁9_<143> = 3 · 33353 · 19906792880765389_<17> · C122
C122 = P34 · P88
P34 = 6333596761890210427769088539424107_<34>
P88 = 5372537550577884027041044748259697776204681547417165620095560642583786697767311429280647_<88>

Number: 67779_142 N=34027486433473648903006226725877484429114615245532918207296038291178904927843612374299078287204050202839724770542660357229 ( 122 digits) SNFS difficulty: 145 digits. Divisors found: r1=6333596761890210427769088539424107 (pp34) r2=5372537550577884027041044748259697776204681547417165620095560642583786697767311429280647 (pp88) Version: Msieve-1.40 Total time: 11.35 hours. Scaled time: 23.67 units (timescale=2.085). Factorization parameters were as follows: name: 67779_142 n: 34027486433473648903006226725877484429114615245532918207296038291178904927843612374299078287204050202839724770542660357229 m: 50000000000000000000000000000 deg: 5 c5: 244 c0: 1375 skew: 1.41 type: snfs lss: 1 rlim: 1890000 alim: 1890000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1890000/1890000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [945000, 2345001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 315046 x 315276 Total sieving time: 10.88 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.34 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,145.000,5,0,0,0,0,0,0,0,0,1890000,1890000,26,26,49,49,2.3,2.3,100000 total time: 11.35 hours. --------- CPU info (if available) ----------
(65·10¹⁰⁹-11)/9 = 7(2)₁₀₈1_<110> = 52391597 · 2542076848723_<13> · C90
C90 = P33 · P58
P33 = 137580139588561846772155174238321_<33>
P58 = 3941529571374024940821143658563287380985182879516137168171_<58>

Tue Oct 27 14:22:59 2009 Msieve v. 1.42 Tue Oct 27 14:22:59 2009 random seeds: e7404b6c 37a5d6c9 Tue Oct 27 14:22:59 2009 factoring 542276188622082695982597047253643601927608428763762474084725223935309903592111092809680891 (90 digits) Tue Oct 27 14:22:59 2009 searching for 15-digit factors Tue Oct 27 14:23:00 2009 commencing quadratic sieve (90-digit input) Tue Oct 27 14:23:00 2009 using multiplier of 1 Tue Oct 27 14:23:00 2009 using 32kb Intel Core sieve core Tue Oct 27 14:23:00 2009 sieve interval: 36 blocks of size 32768 Tue Oct 27 14:23:00 2009 processing polynomials in batches of 6 Tue Oct 27 14:23:00 2009 using a sieve bound of 1618559 (61176 primes) Tue Oct 27 14:23:00 2009 using large prime bound of 135958956 (27 bits) Tue Oct 27 14:23:00 2009 using double large prime bound of 436650541653060 (42-49 bits) Tue Oct 27 14:23:00 2009 using trial factoring cutoff of 49 bits Tue Oct 27 14:23:00 2009 polynomial 'A' values have 11 factors Tue Oct 27 15:37:19 2009 61746 relations (16189 full + 45557 combined from 673042 partial), need 61272 Tue Oct 27 15:37:20 2009 begin with 689231 relations Tue Oct 27 15:37:21 2009 reduce to 152393 relations in 13 passes Tue Oct 27 15:37:21 2009 attempting to read 152393 relations Tue Oct 27 15:37:22 2009 recovered 152393 relations Tue Oct 27 15:37:23 2009 recovered 129486 polynomials Tue Oct 27 15:37:23 2009 attempting to build 61746 cycles Tue Oct 27 15:37:23 2009 found 61746 cycles in 6 passes Tue Oct 27 15:37:23 2009 distribution of cycle lengths: Tue Oct 27 15:37:23 2009 length 1 : 16189 Tue Oct 27 15:37:23 2009 length 2 : 11482 Tue Oct 27 15:37:23 2009 length 3 : 10776 Tue Oct 27 15:37:23 2009 length 4 : 8189 Tue Oct 27 15:37:23 2009 length 5 : 6077 Tue Oct 27 15:37:23 2009 length 6 : 3830 Tue Oct 27 15:37:23 2009 length 7 : 2326 Tue Oct 27 15:37:23 2009 length 9+: 2877 Tue Oct 27 15:37:23 2009 largest cycle: 18 relations Tue Oct 27 15:37:23 2009 matrix is 61176 x 61746 (15.6 MB) with weight 3833340 (62.08/col) Tue Oct 27 15:37:23 2009 sparse part has weight 3833340 (62.08/col) Tue Oct 27 15:37:24 2009 filtering completed in 3 passes Tue Oct 27 15:37:24 2009 matrix is 57219 x 57282 (14.4 MB) with weight 3554565 (62.05/col) Tue Oct 27 15:37:24 2009 sparse part has weight 3554565 (62.05/col) Tue Oct 27 15:37:24 2009 saving the first 48 matrix rows for later Tue Oct 27 15:37:24 2009 matrix is 57171 x 57282 (10.9 MB) with weight 2991811 (52.23/col) Tue Oct 27 15:37:24 2009 sparse part has weight 2516615 (43.93/col) Tue Oct 27 15:37:24 2009 matrix includes 64 packed rows Tue Oct 27 15:37:24 2009 using block size 22912 for processor cache size 1024 kB Tue Oct 27 15:37:25 2009 commencing Lanczos iteration Tue Oct 27 15:37:25 2009 memory use: 10.1 MB Tue Oct 27 15:37:47 2009 lanczos halted after 906 iterations (dim = 57169) Tue Oct 27 15:37:47 2009 recovered 17 nontrivial dependencies Tue Oct 27 15:37:48 2009 prp33 factor: 137580139588561846772155174238321 Tue Oct 27 15:37:48 2009 prp58 factor: 3941529571374024940821143658563287380985182879516137168171 Tue Oct 27 15:37:48 2009 elapsed time 01:14:49
(65·10¹²²+7)/9 = 7(2)₁₂₁3_<123> = 3² · 103 · 241 · 1237726493_<10> · 38487393601_<11> · C98
C98 = P44 · P55
P44 = 11234321827921433174867669812024514743374959_<44>
P55 = 6040654844216834979500238535767959586811972858326905147_<55>

Number: 72223_122 N=67862660571324533702443114986666233918366106026626913499884976055568855064095612384649480248013973 ( 98 digits) SNFS difficulty: 125 digits. Divisors found: r1=11234321827921433174867669812024514743374959 (pp44) r2=6040654844216834979500238535767959586811972858326905147 (pp55) Version: GGNFS-0.77.1-20060513-k8 Total time: 2.78 hours. Scaled time: 5.49 units (timescale=1.977). Factorization parameters were as follows: name: 72223_122 n: 67862660571324533702443114986666233918366106026626913499884976055568855064095612384649480248013973 m: 5000000000000000000000000 deg: 5 c5: 52 c0: 175 skew: 1.27 type: snfs lss: 1 rlim: 850000 alim: 850000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 850000/850000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [425000, 675001) Primes: RFBsize:67617, AFBsize:67460, largePrimes:2468450 encountered Relations: rels:2389203, finalFF:214856 Max relations in full relation-set: 28 Initial matrix: 135144 x 214856 with sparse part having weight 16202448. Pruned matrix : 112573 x 113312 with weight 5963078. Total sieving time: 2.61 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,125,5,0,0,0,0,0,0,0,0,850000,850000,26,26,46,46,2.3,2.3,50000 total time: 2.78 hours. --------- CPU info (if available) ----------
(65·10¹⁶¹+7)/9 = 7(2)₁₆₀3_<162> = 3 · 73 · 4787 · 197829613 · 123623015233_<12> · 46276777179460717_<17> · 63995894158538638194695901113_<29> · C91
C91 = P40 · P52
P40 = 2848409643006055036625993604980263881331_<40>
P52 = 3339296686306871044335539412177570631478147640034229_<52>

Tue Oct 27 16:31:08 2009 Msieve v. 1.42 Tue Oct 27 16:31:08 2009 random seeds: b1198b50 756956c1 Tue Oct 27 16:31:08 2009 factoring 9511684882134657103583478171233840687877877382184865824492238380051531346401527161234078799 (91 digits) Tue Oct 27 16:31:09 2009 searching for 15-digit factors Tue Oct 27 16:31:10 2009 commencing quadratic sieve (91-digit input) Tue Oct 27 16:31:10 2009 using multiplier of 23 Tue Oct 27 16:31:10 2009 using 32kb Intel Core sieve core Tue Oct 27 16:31:10 2009 sieve interval: 36 blocks of size 32768 Tue Oct 27 16:31:10 2009 processing polynomials in batches of 6 Tue Oct 27 16:31:10 2009 using a sieve bound of 1753553 (65751 primes) Tue Oct 27 16:31:10 2009 using large prime bound of 177108853 (27 bits) Tue Oct 27 16:31:10 2009 using double large prime bound of 702801048059511 (42-50 bits) Tue Oct 27 16:31:10 2009 using trial factoring cutoff of 50 bits Tue Oct 27 16:31:10 2009 polynomial 'A' values have 12 factors Tue Oct 27 18:27:20 2009 65975 relations (16850 full + 49125 combined from 800521 partial), need 65847 Tue Oct 27 18:27:21 2009 begin with 817371 relations Tue Oct 27 18:27:22 2009 reduce to 165324 relations in 10 passes Tue Oct 27 18:27:22 2009 attempting to read 165324 relations Tue Oct 27 18:27:24 2009 recovered 165324 relations Tue Oct 27 18:27:24 2009 recovered 147877 polynomials Tue Oct 27 18:27:25 2009 attempting to build 65975 cycles Tue Oct 27 18:27:25 2009 found 65975 cycles in 6 passes Tue Oct 27 18:27:25 2009 distribution of cycle lengths: Tue Oct 27 18:27:25 2009 length 1 : 16850 Tue Oct 27 18:27:25 2009 length 2 : 12355 Tue Oct 27 18:27:25 2009 length 3 : 11631 Tue Oct 27 18:27:25 2009 length 4 : 8792 Tue Oct 27 18:27:25 2009 length 5 : 6353 Tue Oct 27 18:27:25 2009 length 6 : 4131 Tue Oct 27 18:27:25 2009 length 7 : 2598 Tue Oct 27 18:27:25 2009 length 9+: 3265 Tue Oct 27 18:27:25 2009 largest cycle: 22 relations Tue Oct 27 18:27:25 2009 matrix is 65751 x 65975 (16.1 MB) with weight 3946793 (59.82/col) Tue Oct 27 18:27:25 2009 sparse part has weight 3946793 (59.82/col) Tue Oct 27 18:27:26 2009 filtering completed in 3 passes Tue Oct 27 18:27:26 2009 matrix is 62108 x 62171 (15.2 MB) with weight 3745410 (60.24/col) Tue Oct 27 18:27:26 2009 sparse part has weight 3745410 (60.24/col) Tue Oct 27 18:27:26 2009 saving the first 48 matrix rows for later Tue Oct 27 18:27:26 2009 matrix is 62060 x 62171 (8.8 MB) with weight 2840677 (45.69/col) Tue Oct 27 18:27:26 2009 sparse part has weight 1934538 (31.12/col) Tue Oct 27 18:27:26 2009 matrix includes 64 packed rows Tue Oct 27 18:27:26 2009 using block size 24868 for processor cache size 1024 kB Tue Oct 27 18:27:27 2009 commencing Lanczos iteration Tue Oct 27 18:27:27 2009 memory use: 9.5 MB Tue Oct 27 18:27:49 2009 lanczos halted after 983 iterations (dim = 62058) Tue Oct 27 18:27:49 2009 recovered 16 nontrivial dependencies Tue Oct 27 18:27:50 2009 prp40 factor: 2848409643006055036625993604980263881331 Tue Oct 27 18:27:50 2009 prp52 factor: 3339296686306871044335539412177570631478147640034229 Tue Oct 27 18:27:50 2009 elapsed time 01:56:42
(65·10¹⁴¹-11)/9 = 7(2)₁₄₀1_<142> = 3² · 71 · 145991 · 3380926859_<10> · 12718567937_<11> · 6088571724331250328637_<22> · C93
C93 = P34 · P59
P34 = 6943388399896641031086000361099687_<34>
P59 = 42587586623151738614250628439153952183704337824580960958877_<59>

Tue Oct 27 18:51:10 2009 Msieve v. 1.42 Tue Oct 27 18:51:10 2009 random seeds: 8c180bf0 06ebb811 Tue Oct 27 18:51:10 2009 factoring 295702154938785144292115280791360472969719657708376609043932299246578073523096330409704571499 (93 digits) Tue Oct 27 18:51:11 2009 searching for 15-digit factors Tue Oct 27 18:51:11 2009 commencing quadratic sieve (93-digit input) Tue Oct 27 18:51:11 2009 using multiplier of 59 Tue Oct 27 18:51:11 2009 using 32kb Intel Core sieve core Tue Oct 27 18:51:11 2009 sieve interval: 36 blocks of size 32768 Tue Oct 27 18:51:11 2009 processing polynomials in batches of 6 Tue Oct 27 18:51:11 2009 using a sieve bound of 1914637 (71765 primes) Tue Oct 27 18:51:11 2009 using large prime bound of 231671077 (27 bits) Tue Oct 27 18:51:11 2009 using double large prime bound of 1139644007123941 (42-51 bits) Tue Oct 27 18:51:11 2009 using trial factoring cutoff of 51 bits Tue Oct 27 18:51:11 2009 polynomial 'A' values have 12 factors Tue Oct 27 21:14:42 2009 71939 relations (18409 full + 53530 combined from 952627 partial), need 71861 Tue Oct 27 21:14:43 2009 begin with 971036 relations Tue Oct 27 21:14:44 2009 reduce to 182111 relations in 11 passes Tue Oct 27 21:14:44 2009 attempting to read 182111 relations Tue Oct 27 21:14:47 2009 recovered 182111 relations Tue Oct 27 21:14:47 2009 recovered 164123 polynomials Tue Oct 27 21:14:47 2009 attempting to build 71939 cycles Tue Oct 27 21:14:47 2009 found 71939 cycles in 6 passes Tue Oct 27 21:14:47 2009 distribution of cycle lengths: Tue Oct 27 21:14:47 2009 length 1 : 18409 Tue Oct 27 21:14:47 2009 length 2 : 13122 Tue Oct 27 21:14:47 2009 length 3 : 12329 Tue Oct 27 21:14:47 2009 length 4 : 9818 Tue Oct 27 21:14:47 2009 length 5 : 6996 Tue Oct 27 21:14:47 2009 length 6 : 4630 Tue Oct 27 21:14:47 2009 length 7 : 2874 Tue Oct 27 21:14:47 2009 length 9+: 3761 Tue Oct 27 21:14:47 2009 largest cycle: 21 relations Tue Oct 27 21:14:48 2009 matrix is 71765 x 71939 (18.4 MB) with weight 4526395 (62.92/col) Tue Oct 27 21:14:48 2009 sparse part has weight 4526395 (62.92/col) Tue Oct 27 21:14:49 2009 filtering completed in 3 passes Tue Oct 27 21:14:49 2009 matrix is 67785 x 67848 (17.4 MB) with weight 4302286 (63.41/col) Tue Oct 27 21:14:49 2009 sparse part has weight 4302286 (63.41/col) Tue Oct 27 21:14:49 2009 saving the first 48 matrix rows for later Tue Oct 27 21:14:49 2009 matrix is 67737 x 67848 (10.8 MB) with weight 3365472 (49.60/col) Tue Oct 27 21:14:49 2009 sparse part has weight 2433869 (35.87/col) Tue Oct 27 21:14:49 2009 matrix includes 64 packed rows Tue Oct 27 21:14:49 2009 using block size 27139 for processor cache size 1024 kB Tue Oct 27 21:14:50 2009 commencing Lanczos iteration Tue Oct 27 21:14:50 2009 memory use: 11.1 MB Tue Oct 27 21:15:20 2009 lanczos halted after 1073 iterations (dim = 67735) Tue Oct 27 21:15:20 2009 recovered 17 nontrivial dependencies Tue Oct 27 21:15:21 2009 prp34 factor: 6943388399896641031086000361099687 Tue Oct 27 21:15:21 2009 prp59 factor: 42587586623151738614250628439153952183704337824580960958877 Tue Oct 27 21:15:21 2009 elapsed time 02:24:11
Oct 27, 2009 (6th): By Jo Yeong Uk / GMP-ECM / Oct 27, 2009
(64·10¹⁵²+17)/9 = 7(1)₁₅₁3_<153> = 31 · 2963 · 10369 · C144
C144 = P36 · P109
P36 = 283694462391482906919275678331316889_<36>
P109 = 2631821231403694835169657384499841538907632715198481209702013976288681679080749181540420214573026569499688181_<109>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 746633109353561737237420791374811444472516566080481664330335589383152179299440880191222604195404494840956714093295250625621585698340692598988909 (144 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=5550384773 Step 1 took 4836ms Step 2 took 4587ms ********** Factor found in step 2: 283694462391482906919275678331316889 Found probable prime factor of 36 digits: 283694462391482906919275678331316889 Probable prime cofactor 2631821231403694835169657384499841538907632715198481209702013976288681679080749181540420214573026569499688181 has 109 digits
(65·10¹³⁶-11)/9 = 7(2)₁₃₅1_<137> = 123427 · 1375629339975159871097_<22> · C111
C111 = P35 · P76
P35 = 62806303538900550603721255401770903_<35>
P76 = 6772609105223622686935968347184377631672554842728485633440352400986340351953_<76>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 425362543212996505062160779945012195556672752416538326291513581129682622441372293849259290070706914884494623559 (111 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=6175954588 Step 1 took 2668ms Step 2 took 1914ms ********** Factor found in step 2: 62806303538900550603721255401770903 Found probable prime factor of 35 digits: 62806303538900550603721255401770903 Probable prime cofactor 6772609105223622686935968347184377631672554842728485633440352400986340351953 has 76 digits
(65·10¹³⁸-11)/9 = 7(2)₁₃₇1_<139> = 3 · 17 · 103 · 773 · 5441 · C129
C129 = P33 · P97
P33 = 112083887363024514430569516904031_<33>
P97 = 2916500408302875083987535970330480585387768895593985589434940784587907313673484732150584806331979_<97>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 326892703258434457249483455127619453214466851802822900044820676463512268062759713949088227925259582699844814203345266405269307349 (129 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2474648913 Step 1 took 4228ms Step 2 took 4227ms ********** Factor found in step 2: 112083887363024514430569516904031 Found probable prime factor of 33 digits: 112083887363024514430569516904031 Probable prime cofactor 2916500408302875083987535970330480585387768895593985589434940784587907313673484732150584806331979 has 97 digits
(65·10¹⁴⁰+7)/9 = 7(2)₁₃₉3_<141> = 3³ · 62547324597825074395248779_<26> · C114
C114 = P35 · P80
P35 = 22106601597297777135014061131159201_<35>
P80 = 19345339717907152871106612963136797155474171896145552677486729052119091953982231_<80>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 427659717908154394995200702825198766565175314645691050004375381571272656253058536994853204719480586679929186157431 (114 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=534140875 Step 1 took 3510ms Step 2 took 3729ms ********** Factor found in step 2: 22106601597297777135014061131159201 Found probable prime factor of 35 digits: 22106601597297777135014061131159201 Probable prime cofactor 19345339717907152871106612963136797155474171896145552677486729052119091953982231 has 80 digits
Oct 27, 2009 (5th): By Erik Branger / YAFU, Msieve, GGNFS / Oct 27, 2009
(65·10¹²¹-11)/9 = 7(2)₁₂₀1_<122> = 7963 · 534570376243_<12> · 73739065922107105379_<20> · C87
C87 = P42 · P45
P42 = 947352483431407184943321232710242057202163_<42>
P45 = 242873434001740665351347420833894420438989397_<45>

10/26/09 22:29:21 v1.12 @ ERIK-DATOR, starting SIQS on c87: 230086750861062990102879505215238593179218694592354480636195783944430374045677042465711 10/26/09 22:29:21 v1.12 @ ERIK-DATOR, random seeds: 678843804, 631501508 10/26/09 22:29:22 v1.12 @ ERIK-DATOR, ==== sieve params ==== 10/26/09 22:29:22 v1.12 @ ERIK-DATOR, n = 88 digits, 290 bits 10/26/09 22:29:22 v1.12 @ ERIK-DATOR, factor base: 58705 primes (max prime = 1550441) 10/26/09 22:29:22 v1.12 @ ERIK-DATOR, single large prime cutoff: 170548510 (110 * pmax) 10/26/09 22:29:22 v1.12 @ ERIK-DATOR, double large prime range from 43 to 50 bits 10/26/09 22:29:22 v1.12 @ ERIK-DATOR, double large prime cutoff: 656638394910403 10/26/09 22:29:22 v1.12 @ ERIK-DATOR, using 0 large prime slices of factor base 10/26/09 22:29:22 v1.12 @ ERIK-DATOR, buckets hold 1024 elements 10/26/09 22:29:22 v1.12 @ ERIK-DATOR, sieve interval: 18 blocks of size 32768 10/26/09 22:29:22 v1.12 @ ERIK-DATOR, polynomial A has ~ 16860432 factors 10/26/09 22:29:22 v1.12 @ ERIK-DATOR, using multiplier of 7 10/26/09 22:29:22 v1.12 @ ERIK-DATOR, using small prime variation correction of 19 bits 10/26/09 22:29:22 v1.12 @ ERIK-DATOR, using SSE2 for trial division and x128 sieve scanning 10/26/09 22:29:22 v1.12 @ ERIK-DATOR, trial factoring cutoff at 97 bits 10/26/09 22:29:22 v1.12 @ ERIK-DATOR, ==== sieving started ( 2 threads) ==== 10/26/09 22:53:27 v1.12 @ ERIK-DATOR, sieve time = 428.5008, relation time = 216.6216, poly_time = 749.0964 10/26/09 22:53:27 v1.12 @ ERIK-DATOR, 58825 relations found: 19764 full + 39061 from 557035 partial, using 39156060 polys (551 A polys) 10/26/09 22:53:27 v1.12 @ ERIK-DATOR, on average, sieving found 0.01 rels/poly and 398.98 rels/sec 10/26/09 22:53:27 v1.12 @ ERIK-DATOR, trial division touched 11945439 sieve locations out of 46190367866880 10/26/09 22:53:27 v1.12 @ ERIK-DATOR, ==== post processing stage (msieve-1.38) ==== 10/26/09 22:53:27 v1.12 @ ERIK-DATOR, begin with 576799 relations 10/26/09 22:53:28 v1.12 @ ERIK-DATOR, reduce to 121036 relations in 8 passes 10/26/09 22:53:33 v1.12 @ ERIK-DATOR, recovered 121036 relations 10/26/09 22:53:33 v1.12 @ ERIK-DATOR, recovered 98465 polynomials 10/26/09 22:53:33 v1.12 @ ERIK-DATOR, attempting to build 58825 cycles 10/26/09 22:53:33 v1.12 @ ERIK-DATOR, found 58825 cycles in 4 passes 10/26/09 22:53:33 v1.12 @ ERIK-DATOR, distribution of cycle lengths: 10/26/09 22:53:33 v1.12 @ ERIK-DATOR, length 1 : 19764 10/26/09 22:53:33 v1.12 @ ERIK-DATOR, length 2 : 15983 10/26/09 22:53:33 v1.12 @ ERIK-DATOR, length 3 : 10840 10/26/09 22:53:33 v1.12 @ ERIK-DATOR, length 4 : 6126 10/26/09 22:53:33 v1.12 @ ERIK-DATOR, length 5 : 3262 10/26/09 22:53:33 v1.12 @ ERIK-DATOR, length 6 : 1595 10/26/09 22:53:33 v1.12 @ ERIK-DATOR, length 7 : 705 10/26/09 22:53:33 v1.12 @ ERIK-DATOR, length 9+: 550 10/26/09 22:53:33 v1.12 @ ERIK-DATOR, largest cycle: 18 relations 10/26/09 22:53:33 v1.12 @ ERIK-DATOR, matrix is 58705 x 58825 (11.7 MB) with weight 2823437 (48.00/col) 10/26/09 22:53:33 v1.12 @ ERIK-DATOR, sparse part has weight 2823437 (48.00/col) 10/26/09 22:53:34 v1.12 @ ERIK-DATOR, filtering completed in 4 passes 10/26/09 22:53:34 v1.12 @ ERIK-DATOR, matrix is 51811 x 51875 (10.6 MB) with weight 2563413 (49.42/col) 10/26/09 22:53:34 v1.12 @ ERIK-DATOR, sparse part has weight 2563413 (49.42/col) 10/26/09 22:53:34 v1.12 @ ERIK-DATOR, saving the first 48 matrix rows for later 10/26/09 22:53:34 v1.12 @ ERIK-DATOR, matrix is 51763 x 51875 (9.0 MB) with weight 2223575 (42.86/col) 10/26/09 22:53:34 v1.12 @ ERIK-DATOR, sparse part has weight 2036371 (39.26/col) 10/26/09 22:53:34 v1.12 @ ERIK-DATOR, matrix includes 64 packed rows 10/26/09 22:53:34 v1.12 @ ERIK-DATOR, using block size 20750 for processor cache size 2048 kB 10/26/09 22:53:34 v1.12 @ ERIK-DATOR, commencing Lanczos iteration 10/26/09 22:53:34 v1.12 @ ERIK-DATOR, memory use: 8.0 MB 10/26/09 22:53:51 v1.12 @ ERIK-DATOR, lanczos halted after 820 iterations (dim = 51759) 10/26/09 22:53:51 v1.12 @ ERIK-DATOR, recovered 16 nontrivial dependencies 10/26/09 22:53:52 v1.12 @ ERIK-DATOR, prp45 = 242873434001740665351347420833894420438989397 10/26/09 22:53:56 v1.12 @ ERIK-DATOR, prp42 = 947352483431407184943321232710242057202163 10/26/09 22:53:56 v1.12 @ ERIK-DATOR, Lanczos elapsed time = 23.8370 seconds. 10/26/09 22:53:56 v1.12 @ ERIK-DATOR, Sqrt elapsed time = 5.6940 seconds. 10/26/09 22:53:56 v1.12 @ ERIK-DATOR, SIQS elapsed time = 1475.2452 seconds.
(65·10¹⁴⁰-11)/9 = 7(2)₁₃₉1_<141> = 7 · 241 · C138
C138 = P61 · P78
P61 = 1977175504445211461870746854270739911051029758911560186271011_<61>
P78 = 216526244460396024191855897937745004522218028630947175795677723021683328286153_<78>

Number: 72221_140 N=428110386616610683000724494500428110386616610683000724494500428110386616610683000724494500428110386616610683000724494500428110386616610683 ( 138 digits) SNFS difficulty: 141 digits. Divisors found: r1=1977175504445211461870746854270739911051029758911560186271011 (pp61) r2=216526244460396024191855897937745004522218028630947175795677723021683328286153 (pp78) Version: Msieve-1.40 Total time: 5.60 hours. Scaled time: 4.90 units (timescale=0.875). Factorization parameters were as follows: n: 428110386616610683000724494500428110386616610683000724494500428110386616610683000724494500428110386616610683000724494500428110386616610683 m: 10000000000000000000000000000 deg: 5 c5: 65 c0: -11 skew: 0.70 type: snfs lss: 1 rlim: 1620000 alim: 1620000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1620000/1620000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [810000, 1610001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 234432 x 234658 Total sieving time: 5.39 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.12 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,141.000,5,0,0,0,0,0,0,0,0,1620000,1620000,26,26,48,48,2.3,2.3,100000 total time: 5.60 hours. --------- CPU info (if available) ----------
(65·10¹²⁹+7)/9 = 7(2)₁₂₈3_<130> = 73 · 2221 · 2567729 · C119
C119 = P44 · P75
P44 = 85683277507409068791600540542053437197885827_<44>
P75 = 202466964608723252374887795280215191067174586508857815139998546556449041857_<75>

Number: 72223_129 N=17348033114652005022752627590558703019224037688666980158306193742390894985894433406088781202803253598064633340230060739 ( 119 digits) SNFS difficulty: 131 digits. Divisors found: r1=85683277507409068791600540542053437197885827 (pp44) r2=202466964608723252374887795280215191067174586508857815139998546556449041857 (pp75) Version: Msieve-1.40 Total time: 2.64 hours. Scaled time: 2.63 units (timescale=0.995). Factorization parameters were as follows: n: 17348033114652005022752627590558703019224037688666980158306193742390894985894433406088781202803253598064633340230060739 m: 100000000000000000000000000 deg: 5 c5: 13 c0: 14 skew: 1.01 type: snfs lss: 1 rlim: 1070000 alim: 1070000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1070000/1070000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [535000, 935001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 145078 x 145303 Total sieving time: 2.52 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.06 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,131.000,5,0,0,0,0,0,0,0,0,1070000,1070000,26,26,47,47,2.3,2.3,50000 total time: 2.64 hours. --------- CPU info (if available) ----------
(65·10¹⁴¹+7)/9 = 7(2)₁₄₀3_<142> = 1407927869_<10> · C133
C133 = P53 · P81
P53 = 12049710125367851790960582688070194854908188364815339_<53>
P81 = 425709990455910147905908526532864228292366077716772356573508558892819462447043953_<81>

Number: 72223_141 N=5129681982466832057731092630443713606341165636960782557122762815502036363357349113047653027331489112118869650858670674003273261595067 ( 133 digits) SNFS difficulty: 144 digits. Divisors found: r1=12049710125367851790960582688070194854908188364815339 (pp53) r2=425709990455910147905908526532864228292366077716772356573508558892819462447043953 (pp81) Version: Msieve v. 1.43 Total time: 11.54 hours. Scaled time: 9.10 units (timescale=0.789). Factorization parameters were as follows: n: 5129681982466832057731092630443713606341165636960782557122762815502036363357349113047653027331489112118869650858670674003273261595067 m: 20000000000000000000000000000 deg: 5 c5: 325 c0: 112 skew: 0.81 type: snfs lss: 1 rlim: 1760000 alim: 1760000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1760000/1760000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [880000, 1880001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 304431 x 304677 Total sieving time: 10.67 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.46 hours. Time per square root: 0.30 hours. Prototype def-par.txt line would be: snfs,144.000,5,0,0,0,0,0,0,0,0,1760000,1760000,26,26,49,49,2.3,2.3,100000 total time: 11.54 hours. --------- CPU info (if available) ----------
(65·10¹⁰⁸-11)/9 = 7(2)₁₀₇1_<109> = 3 · 23 · 9033556013789_<13> · C95
C95 = P45 · P50
P45 = 135554491375990857956197246460694492102127861_<45>
P50 = 85476966858717394152054163418298515138093927220521_<50>

Number: 72221_108 N=11586786766895863381830670020753519733562146967072224373606260076037382144838546474453485035581 ( 95 digits) SNFS difficulty: 110 digits. Divisors found: r1=135554491375990857956197246460694492102127861 (pp45) r2=85476966858717394152054163418298515138093927220521 (pp50) Version: Msieve-1.40 Total time: 0.59 hours. Scaled time: 0.59 units (timescale=1.002). Factorization parameters were as follows: n: 11586786766895863381830670020753519733562146967072224373606260076037382144838546474453485035581 m: 5000000000000000000000 deg: 5 c5: 104 c0: -55 skew: 0.88 type: snfs lss: 1 rlim: 490000 alim: 490000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 Factor base limits: 490000/490000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [245000, 345001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 45830 x 46055 Total sieving time: 0.56 hours. Total relation processing time: 0.01 hours. Matrix solve time: 0.01 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,110.000,5,0,0,0,0,0,0,0,0,490000,490000,25,25,44,44,2.2,2.2,50000 total time: 0.59 hours. --------- CPU info (if available) ----------
Oct 27, 2009 (4th): By Wataru Sakai / GMP-ECM 6.2.1, Msieve / Oct 27, 2009
(59·10¹⁸⁹+13)/9 = 6(5)₁₈₈7_<190> = 225241963 · 31687580934872183_<17> · 261849580258534788772143093627569_<33> · C133
C133 = P44 · P89
P44 = 84827586340642371205886492540524983243965279_<44>
P89 = 41350629053536239606694402476456416541139861065143806414400328891246290212348829620411783_<89>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2453899015 Step 1 took 38020ms Step 2 took 14078ms ********** Factor found in step 2: 84827586340642371205886492540524983243965279 Found probable prime factor of 44 digits: 84827586340642371205886492540524983243965279 Probable prime cofactor 41350629053536239606694402476456416541139861065143806414400328891246290212348829620411783 has 89 digits
(11·10¹⁹³+1)/3 = 3(6)₁₉₂7_<194> = 37 · 1949 · C189
C189 = P49 · P65 · P76
P49 = 3877282014566842518519492328248181190291969603383_<49>
P65 = 92484341434178074305109486526779408950878040850072954005996360127_<65>
P76 = 1417954412002055454225203117654102106991785323552900390351400853029752285699_<76>

Number: 36667_193 N=508461257563361206254997943043094402766029241144684962027188810154433551047199071827086193427907127240118517696762950739348892247814772186244736270390452022057973828112360693171365310924059 ( 189 digits) SNFS difficulty: 195 digits. Divisors found: r1=3877282014566842518519492328248181190291969603383 r2=92484341434178074305109486526779408950878040850072954005996360127 r3=1417954412002055454225203117654102106991785323552900390351400853029752285699 Version: Total time: 548.33 hours. Scaled time: 1104.89 units (timescale=2.015). Factorization parameters were as follows: n: 508461257563361206254997943043094402766029241144684962027188810154433551047199071827086193427907127240118517696762950739348892247814772186244736270390452022057973828112360693171365310924059 m: 500000000000000000000000000000000000000 deg: 5 c5: 88 c0: 25 skew: 0.78 type: snfs lss: 1 rlim: 12700000 alim: 12700000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5Factor base limits: 12700000/12700000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [6350000, 12050001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1962220 x 1962468 Total sieving time: 548.33 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,195,5,0,0,0,0,0,0,0,0,12700000,12700000,28,28,55,55,2.5,2.5,100000 total time: 548.33 hours. --------- CPU info (if available) ----------
(65·10¹⁸⁹+43)/9 = 7(2)₁₈₈7_<190> = 3 · 11 · C189
C189 = P93 · P96
P93 = 344169962009931548308268017081595995989862134133897845813087998330100327017231481133237154389_<93>
P96 = 635892852406752029790139607998304098096231541911114002251357000552628373073014289921768913242471_<96>

Number: 72227_189 N=218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855219 ( 189 digits) SNFS difficulty: 191 digits. Divisors found: r1=344169962009931548308268017081595995989862134133897845813087998330100327017231481133237154389 r2=635892852406752029790139607998304098096231541911114002251357000552628373073014289921768913242471 Version: Total time: 327.17 hours. Scaled time: 656.96 units (timescale=2.008). Factorization parameters were as follows: n: 218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855218855219 m: 100000000000000000000000000000000000000 deg: 5 c5: 13 c0: 86 skew: 1.46 type: snfs lss: 1 rlim: 10700000 alim: 10700000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 Factor base limits: 10700000/10700000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [5350000, 8950001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1761109 x 1761357 Total sieving time: 327.17 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,191,5,0,0,0,0,0,0,0,0,10700000,10700000,28,28,54,54,2.5,2.5,100000 total time: 327.17 hours. --------- CPU info (if available) ----------
7·10¹⁷³-9 = 6(9)₁₇₂1_<174> = 17 · 23 · 16421 · 951988489 · 967778104050840161_<18> · C141
C141 = P61 · P80
P61 = 5822198849636541604216008139984546047314947195596463077900521_<61>
P80 = 20324841068780494305293498995060419802226786782151713853158153045709315773873709_<80>

Number: 69991_173 N=118335266289699330717287805739976609910028642379095256867623958931583444124800011987668345641662168237014794505569635206720802429547119302389 ( 141 digits) SNFS difficulty: 175 digits. Divisors found: r1=5822198849636541604216008139984546047314947195596463077900521 r2=20324841068780494305293498995060419802226786782151713853158153045709315773873709 Version: Total time: 117.44 hours. Scaled time: 236.63 units (timescale=2.015). Factorization parameters were as follows: n: 118335266289699330717287805739976609910028642379095256867623958931583444124800011987668345641662168237014794505569635206720802429547119302389 m: 50000000000000000000000000000000000 deg: 5 c5: 56 c0: -225 skew: 1.32 type: snfs lss: 1 rlim: 5800000 alim: 5800000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5Factor base limits: 5800000/5800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved rational special-q in [2900000, 6500001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1100358 x 1100606 Total sieving time: 117.44 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,175,5,0,0,0,0,0,0,0,0,5800000,5800000,28,28,52,52,2.5,2.5,100000 total time: 117.44 hours. --------- CPU info (if available) ----------
(19·10¹⁸⁹+53)/9 = 2(1)₁₈₈7_<190> = 137 · C188
C188 = P53 · P135
P53 = 50276311039073491284553796865897030204461721150551647_<53>
P135 = 306497629512232293365247269171182637897810549798966215737832495828240735616622890851416942888914546319515586789212490295293970999607803_<135>

Number: 21117_189 N=15409570154095701540957015409570154095701540957015409570154095701540957015409570154095701540957015409570154095701540957015409570154095701540957015409570154095701540957015409570154095701541 ( 188 digits) SNFS difficulty: 190 digits. Divisors found: r1=50276311039073491284553796865897030204461721150551647 r2=306497629512232293365247269171182637897810549798966215737832495828240735616622890851416942888914546319515586789212490295293970999607803 Version: Total time: 526.99 hours. Scaled time: 1061.88 units (timescale=2.015). Factorization parameters were as follows: n: 15409570154095701540957015409570154095701540957015409570154095701540957015409570154095701540957015409570154095701540957015409570154095701540957015409570154095701540957015409570154095701541 m: 50000000000000000000000000000000000000 deg: 5 c5: 304 c0: 265 skew: 0.97 type: snfs lss: 1 rlim: 10700000 alim: 10700000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5Factor base limits: 10700000/10700000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [5350000, 11050001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1964631 x 1964879 Total sieving time: 526.99 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,190,5,0,0,0,0,0,0,0,0,10700000,10700000,28,28,54,54,2.5,2.5,100000 total time: 526.99 hours. --------- CPU info (if available) ----------
(11·10¹⁹⁴-17)/3 = 3(6)₁₉₃1_<195> = 43 · 53 · C192
C192 = P44 · P61 · P87
P44 = 78977963478275827768612875134173255212037391_<44>
P61 = 7989706671541663001611625673535523086770395124467865271255451_<61>
P87 = 254970736930429047359472790175682836301063560469885661449512858357441037849002410792199_<87>

Number: 36661_194 N=160889278923504461020915606260055579932719028813807225391253473745794939300862951586953342109112183706303934474184583881819511481643995904636536492613719467602749744039783530788357466725171859 ( 192 digits) SNFS difficulty: 196 digits. Divisors found: r1=78977963478275827768612875134173255212037391 r2=7989706671541663001611625673535523086770395124467865271255451 r3=254970736930429047359472790175682836301063560469885661449512858357441037849002410792199 Version: Total time: 613.96 hours. Scaled time: 1235.91 units (timescale=2.013). Factorization parameters were as follows: n: 160889278923504461020915606260055579932719028813807225391253473745794939300862951586953342109112183706303934474184583881819511481643995904636536492613719467602749744039783530788357466725171859 m: 1000000000000000000000000000000000000000 deg: 5 c5: 11 c0: -170 skew: 1.73 type: snfs lss: 1 rlim: 13000000 alim: 13000000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5 Factor base limits: 13000000/13000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [6500000, 13800001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2233237 x 2233485 Total sieving time: 613.96 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,196,5,0,0,0,0,0,0,0,0,13000000,13000000,28,28,55,55,2.5,2.5,100000 total time: 613.96 hours. --------- CPU info (if available) ----------
Oct 27, 2009 (3rd): By Dmitry Domanov / msieve/SIQS, GGNFS/msieve / Oct 27, 2009
(65·10¹⁰⁷-11)/9 = 7(2)₁₀₆1_<108> = 36749656866201527263_<20> · C89
C89 = P36 · P54
P36 = 174577584931942788813973330285134439_<36>
P54 = 112571661871895252862906862024566402469110010962824053_<54>

Tue Oct 27 00:50:36 2009 Msieve v. 1.43 Tue Oct 27 00:50:36 2009 random seeds: cb1332a0 13eb75b0 Tue Oct 27 00:50:36 2009 factoring 19652488861370739252193054495891224009287472706110752921759607452304062429675176207861267 (89 digits) Tue Oct 27 00:50:37 2009 searching for 15-digit factors Tue Oct 27 00:50:37 2009 commencing quadratic sieve (89-digit input) Tue Oct 27 00:50:37 2009 using multiplier of 3 Tue Oct 27 00:50:37 2009 using VC8 32kb sieve core Tue Oct 27 00:50:37 2009 sieve interval: 30 blocks of size 32768 Tue Oct 27 00:50:37 2009 processing polynomials in batches of 7 Tue Oct 27 00:50:37 2009 using a sieve bound of 1544869 (58667 primes) Tue Oct 27 00:50:37 2009 using large prime bound of 123589520 (26 bits) Tue Oct 27 00:50:37 2009 using double large prime bound of 367761997746960 (42-49 bits) Tue Oct 27 00:50:37 2009 using trial factoring cutoff of 49 bits Tue Oct 27 00:50:37 2009 polynomial 'A' values have 11 factors Tue Oct 27 01:40:58 2009 58889 relations (15988 full + 42901 combined from 620648 partial), need 58763 Tue Oct 27 01:41:02 2009 begin with 636636 relations Tue Oct 27 01:41:02 2009 reduce to 142394 relations in 11 passes Tue Oct 27 01:41:02 2009 attempting to read 142394 relations Tue Oct 27 01:41:03 2009 recovered 142394 relations Tue Oct 27 01:41:03 2009 recovered 118558 polynomials Tue Oct 27 01:41:04 2009 attempting to build 58889 cycles Tue Oct 27 01:41:04 2009 found 58889 cycles in 5 passes Tue Oct 27 01:41:04 2009 distribution of cycle lengths: Tue Oct 27 01:41:04 2009 length 1 : 15988 Tue Oct 27 01:41:04 2009 length 2 : 11412 Tue Oct 27 01:41:04 2009 length 3 : 10470 Tue Oct 27 01:41:04 2009 length 4 : 7779 Tue Oct 27 01:41:04 2009 length 5 : 5448 Tue Oct 27 01:41:04 2009 length 6 : 3426 Tue Oct 27 01:41:04 2009 length 7 : 2061 Tue Oct 27 01:41:04 2009 length 9+: 2305 Tue Oct 27 01:41:04 2009 largest cycle: 18 relations Tue Oct 27 01:41:04 2009 matrix is 58667 x 58889 (14.3 MB) with weight 3504276 (59.51/col) Tue Oct 27 01:41:04 2009 sparse part has weight 3504276 (59.51/col) Tue Oct 27 01:41:04 2009 filtering completed in 3 passes Tue Oct 27 01:41:04 2009 matrix is 54552 x 54616 (13.4 MB) with weight 3281370 (60.08/col) Tue Oct 27 01:41:04 2009 sparse part has weight 3281370 (60.08/col) Tue Oct 27 01:41:04 2009 saving the first 48 matrix rows for later Tue Oct 27 01:41:04 2009 matrix is 54504 x 54616 (9.7 MB) with weight 2701329 (49.46/col) Tue Oct 27 01:41:04 2009 sparse part has weight 2208475 (40.44/col) Tue Oct 27 01:41:04 2009 matrix includes 64 packed rows Tue Oct 27 01:41:04 2009 using block size 21846 for processor cache size 6144 kB Tue Oct 27 01:41:05 2009 commencing Lanczos iteration Tue Oct 27 01:41:05 2009 memory use: 9.2 MB Tue Oct 27 01:41:20 2009 lanczos halted after 863 iterations (dim = 54500) Tue Oct 27 01:41:20 2009 recovered 15 nontrivial dependencies Tue Oct 27 01:41:20 2009 prp36 factor: 174577584931942788813973330285134439 Tue Oct 27 01:41:20 2009 prp54 factor: 112571661871895252862906862024566402469110010962824053 Tue Oct 27 01:41:20 2009 elapsed time 00:50:44
2·10¹⁹¹+9 = 2(0)₁₉₀9_<192> = 139787422364207720750158040677389843257571643_<45> · C148
C148 = P68 · P80
P68 = 46096944919325148346223203940223926055682830814085225169569170904023_<68>
P80 = 31037716041925551555377656141714970107015368138481092969610634477807320110383981_<80>

Number: 209-191 N=1430743886806296706788516093667434949145159858014350886258366962866810355411884866166709798529837275207436439253831768696683312353651987615427655563 ( 148 digits) SNFS difficulty: 191 digits. Divisors found: r1=46096944919325148346223203940223926055682830814085225169569170904023 (pp68) r2=31037716041925551555377656141714970107015368138481092969610634477807320110383981 (pp80) Version: Msieve-1.40 Total time: 245.12 hours. Scaled time: 458.63 units (timescale=1.871). Factorization parameters were as follows: n: 1430743886806296706788516093667434949145159858014350886258366962866810355411884866166709798529837275207436439253831768696683312353651987615427655563 m: 100000000000000000000000000000000000000 deg: 5 c5: 20 c0: 9 skew: 0.85 type: snfs lss: 1 rlim: 10800000 alim: 10800000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 Factor base limits: 10800000/10800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [5400000, 9300001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1851073 x 1851298 Total sieving time: 240.25 hours. Total relation processing time: 0.23 hours. Matrix solve time: 4.45 hours. Time per square root: 0.21 hours. Prototype def-par.txt line would be: snfs,191.000,5,0,0,0,0,0,0,0,0,10800000,10800000,28,28,54,54,2.5,2.5,100000 total time: 245.12 hours. --------- CPU info (if available) ----------
(65·10¹²⁵-11)/9 = 7(2)₁₂₄1_<126> = C126
C126 = P41 · P85
P41 = 91555041401965548538648038653167603029653_<41>
P85 = 7888393813851928434485152622480874620149146146332238895830736022441467295327701644057_<85>

Number: s126 N=722222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221 ( 126 digits) SNFS difficulty: 126 digits. Divisors found: r1=91555041401965548538648038653167603029653 (pp41) r2=7888393813851928434485152622480874620149146146332238895830736022441467295327701644057 (pp85) Version: Msieve-1.40 Total time: 1.50 hours. Scaled time: 2.94 units (timescale=1.963). Factorization parameters were as follows: n: 722222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221 m: 10000000000000000000000000 deg: 5 c5: 65 c0: -11 skew: 0.70 type: snfs lss: 1 rlim: 910000 alim: 910000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3Factor base limits: 910000/910000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [455000, 755001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 110745 x 110974 Total sieving time: 1.41 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.03 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,126.000,5,0,0,0,0,0,0,0,0,910000,910000,26,26,46,46,2.3,2.3,50000 total time: 1.50 hours. --------- CPU info (if available) ----------
(62·10¹³²-71)/9 = 6(8)₁₃₁1_<133> = 5717 · C130
C130 = P41 · P89
P41 = 14196147689937141374294318249731425936067_<41>
P89 = 84880998342609810093756094165793232255873270007284083264233059727258303257959873758507279_<89>

Number: s130 N=1204983188540998581229471556566186616912522107554467183643324976191864419956076419256408761393893456163877713641575807047208131693 ( 130 digits) SNFS difficulty: 134 digits. Divisors found: r1=14196147689937141374294318249731425936067 (pp41) r2=84880998342609810093756094165793232255873270007284083264233059727258303257959873758507279 (pp89) Version: Msieve-1.40 Total time: 3.18 hours. Scaled time: 5.79 units (timescale=1.823). Factorization parameters were as follows: n: 1204983188540998581229471556566186616912522107554467183643324976191864419956076419256408761393893456163877713641575807047208131693 m: 200000000000000000000000000 deg: 5 c5: 775 c0: -284 skew: 0.82 type: snfs lss: 1 rlim: 1220000 alim: 1220000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3Factor base limits: 1220000/1220000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [610000, 1285001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 206175 x 206400 Total sieving time: 3.08 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.05 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,134.000,5,0,0,0,0,0,0,0,0,1220000,1220000,26,26,47,47,2.3,2.3,75000 total time: 3.18 hours. --------- CPU info (if available) ----------
(65·10¹³⁰+7)/9 = 7(2)₁₂₉3_<131> = C131
C131 = P53 · P79
P53 = 46485863897376296550853545500186122961951356602030151_<53>
P79 = 1553638378791073916029398963967193954361536667650255332339812815429978361841273_<79>

Number: s131 N=72222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222223 ( 131 digits) SNFS difficulty: 131 digits. Divisors found: r1=46485863897376296550853545500186122961951356602030151 (pp53) r2=1553638378791073916029398963967193954361536667650255332339812815429978361841273 (pp79) Version: Msieve-1.40 Total time: 2.03 hours. Scaled time: 3.81 units (timescale=1.877). Factorization parameters were as follows: n: 72222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222223 m: 100000000000000000000000000 deg: 5 c5: 65 c0: 7 skew: 0.64 type: snfs lss: 1 rlim: 1100000 alim: 1100000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3Factor base limits: 1100000/1100000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [550000, 950001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 157737 x 157962 Total sieving time: 1.93 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.06 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,131.000,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000 total time: 2.03 hours. --------- CPU info (if available) ----------
Oct 27, 2009 (2nd): By Norbert Schneider / Msieve / Oct 27, 2009
(61·10¹³⁰+11)/9 = 6(7)₁₂₉9_<131> = 3³ · 12141019215809417_<17> · 258286671235162236352303_<24> · C90
C90 = P40 · P51
P40 = 2603800835257585405318811667397972553087_<40>
P51 = 307438786873328469652390333446782493394750798060721_<51>

Mon Oct 26 19:16:40 2009 Mon Oct 26 19:16:40 2009 Mon Oct 26 19:16:40 2009 Msieve v. 1.43 Mon Oct 26 19:16:40 2009 random seeds: a73f8f44 bd2ae005 Mon Oct 26 19:16:40 2009 factoring 800509370051351453037656179793997623801994692989397392614271301898208518060262904821995727 (90 digits) Mon Oct 26 19:16:45 2009 searching for 15-digit factors Mon Oct 26 19:16:46 2009 commencing quadratic sieve (90-digit input) Mon Oct 26 19:16:48 2009 using multiplier of 13 Mon Oct 26 19:16:48 2009 using 64kb Pentium 4 sieve core Mon Oct 26 19:16:48 2009 sieve interval: 18 blocks of size 65536 Mon Oct 26 19:16:48 2009 processing polynomials in batches of 6 Mon Oct 26 19:16:48 2009 using a sieve bound of 1618703 (61070 primes) Mon Oct 26 19:16:49 2009 using large prime bound of 135971052 (27 bits) Mon Oct 26 19:16:49 2009 using double large prime bound of 436720526960928 (42-49 bits) Mon Oct 26 19:16:49 2009 using trial factoring cutoff of 49 bits Mon Oct 26 19:16:49 2009 polynomial 'A' values have 12 factors Mon Oct 26 22:15:13 2009 61446 relations (16348 full + 45098 combined from 666206 partial), need 61166 Mon Oct 26 22:15:15 2009 begin with 682554 relations Mon Oct 26 22:15:16 2009 reduce to 150056 relations in 10 passes Mon Oct 26 22:15:16 2009 attempting to read 150056 relations Mon Oct 26 22:15:19 2009 recovered 150056 relations Mon Oct 26 22:15:19 2009 recovered 129311 polynomials Mon Oct 26 22:15:19 2009 attempting to build 61446 cycles Mon Oct 26 22:15:19 2009 found 61446 cycles in 6 passes Mon Oct 26 22:15:19 2009 distribution of cycle lengths: Mon Oct 26 22:15:19 2009 length 1 : 16348 Mon Oct 26 22:15:19 2009 length 2 : 11864 Mon Oct 26 22:15:19 2009 length 3 : 10847 Mon Oct 26 22:15:19 2009 length 4 : 8262 Mon Oct 26 22:15:19 2009 length 5 : 5686 Mon Oct 26 22:15:19 2009 length 6 : 3736 Mon Oct 26 22:15:19 2009 length 7 : 2192 Mon Oct 26 22:15:19 2009 length 9+: 2511 Mon Oct 26 22:15:19 2009 largest cycle: 20 relations Mon Oct 26 22:15:19 2009 matrix is 61070 x 61446 (15.3 MB) with weight 3754514 (61.10/col) Mon Oct 26 22:15:19 2009 sparse part has weight 3754514 (61.10/col) Mon Oct 26 22:15:21 2009 filtering completed in 3 passes Mon Oct 26 22:15:21 2009 matrix is 57065 x 57129 (14.3 MB) with weight 3510750 (61.45/col) Mon Oct 26 22:15:21 2009 sparse part has weight 3510750 (61.45/col) Mon Oct 26 22:15:22 2009 saving the first 48 matrix rows for later Mon Oct 26 22:15:22 2009 matrix is 57017 x 57129 (9.2 MB) with weight 2773047 (48.54/col) Mon Oct 26 22:15:22 2009 sparse part has weight 2059967 (36.06/col) Mon Oct 26 22:15:22 2009 matrix includes 64 packed rows Mon Oct 26 22:15:22 2009 using block size 10922 for processor cache size 256 kB Mon Oct 26 22:15:22 2009 commencing Lanczos iteration Mon Oct 26 22:15:22 2009 memory use: 9.3 MB Mon Oct 26 22:15:54 2009 lanczos halted after 904 iterations (dim = 57015) Mon Oct 26 22:15:54 2009 recovered 17 nontrivial dependencies Mon Oct 26 22:15:56 2009 prp40 factor: 2603800835257585405318811667397972553087 Mon Oct 26 22:15:56 2009 prp51 factor: 307438786873328469652390333446782493394750798060721 Mon Oct 26 22:15:56 2009 elapsed time 02:59:16
Oct 27, 2009: By Lionel Debroux / GMP-ECM
Factorizations of 722...221 and Factorizations of 722...223 have been extended up to n=200. Composite numbers that appeared newly have passed 150 times ECM runs at level 35. Unknown factors have probably 30 digits or more.
Oct 26, 2009 (7th): By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Oct 26, 2009
(83·10¹⁴⁶+7)/9 = 9(2)₁₄₅3_<147> = 13 · 6112473163_<10> · 70315458832223316419214342764791_<32> · C105
C105 = P52 · P53
P52 = 5791378332563386734299789562740645717003706558548593_<52>
P53 = 28499846000487846733642226699203988710334388566768759_<53>

Number: 92223_146 N=165053390608618612168814333894623116123683611767851606138040337603496776755267221271940941504830895806087 ( 105 digits) Divisors found: r1=5791378332563386734299789562740645717003706558548593 r2=28499846000487846733642226699203988710334388566768759 Version: Total time: 4.39 hours. Scaled time: 10.46 units (timescale=2.385). Factorization parameters were as follows: name: 92223_146 n: 165053390608618612168814333894623116123683611767851606138040337603496776755267221271940941504830895806087 skew: 19553.75 # norm 1.36e+14 c5: 5700 c4: 235810005 c3: 245079180905 c2: -154319593207427431 c1: -148483831425267567230 c0: -814720965704383267381256 # alpha -5.81 Y1: 82920931379 Y0: -123693679908535878411 # Murphy_E 2.07e-09 # M 16105943711929144827060288703611641223991067736201404894401156909521716930802385512633608291851676404138 type: gnfs rlim: 2000000 alim: 2000000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1000000, 1650001) Primes: rational ideals reading, algebraic ideals reading, Relations: 6891219 Max relations in full relation-set: Initial matrix: Pruned matrix : 274339 x 274587 Polynomial selection time: 0.36 hours. Total sieving time: 3.24 hours. Total relation processing time: 0.43 hours. Matrix solve time: 0.17 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: gnfs,104,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2000000,2000000,27,27,50,50,2.6,2.6,50000 total time: 4.39 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
(62·10¹⁴⁴-71)/9 = 6(8)₁₄₃1_<145> = 173 · 617 · 1283 · 92610038086816262454859531913_<29> · C108
C108 = P35 · P74
P35 = 45060620799576548736690063731376301_<35>
P74 = 12054134222394110709717782635167614241122684394866782704597181919381457779_<74>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 543166771262499552479231555893942724170566107989350047498766678598794980817702546211216551464640875392695479 (108 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4831068078 Step 1 took 2670ms Step 2 took 1844ms ********** Factor found in step 2: 45060620799576548736690063731376301 Found probable prime factor of 35 digits: 45060620799576548736690063731376301 Probable prime cofactor 12054134222394110709717782635167614241122684394866782704597181919381457779 has 74 digits
(26·10¹⁸⁰-11)/3 = 8(6)₁₇₉3_<181> = 3540853596198710609_<19> · 750709090610386998791821_<24> · 311104155382289880239512627969_<30> · C110
C110 = P41 · P69
P41 = 72785908957299479303025193305881070533587_<41>
P69 = 143985688074871851263884561113056280933967878093323444574394933207489_<69>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 10480129183371743899045412556645811521917224266909621512471309641624950039890299342336256862579936558614433043 (110 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=5524291184 Step 1 took 3526ms Step 2 took 3900ms ********** Factor found in step 2: 72785908957299479303025193305881070533587 Found probable prime factor of 41 digits: 72785908957299479303025193305881070533587 Probable prime cofactor 143985688074871851263884561113056280933967878093323444574394933207489 has 69 digits
Oct 26, 2009 (6th): By Sinkiti Sibata / Msieve, GGNFS / Oct 26, 2009
(83·10¹⁴⁰+7)/9 = 9(2)₁₃₉3_<141> = 13 · 59 · 179 · 196835519 · 780759681572696281_<18> · C110
C110 = P54 · P56
P54 = 950945206033983716590046745708439382556184867498061651_<54>
P56 = 45963262403462441886100482311242817697783998352022258799_<56>

Number: 92223_140 N=43708544036254649395714070133193976331990037910375971143155353250353772955674359691405658669750880139179217149 ( 110 digits) SNFS difficulty: 141 digits. Divisors found: r1=950945206033983716590046745708439382556184867498061651 (pp54) r2=45963262403462441886100482311242817697783998352022258799 (pp56) Version: Msieve-1.40 Total time: 6.58 hours. Scaled time: 13.36 units (timescale=2.032). Factorization parameters were as follows: name: 92223_140 n: 43708544036254649395714070133193976331990037910375971143155353250353772955674359691405658669750880139179217149 m: 10000000000000000000000000000 deg: 5 c5: 83 c0: 7 skew: 0.61 type: snfs lss: 1 rlim: 1620000 alim: 1620000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1620000/1620000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [810000, 1610001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 235126 x 235372 Total sieving time: 6.28 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.20 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,141.000,5,0,0,0,0,0,0,0,0,1620000,1620000,26,26,48,48,2.3,2.3,100000 total time: 6.58 hours. --------- CPU info (if available) ----------
(61·10¹³⁶+11)/9 = 6(7)₁₃₅9_<137> = 3 · 2213363 · 20975235357953_<14> · C117
C117 = P38 · P79
P38 = 56099438243208509545785301147285196647_<38>
P79 = 8674572279336327283237021925543194621541044909983854234310679612701120002673821_<79>

Number: 67779_136 N=486638631870876768578237462710217409611440936923179732511602138246948855664505898321050283688239457736079891783878187 ( 117 digits) SNFS difficulty: 138 digits. Divisors found: r1=56099438243208509545785301147285196647 (pp38) r2=8674572279336327283237021925543194621541044909983854234310679612701120002673821 (pp79) Version: Msieve-1.40 Total time: 5.94 hours. Scaled time: 12.39 units (timescale=2.085). Factorization parameters were as follows: name: 67779_136 n: 486638631870876768578237462710217409611440936923179732511602138246948855664505898321050283688239457736079891783878187 m: 2000000000000000000000000000 deg: 5 c5: 305 c0: 176 skew: 0.90 type: snfs lss: 1 rlim: 1450000 alim: 1450000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1450000/1450000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [725000, 1475001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 247395 x 247643 Total sieving time: 5.59 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.20 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,138.000,5,0,0,0,0,0,0,0,0,1450000,1450000,26,26,48,48,2.3,2.3,75000 total time: 5.94 hours. --------- CPU info (if available) ----------
(62·10¹³⁶-71)/9 = 6(8)₁₃₅1_<137> = 797 · 91957 · 141665756784889_<15> · C115
C115 = P41 · P74
P41 = 87940173824683258876381753531354451770847_<41>
P74 = 75449064368628461623561903771559610802465731814491611535253595307663468583_<74>

SNFS difficulty: 138 digits. Divisors found: r1=87940173824683258876381753531354451770847 (pp41) r2=75449064368628461623561903771559610802465731814491611535253595307663468583 (pp74) Version: GGNFS-0.77.1-20060513-k8 Total time: 8.91 hours. Scaled time: 17.36 units (timescale=1.949). Factorization parameters were as follows: name: 68881_136 n: 6635003835486902970594310750805950658360102961790601430840554603116519491417799716317124902425292622802174699799801 m: 2000000000000000000000000000 deg: 5 c5: 155 c0: -568 skew: 1.30 type: snfs lss: 1 rlim: 1430000 alim: 1430000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1430000/1430000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [715000, 1540001) Primes: RFBsize:109205, AFBsize:109291, largePrimes:3393933 encountered Relations: rels:3341469, finalFF:248129 Max relations in full relation-set: 28 Initial matrix: 218563 x 248129 with sparse part having weight 22264177. Pruned matrix : 209570 x 210726 with weight 16662072. Total sieving time: 8.30 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.42 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,138,5,0,0,0,0,0,0,0,0,1430000,1430000,26,26,48,48,2.3,2.3,75000 total time: 8.91 hours. --------- CPU info (if available) ----------
(61·10¹⁴⁰+11)/9 = 6(7)₁₃₉9_<141> = 7 · 173 · 4668508477118735351_<19> · 11868308233560420583480229_<26> · C95
C95 = P38 · P57
P38 = 34654709996381233356360236722003259611_<38>
P57 = 291483479342020082267398383224796794589186280350551363081_<57>

Number: 67779_140 N=10101275445333886072937871136953074721594155330052969136352011175659007415845411001561163821491 ( 95 digits) Divisors found: r1=34654709996381233356360236722003259611 (pp38) r2=291483479342020082267398383224796794589186280350551363081 (pp57) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 10.42 hours. Scaled time: 4.92 units (timescale=0.472). Factorization parameters were as follows: name: 67779_140 n: 10101275445333886072937871136953074721594155330052969136352011175659007415845411001561163821491 m: 7926501998682499714959 deg: 4 c4: 2558880 c3: 12052800 c2: -345390808657415679 c1: 764061773339347700034 c0: -2640085652055857279596 skew: 1635.250 type: gnfs # adj. I(F,S) = 57.775 # E(F1,F2) = 3.595557e-05 # GGNFS version 0.77.1-20050930-pentium4 polyselect. # Options were: # lcd=1, enumLCD=24, maxS1=60.00000000, seed=1256504580. # maxskew=2000.0 # These parameters should be manually set: rlim: 1200000 alim: 1200000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.4 alambda: 2.4 qintsize: 60000 type: gnfs Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved algebraic special-q in [600000, 1440001) Primes: RFBsize:92938, AFBsize:93122, largePrimes:1879615 encountered Relations: rels:1950424, finalFF:223451 Max relations in full relation-set: 28 Initial matrix: 186133 x 223451 with sparse part having weight 18769959. Pruned matrix : 169528 x 170522 with weight 12045876. Polynomial selection time: 0.17 hours. Total sieving time: 9.52 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.54 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: gnfs,94,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000 total time: 10.42 hours. --------- CPU info (if available) ----------
(61·10¹³⁷+11)/9 = 6(7)₁₃₆9_<138> = 41854649 · C131
C131 = P43 · P89
P43 = 1497100862179284466393211599484926776042967_<43>
P89 = 10816644611377158968597922580922419233088088735788862949569901953744310105884107215906413_<89>

Number: 67779_137 N=16193607973579656056314742426290034776728811601735754080216460010876635897192156067962194063024582472971587404251742208560338847371 ( 131 digits) SNFS difficulty: 140 digits. Divisors found: r1=1497100862179284466393211599484926776042967 (pp43) r2=10816644611377158968597922580922419233088088735788862949569901953744310105884107215906413 (pp89) Version: Msieve-1.40 Total time: 7.87 hours. Scaled time: 16.35 units (timescale=2.078). Factorization parameters were as follows: name: 67779_137 n: 16193607973579656056314742426290034776728811601735754080216460010876635897192156067962194063024582472971587404251742208560338847371 m: 5000000000000000000000000000 deg: 5 c5: 244 c0: 1375 skew: 1.41 type: snfs lss: 1 rlim: 1560000 alim: 1560000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1560000/1560000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [780000, 1780001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 240232 x 240464 Total sieving time: 7.52 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.19 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,140.000,5,0,0,0,0,0,0,0,0,1560000,1560000,26,26,48,48,2.3,2.3,100000 total time: 7.87 hours. --------- CPU info (if available) ----------
(62·10¹³⁸-71)/9 = 6(8)₁₃₇1_<139> = 178973 · 371864911123_<12> · C123
C123 = P42 · P81
P42 = 586223530914985362890505263147233484304329_<42>
P81 = 176568494706771364851457868738726420430749628421559284794116630853036260388793391_<81>

Number: 68881_138 N=103508606415347412610445012420502440976795110134999813227178254855128575837561314714804310858344623651363750600965347889639 ( 123 digits) SNFS difficulty: 141 digits. Divisors found: r1=586223530914985362890505263147233484304329 (pp42) r2=176568494706771364851457868738726420430749628421559284794116630853036260388793391 (pp81) Version: GGNFS-0.77.1-20060513-k8 Total time: 14.59 hours. Scaled time: 28.97 units (timescale=1.985). Factorization parameters were as follows: name: 68881_138 n: 103508606415347412610445012420502440976795110134999813227178254855128575837561314714804310858344623651363750600965347889639 m: 5000000000000000000000000000 deg: 5 c5: 496 c0: -1775 skew: 1.29 type: snfs lss: 1 rlim: 1580000 alim: 1580000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1580000/1580000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [790000, 2090001) Primes: RFBsize:119758, AFBsize:119825, largePrimes:3944588 encountered Relations: rels:4138860, finalFF:373069 Max relations in full relation-set: 28 Initial matrix: 239650 x 373069 with sparse part having weight 41359806. Pruned matrix : 204694 x 205956 with weight 20997592. Total sieving time: 13.95 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.43 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,141,5,0,0,0,0,0,0,0,0,1580000,1580000,26,26,48,48,2.3,2.3,100000 total time: 14.59 hours. --------- CPU info (if available) ----------
Oct 26, 2009 (5th): By Erik Branger / GGNFS, Msieve, YAFU / Oct 26, 2009
(64·10¹³⁸+17)/9 = 7(1)₁₃₇3_<139> = 3 · 293 · 1997 · 8020147355672225249324209607_<28> · C105
C105 = P40 · P66
P40 = 1025076302214321651403303364378397080819_<40>
P66 = 492756070518680163420363928894391737927860973928594193525801851047_<66>

Number: 71113_138 N=505112570660948178612268467748518628903549911512652796501301806603729962592526334904318991700411458767493 ( 105 digits) SNFS difficulty: 140 digits. Divisors found: r1=1025076302214321651403303364378397080819 (pp40) r2=492756070518680163420363928894391737927860973928594193525801851047 (pp66) Version: Msieve-1.40 Total time: 5.34 hours. Scaled time: 5.21 units (timescale=0.977). Factorization parameters were as follows: n: 505112570660948178612268467748518628903549911512652796501301806603729962592526334904318991700411458767493 m: 4000000000000000000000000000 deg: 5 c5: 125 c0: 34 skew: 0.77 type: snfs lss: 1 rlim: 1510000 alim: 1510000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1510000/1510000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [755000, 1505001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 240146 x 240371 Total sieving time: 5.01 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.13 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,140.000,5,0,0,0,0,0,0,0,0,1510000,1510000,26,26,48,48,2.3,2.3,75000 total time: 5.34 hours. --------- CPU info (if available) ----------
(62·10¹³⁵-71)/9 = 6(8)₁₃₄1_<136> = 7² · 19 · 3908604569_<10> · 4071319992583851580553_<22> · 6092834482135211337409_<22> · C80
C80 = P34 · P47
P34 = 3023609198798573489557559745506843_<34>
P47 = 25240472910189074574471536572739850312627201889_<47>

10/25/09 16:58:59 v1.12 @ ERIK-DATOR, starting SIQS on c80: 76317326073273886332452818555423918091234042295879702293589897638297267192026427 10/25/09 16:58:59 v1.12 @ ERIK-DATOR, random seeds: 2974791847, 2559185332 10/25/09 16:58:59 v1.12 @ ERIK-DATOR, ==== sieve params ==== 10/25/09 16:58:59 v1.12 @ ERIK-DATOR, n = 81 digits, 267 bits 10/25/09 16:58:59 v1.12 @ ERIK-DATOR, factor base: 43638 primes (max prime = 1126361) 10/25/09 16:58:59 v1.12 @ ERIK-DATOR, single large prime cutoff: 107004295 (95 * pmax) 10/25/09 16:58:59 v1.12 @ ERIK-DATOR, using 0 large prime slices of factor base 10/25/09 16:58:59 v1.12 @ ERIK-DATOR, buckets hold 1024 elements 10/25/09 16:58:59 v1.12 @ ERIK-DATOR, sieve interval: 14 blocks of size 32768 10/25/09 16:58:59 v1.12 @ ERIK-DATOR, polynomial A has ~ 568396561 factors 10/25/09 16:58:59 v1.12 @ ERIK-DATOR, using multiplier of 2 10/25/09 16:58:59 v1.12 @ ERIK-DATOR, using small prime variation correction of 21 bits 10/25/09 16:58:59 v1.12 @ ERIK-DATOR, using SSE2 for trial division and x64 sieve scanning 10/25/09 16:58:59 v1.12 @ ERIK-DATOR, trial factoring cutoff at 92 bits 10/25/09 16:58:59 v1.12 @ ERIK-DATOR, ==== sieving started ( 2 threads) ==== 10/25/09 17:04:18 v1.12 @ ERIK-DATOR, sieve time = 94.7714, relation time = 39.4308, poly_time = 161.4446 10/25/09 17:04:18 v1.12 @ ERIK-DATOR, 43726 relations found: 22156 full + 21570 from 236834 partial, using 7943760 polys (351 A polys) 10/25/09 17:04:18 v1.12 @ ERIK-DATOR, on average, sieving found 0.03 rels/poly and 811.84 rels/sec 10/25/09 17:04:18 v1.12 @ ERIK-DATOR, trial division touched 4575910 sieve locations out of 7288431575040 10/25/09 17:04:18 v1.12 @ ERIK-DATOR, ==== post processing stage (msieve-1.38) ==== 10/25/09 17:04:26 v1.12 @ ERIK-DATOR, begin with 258990 relations 10/25/09 17:04:26 v1.12 @ ERIK-DATOR, reduce to 62563 relations in 2 passes 10/25/09 17:04:34 v1.12 @ ERIK-DATOR, recovered 62563 relations 10/25/09 17:04:34 v1.12 @ ERIK-DATOR, recovered 44959 polynomials 10/25/09 17:04:34 v1.12 @ ERIK-DATOR, attempting to build 43726 cycles 10/25/09 17:04:34 v1.12 @ ERIK-DATOR, found 43726 cycles in 1 passes 10/25/09 17:04:34 v1.12 @ ERIK-DATOR, distribution of cycle lengths: 10/25/09 17:04:34 v1.12 @ ERIK-DATOR, length 1 : 22156 10/25/09 17:04:34 v1.12 @ ERIK-DATOR, length 2 : 21570 10/25/09 17:04:34 v1.12 @ ERIK-DATOR, largest cycle: 2 relations 10/25/09 17:04:34 v1.12 @ ERIK-DATOR, matrix is 43638 x 43726 (5.7 MB) with weight 1316031 (30.10/col) 10/25/09 17:04:34 v1.12 @ ERIK-DATOR, sparse part has weight 1316031 (30.10/col) 10/25/09 17:04:34 v1.12 @ ERIK-DATOR, filtering completed in 3 passes 10/25/09 17:04:34 v1.12 @ ERIK-DATOR, matrix is 31257 x 31321 (4.5 MB) with weight 1063089 (33.94/col) 10/25/09 17:04:34 v1.12 @ ERIK-DATOR, sparse part has weight 1063089 (33.94/col) 10/25/09 17:04:34 v1.12 @ ERIK-DATOR, saving the first 48 matrix rows for later 10/25/09 17:04:34 v1.12 @ ERIK-DATOR, matrix is 31209 x 31321 (3.8 MB) with weight 875970 (27.97/col) 10/25/09 17:04:34 v1.12 @ ERIK-DATOR, sparse part has weight 800848 (25.57/col) 10/25/09 17:04:34 v1.12 @ ERIK-DATOR, matrix includes 64 packed rows 10/25/09 17:04:34 v1.12 @ ERIK-DATOR, using block size 12528 for processor cache size 2048 kB 10/25/09 17:04:34 v1.12 @ ERIK-DATOR, commencing Lanczos iteration 10/25/09 17:04:34 v1.12 @ ERIK-DATOR, memory use: 3.8 MB 10/25/09 17:04:39 v1.12 @ ERIK-DATOR, lanczos halted after 495 iterations (dim = 31207) 10/25/09 17:04:39 v1.12 @ ERIK-DATOR, recovered 16 nontrivial dependencies 10/25/09 17:04:40 v1.12 @ ERIK-DATOR, prp34 = 3023609198798573489557559745506843 10/25/09 17:04:41 v1.12 @ ERIK-DATOR, prp47 = 25240472910189074574471536572739850312627201889 10/25/09 17:04:41 v1.12 @ ERIK-DATOR, Lanczos elapsed time = 21.1420 seconds. 10/25/09 17:04:41 v1.12 @ ERIK-DATOR, Sqrt elapsed time = 1.4820 seconds. 10/25/09 17:04:41 v1.12 @ ERIK-DATOR, SIQS elapsed time = 341.6886 seconds.
(61·10¹⁴⁸+11)/9 = 6(7)₁₄₇9_<149> = 3² · 17 · 15319 · 159589 · 97217642812415666311_<20> · 268978493809359271513416809599_<30> · C88
C88 = P41 · P48
P41 = 15778348857742482280322540725154142893917_<41>
P48 = 439175725135905508379395921376984663405910180421_<48>

10/25/09 17:09:43 v1.12 @ ERIK-DATOR, starting SIQS on c88: 6929467801046341041659258046990532322098586303429838696777373698294583310076464533399057 10/25/09 17:09:43 v1.12 @ ERIK-DATOR, random seeds: 2974791847, 2559185332 10/25/09 17:09:44 v1.12 @ ERIK-DATOR, ==== sieve params ==== 10/25/09 17:09:44 v1.12 @ ERIK-DATOR, n = 88 digits, 292 bits 10/25/09 17:09:44 v1.12 @ ERIK-DATOR, factor base: 61677 primes (max prime = 1631843) 10/25/09 17:09:44 v1.12 @ ERIK-DATOR, single large prime cutoff: 179502730 (110 * pmax) 10/25/09 17:09:44 v1.12 @ ERIK-DATOR, double large prime range from 43 to 50 bits 10/25/09 17:09:44 v1.12 @ ERIK-DATOR, double large prime cutoff: 719992387123441 10/25/09 17:09:44 v1.12 @ ERIK-DATOR, using 3224628 large prime slices of factor base 10/25/09 17:09:44 v1.12 @ ERIK-DATOR, buckets hold 1024 elements 10/25/09 17:09:44 v1.12 @ ERIK-DATOR, sieve interval: 18 blocks of size 32768 10/25/09 17:09:44 v1.12 @ ERIK-DATOR, polynomial A has ~ 24220 factors 10/25/09 17:09:44 v1.12 @ ERIK-DATOR, using multiplier of 1 10/25/09 17:09:44 v1.12 @ ERIK-DATOR, using small prime variation correction of 18 bits 10/25/09 17:09:44 v1.12 @ ERIK-DATOR, using SSE2 for trial division and x128 sieve scanning 10/25/09 17:09:44 v1.12 @ ERIK-DATOR, trial factoring cutoff at 99 bits 10/25/09 17:09:44 v1.12 @ ERIK-DATOR, ==== sieving started ( 2 threads) ==== 10/25/09 17:41:01 v1.12 @ ERIK-DATOR, sieve time = 533.6376, relation time = 233.5958, poly_time = 958.4928 10/25/09 17:41:01 v1.12 @ ERIK-DATOR, 62052 relations found: 18755 full + 43297 from 625600 partial, using 72681032 polys (751 A polys) 10/25/09 17:41:01 v1.12 @ ERIK-DATOR, on average, sieving found 0.01 rels/poly and 343.14 rels/sec 10/25/09 17:41:01 v1.12 @ ERIK-DATOR, trial division touched 13403412 sieve locations out of 85738034036736 10/25/09 17:41:01 v1.12 @ ERIK-DATOR, ==== post processing stage (msieve-1.38) ==== 10/25/09 17:41:04 v1.12 @ ERIK-DATOR, begin with 644355 relations 10/25/09 17:41:04 v1.12 @ ERIK-DATOR, reduce to 134988 relations in 10 passes 10/25/09 17:41:14 v1.12 @ ERIK-DATOR, recovered 134988 relations 10/25/09 17:41:14 v1.12 @ ERIK-DATOR, recovered 113960 polynomials 10/25/09 17:41:14 v1.12 @ ERIK-DATOR, attempting to build 62052 cycles 10/25/09 17:41:14 v1.12 @ ERIK-DATOR, found 62052 cycles in 5 passes 10/25/09 17:41:14 v1.12 @ ERIK-DATOR, distribution of cycle lengths: 10/25/09 17:41:14 v1.12 @ ERIK-DATOR, length 1 : 18755 10/25/09 17:41:14 v1.12 @ ERIK-DATOR, length 2 : 15491 10/25/09 17:41:14 v1.12 @ ERIK-DATOR, length 3 : 11875 10/25/09 17:41:14 v1.12 @ ERIK-DATOR, length 4 : 7479 10/25/09 17:41:14 v1.12 @ ERIK-DATOR, length 5 : 4105 10/25/09 17:41:14 v1.12 @ ERIK-DATOR, length 6 : 2226 10/25/09 17:41:14 v1.12 @ ERIK-DATOR, length 7 : 1131 10/25/09 17:41:14 v1.12 @ ERIK-DATOR, length 9+: 990 10/25/09 17:41:14 v1.12 @ ERIK-DATOR, largest cycle: 16 relations 10/25/09 17:41:15 v1.12 @ ERIK-DATOR, matrix is 61677 x 62052 (13.1 MB) with weight 3173720 (51.15/col) 10/25/09 17:41:15 v1.12 @ ERIK-DATOR, sparse part has weight 3173720 (51.15/col) 10/25/09 17:41:15 v1.12 @ ERIK-DATOR, filtering completed in 4 passes 10/25/09 17:41:15 v1.12 @ ERIK-DATOR, matrix is 55966 x 56030 (11.9 MB) with weight 2905052 (51.85/col) 10/25/09 17:41:15 v1.12 @ ERIK-DATOR, sparse part has weight 2905052 (51.85/col) 10/25/09 17:41:16 v1.12 @ ERIK-DATOR, saving the first 48 matrix rows for later 10/25/09 17:41:16 v1.12 @ ERIK-DATOR, matrix is 55918 x 56030 (10.4 MB) with weight 2572396 (45.91/col) 10/25/09 17:41:16 v1.12 @ ERIK-DATOR, sparse part has weight 2378132 (42.44/col) 10/25/09 17:41:16 v1.12 @ ERIK-DATOR, matrix includes 64 packed rows 10/25/09 17:41:16 v1.12 @ ERIK-DATOR, using block size 22412 for processor cache size 2048 kB 10/25/09 17:41:16 v1.12 @ ERIK-DATOR, commencing Lanczos iteration 10/25/09 17:41:16 v1.12 @ ERIK-DATOR, memory use: 9.1 MB 10/25/09 17:42:19 v1.12 @ ERIK-DATOR, lanczos halted after 886 iterations (dim = 55914) 10/25/09 17:42:19 v1.12 @ ERIK-DATOR, recovered 14 nontrivial dependencies 10/25/09 17:42:20 v1.12 @ ERIK-DATOR, prp41 = 15778348857742482280322540725154142893917 10/25/09 17:42:22 v1.12 @ ERIK-DATOR, prp48 = 439175725135905508379395921376984663405910180421 10/25/09 17:42:22 v1.12 @ ERIK-DATOR, Lanczos elapsed time = 77.8740 seconds. 10/25/09 17:42:22 v1.12 @ ERIK-DATOR, Sqrt elapsed time = 3.1200 seconds. 10/25/09 17:42:22 v1.12 @ ERIK-DATOR, SIQS elapsed time = 1958.8982 seconds.
(62·10¹²⁹-71)/9 = 6(8)₁₂₈1_<130> = 7 · 74507 · 863695087070633_<15> · 446537572767580550602547_<24> · C86
C86 = P29 · P58
P29 = 27413652247099964745959987129_<29>
P58 = 1249305658838193522558789938622451015178573054392034321111_<58>

Sun Oct 25 17:00:39 2009 Msieve v. 1.43 Sun Oct 25 17:00:39 2009 random seeds: 312f2c38 e5b608c2 Sun Oct 25 17:00:39 2009 factoring 34248030881724345791926751354933118415888088772687415035676269296160679100087812980319 (86 digits) Sun Oct 25 17:00:40 2009 searching for 15-digit factors Sun Oct 25 17:00:41 2009 commencing quadratic sieve (86-digit input) Sun Oct 25 17:00:41 2009 using multiplier of 1 Sun Oct 25 17:00:41 2009 using 64kb Pentium 4 sieve core Sun Oct 25 17:00:41 2009 sieve interval: 8 blocks of size 65536 Sun Oct 25 17:00:41 2009 processing polynomials in batches of 13 Sun Oct 25 17:00:41 2009 using a sieve bound of 1461403 (55559 primes) Sun Oct 25 17:00:41 2009 using large prime bound of 116912240 (26 bits) Sun Oct 25 17:00:41 2009 using double large prime bound of 332772803587280 (41-49 bits) Sun Oct 25 17:00:41 2009 using trial factoring cutoff of 49 bits Sun Oct 25 17:00:41 2009 polynomial 'A' values have 11 factors Sun Oct 25 17:52:41 2009 55902 relations (16079 full + 39823 combined from 580400 partial), need 55655 Sun Oct 25 17:52:43 2009 begin with 596479 relations Sun Oct 25 17:52:44 2009 reduce to 132644 relations in 9 passes Sun Oct 25 17:52:44 2009 attempting to read 132644 relations Sun Oct 25 17:52:48 2009 recovered 132644 relations Sun Oct 25 17:52:48 2009 recovered 108900 polynomials Sun Oct 25 17:52:48 2009 attempting to build 55902 cycles Sun Oct 25 17:52:48 2009 found 55902 cycles in 5 passes Sun Oct 25 17:52:48 2009 distribution of cycle lengths: Sun Oct 25 17:52:48 2009 length 1 : 16079 Sun Oct 25 17:52:48 2009 length 2 : 11136 Sun Oct 25 17:52:48 2009 length 3 : 9863 Sun Oct 25 17:52:48 2009 length 4 : 7144 Sun Oct 25 17:52:48 2009 length 5 : 4967 Sun Oct 25 17:52:48 2009 length 6 : 3039 Sun Oct 25 17:52:48 2009 length 7 : 1735 Sun Oct 25 17:52:48 2009 length 9+: 1939 Sun Oct 25 17:52:48 2009 largest cycle: 18 relations Sun Oct 25 17:52:49 2009 matrix is 55559 x 55902 (12.1 MB) with weight 2954402 (52.85/col) Sun Oct 25 17:52:49 2009 sparse part has weight 2954402 (52.85/col) Sun Oct 25 17:52:50 2009 filtering completed in 3 passes Sun Oct 25 17:52:50 2009 matrix is 50604 x 50668 (11.1 MB) with weight 2695723 (53.20/col) Sun Oct 25 17:52:50 2009 sparse part has weight 2695723 (53.20/col) Sun Oct 25 17:52:50 2009 saving the first 48 matrix rows for later Sun Oct 25 17:52:50 2009 matrix is 50556 x 50668 (6.1 MB) with weight 1989485 (39.27/col) Sun Oct 25 17:52:50 2009 sparse part has weight 1292326 (25.51/col) Sun Oct 25 17:52:50 2009 matrix includes 64 packed rows Sun Oct 25 17:52:50 2009 using block size 20267 for processor cache size 512 kB Sun Oct 25 17:52:50 2009 commencing Lanczos iteration Sun Oct 25 17:52:50 2009 memory use: 7.0 MB Sun Oct 25 17:53:10 2009 lanczos halted after 801 iterations (dim = 50550) Sun Oct 25 17:53:11 2009 recovered 15 nontrivial dependencies Sun Oct 25 17:53:11 2009 prp29 factor: 27413652247099964745959987129 Sun Oct 25 17:53:11 2009 prp58 factor: 1249305658838193522558789938622451015178573054392034321111 Sun Oct 25 17:53:11 2009 elapsed time 00:52:32
(61·10¹²⁶+11)/9 = 6(7)₁₂₅9_<127> = 4583 · 6317 · 17909 · 3879167 · 10801069060460037677_<20> · C90
C90 = P43 · P48
P43 = 2195586039900908690698168329609801270916603_<43>
P48 = 142101798548019649379224996185134551483183791973_<48>

10/25/09 17:45:35 v1.12 @ ERIK-DATOR, starting SIQS on c90: 311996725136843158550452678007225947321786519109975065421192818805281768398691918983827719 10/25/09 17:45:35 v1.12 @ ERIK-DATOR, random seeds: 2974791847, 2559185332 10/25/09 17:45:35 v1.12 @ ERIK-DATOR, ==== sieve params ==== 10/25/09 17:45:35 v1.12 @ ERIK-DATOR, n = 90 digits, 298 bits 10/25/09 17:45:35 v1.12 @ ERIK-DATOR, factor base: 65244 primes (max prime = 1734011) 10/25/09 17:45:35 v1.12 @ ERIK-DATOR, single large prime cutoff: 190741210 (110 * pmax) 10/25/09 17:45:35 v1.12 @ ERIK-DATOR, double large prime range from 43 to 50 bits 10/25/09 17:45:35 v1.12 @ ERIK-DATOR, double large prime cutoff: 803156465804099 10/25/09 17:45:35 v1.12 @ ERIK-DATOR, using 3750192 large prime slices of factor base 10/25/09 17:45:35 v1.12 @ ERIK-DATOR, buckets hold 1024 elements 10/25/09 17:45:35 v1.12 @ ERIK-DATOR, sieve interval: 18 blocks of size 32768 10/25/09 17:45:35 v1.12 @ ERIK-DATOR, polynomial A has ~ 112967 factors 10/25/09 17:45:35 v1.12 @ ERIK-DATOR, using multiplier of 1 10/25/09 17:45:35 v1.12 @ ERIK-DATOR, using small prime variation correction of 19 bits 10/25/09 17:45:35 v1.12 @ ERIK-DATOR, using SSE2 for trial division and x128 sieve scanning 10/25/09 17:45:35 v1.12 @ ERIK-DATOR, trial factoring cutoff at 97 bits 10/25/09 17:45:35 v1.12 @ ERIK-DATOR, ==== sieving started ( 2 threads) ==== 10/25/09 18:24:28 v1.12 @ ERIK-DATOR, sieve time = 658.7142, relation time = 356.6018, poly_time = 1203.0792 10/25/09 18:24:28 v1.12 @ ERIK-DATOR, 65578 relations found: 18773 full + 46805 from 764136 partial, using 103699520 polys (895 A polys) 10/25/09 18:24:28 v1.12 @ ERIK-DATOR, on average, sieving found 0.01 rels/poly and 335.54 rels/sec 10/25/09 18:24:28 v1.12 @ ERIK-DATOR, trial division touched 24098010 sieve locations out of 122328931368960 10/25/09 18:24:28 v1.12 @ ERIK-DATOR, ==== post processing stage (msieve-1.38) ==== 10/25/09 18:24:28 v1.12 @ ERIK-DATOR, begin with 782909 relations 10/25/09 18:24:29 v1.12 @ ERIK-DATOR, reduce to 153559 relations in 9 passes 10/25/09 18:24:38 v1.12 @ ERIK-DATOR, recovered 153559 relations 10/25/09 18:24:38 v1.12 @ ERIK-DATOR, recovered 130881 polynomials 10/25/09 18:24:38 v1.12 @ ERIK-DATOR, attempting to build 65578 cycles 10/25/09 18:24:38 v1.12 @ ERIK-DATOR, found 65578 cycles in 5 passes 10/25/09 18:24:38 v1.12 @ ERIK-DATOR, distribution of cycle lengths: 10/25/09 18:24:38 v1.12 @ ERIK-DATOR, length 1 : 18773 10/25/09 18:24:38 v1.12 @ ERIK-DATOR, length 2 : 13847 10/25/09 18:24:38 v1.12 @ ERIK-DATOR, length 3 : 12128 10/25/09 18:24:38 v1.12 @ ERIK-DATOR, length 4 : 8263 10/25/09 18:24:38 v1.12 @ ERIK-DATOR, length 5 : 5490 10/25/09 18:24:38 v1.12 @ ERIK-DATOR, length 6 : 3283 10/25/09 18:24:38 v1.12 @ ERIK-DATOR, length 7 : 1832 10/25/09 18:24:38 v1.12 @ ERIK-DATOR, length 9+: 1962 10/25/09 18:24:38 v1.12 @ ERIK-DATOR, largest cycle: 17 relations 10/25/09 18:24:39 v1.12 @ ERIK-DATOR, matrix is 65244 x 65578 (15.3 MB) with weight 3744054 (57.09/col) 10/25/09 18:24:39 v1.12 @ ERIK-DATOR, sparse part has weight 3744054 (57.09/col) 10/25/09 18:24:39 v1.12 @ ERIK-DATOR, filtering completed in 4 passes 10/25/09 18:24:39 v1.12 @ ERIK-DATOR, matrix is 60363 x 60427 (14.2 MB) with weight 3485480 (57.68/col) 10/25/09 18:24:39 v1.12 @ ERIK-DATOR, sparse part has weight 3485480 (57.68/col) 10/25/09 18:24:39 v1.12 @ ERIK-DATOR, saving the first 48 matrix rows for later 10/25/09 18:24:39 v1.12 @ ERIK-DATOR, matrix is 60315 x 60427 (12.3 MB) with weight 3066599 (50.75/col) 10/25/09 18:24:39 v1.12 @ ERIK-DATOR, sparse part has weight 2853662 (47.22/col) 10/25/09 18:24:39 v1.12 @ ERIK-DATOR, matrix includes 64 packed rows 10/25/09 18:24:39 v1.12 @ ERIK-DATOR, using block size 24170 for processor cache size 2048 kB 10/25/09 18:24:40 v1.12 @ ERIK-DATOR, commencing Lanczos iteration 10/25/09 18:24:40 v1.12 @ ERIK-DATOR, memory use: 10.5 MB 10/25/09 18:25:48 v1.12 @ ERIK-DATOR, lanczos halted after 955 iterations (dim = 60312) 10/25/09 18:25:49 v1.12 @ ERIK-DATOR, recovered 16 nontrivial dependencies 10/25/09 18:25:49 v1.12 @ ERIK-DATOR, prp48 = 142101798548019649379224996185134551483183791973 10/25/09 18:25:50 v1.12 @ ERIK-DATOR, prp43 = 2195586039900908690698168329609801270916603 10/25/09 18:25:50 v1.12 @ ERIK-DATOR, Lanczos elapsed time = 80.6840 seconds. 10/25/09 18:25:50 v1.12 @ ERIK-DATOR, Sqrt elapsed time = 1.4040 seconds. 10/25/09 18:25:50 v1.12 @ ERIK-DATOR, SIQS elapsed time = 2415.3788 seconds.
(64·10¹⁴⁸+71)/9 = 7(1)₁₄₇9_<149> = 178488573881573_<15> · C135
C135 = P54 · P81
P54 = 975169651366129558075327576737355940889743354566764389_<54>
P81 = 408551555183519006487997988119774128669000839667774060646809837018531358174074727_<81>

Number: 71119_148 N=398407077633402270859097355117764757231141518424162589329272214800757115653354785873245636091652410515292878810302450340483976288496803 ( 135 digits) SNFS difficulty: 150 digits. Divisors found: r1=975169651366129558075327576737355940889743354566764389 (pp54) r2=408551555183519006487997988119774128669000839667774060646809837018531358174074727 (pp81) Version: Msieve-1.40 Total time: 16.08 hours. Scaled time: 15.11 units (timescale=0.940). Factorization parameters were as follows: n: 398407077633402270859097355117764757231141518424162589329272214800757115653354785873245636091652410515292878810302450340483976288496803 m: 400000000000000000000000000000 deg: 5 c5: 125 c0: 142 skew: 1.03 type: snfs lss: 1 rlim: 2200000 alim: 2200000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 Factor base limits: 2200000/2200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1100000, 1900001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 410063 x 410289 Total sieving time: 15.38 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.38 hours. Time per square root: 0.23 hours. Prototype def-par.txt line would be: snfs,150.000,5,0,0,0,0,0,0,0,0,2200000,2200000,27,27,49,49,2.4,2.4,100000 total time: 16.08 hours. --------- CPU info (if available) ----------
(62·10¹³³-71)/9 = 6(8)₁₃₂1_<134> = 43 · 163 · 2767 · 3169 · C124
C124 = P54 · P70
P54 = 660658928585086985809163336350428170481943780205911441_<54>
P70 = 1696619339049209242025102064325212037235881003135077451714444644950863_<70>

Number: 68881_133 N=1120886714752989012233833245860000318452629651590483870856165594382614990996828653825284052587494909528216045838705574523583 ( 124 digits) SNFS difficulty: 136 digits. Divisors found: r1=660658928585086985809163336350428170481943780205911441 (pp54) r2=1696619339049209242025102064325212037235881003135077451714444644950863 (pp70) Version: Msieve v. 1.43 Total time: 7.68 hours. Scaled time: 6.05 units (timescale=0.788). Factorization parameters were as follows: n: 1120886714752989012233833245860000318452629651590483870856165594382614990996828653825284052587494909528216045838705574523583 m: 500000000000000000000000000 deg: 5 c5: 496 c0: -1775 skew: 1.29 type: snfs lss: 1 rlim: 1300000 alim: 1300000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [650000, 1400001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 211824 x 212049 Total sieving time: 7.30 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.23 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,136.000,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,48,48,2.3,2.3,75000 total time: 7.68 hours. --------- CPU info (if available) ----------
Oct 26, 2009 (4th): By Dmitry Domanov / ECMNET, GMP-ECM / Oct 26, 2009
(64·10¹⁸⁷+71)/9 = 7(1)₁₈₆9_<188> = C188
C188 = P40 · C148
P40 = 7275715586058467200945112931785663485369_<40>
C148 = [9773761806656149658840124430630023407923748725432364869224515384214314070359484134600992488023678710746726151284389176767268774084013256015079671751_<148>]

Factor=7275715586058467200945112931785663485369 Method=ECM B1=11000000 Sigma=3065088127
Oct 26, 2009 (3rd): By Robert Backstrom / GGNFS, Msieve, GMP-ECM / Oct 26, 2009
(64·10¹⁴⁵+71)/9 = 7(1)₁₄₄9_<146> = 195178673 · 13433198376877_<14> · C125
C125 = P58 · P67
P58 = 3985975919104421112065980519315938875570010459634054863923_<58>
P67 = 6804418311733872599573710011672467323159706487887800210790835847993_<67>

Number: n N=27122247534084376245588110450780566165130294252738929924863032247137344769809668138430297488719079932927938298601631927656539 ( 125 digits) SNFS difficulty: 146 digits. Divisors found: Mon Oct 26 05:47:24 2009 prp58 factor: 3985975919104421112065980519315938875570010459634054863923 Mon Oct 26 05:47:24 2009 prp67 factor: 6804418311733872599573710011672467323159706487887800210790835847993 Mon Oct 26 05:47:24 2009 elapsed time 00:38:06 (Msieve 1.42 - dependency 6) Version: GGNFS-0.77.1-20051202-athlon Total time: 7.17 hours. Scaled time: 13.11 units (timescale=1.829). Factorization parameters were as follows: name: KA_7_1_144_9 n: 27122247534084376245588110450780566165130294252738929924863032247137344769809668138430297488719079932927938298601631927656539 m: 200000000000000000000000000000 deg: 5 c5: 2 c0: 71 skew: 2.04 type: snfs lss: 1 rlim: 1960000 alim: 1960000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 qintsize: 20000 Factor base limits: 1960000/1960000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved special-q in [980000, 2260327) Primes: RFBsize:146186, AFBsize:145537, largePrimes:3949671 encountered Relations: rels:3857064, finalFF:293739 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 617581 hash collisions in 4330650 relations Msieve: matrix is 336970 x 337195 (89.4 MB) Total sieving time: 7.09 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1960000,1960000,26,26,49,49,2.3,2.3,100000 total time: 7.17 hours. --------- CPU info (if available) ----------
(61·10¹³⁴+11)/9 = 6(7)₁₃₃9_<135> = 7 · 956689 · 147489889 · C120
C120 = P40 · P81
P40 = 1605024511121898730823739355562491316477_<40>
P81 = 427537867971104787643044373647126483897763339452030506462774083723736087616393641_<81>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 686208757526421347401301256515966628463717052016141591646519249049878232120521785773458876968529245559700231093141322757 (120 digits) Using B1=2118000, B2=2854078510, polynomial Dickson(6), sigma=3579718577 Step 1 took 18312ms Step 2 took 7875ms ********** Factor found in step 2: 1605024511121898730823739355562491316477 Found probable prime factor of 40 digits: 1605024511121898730823739355562491316477 Probable prime cofactor 427537867971104787643044373647126483897763339452030506462774083723736087616393641 has 81 digits
Oct 26, 2009 (2nd): By Wataru Sakai / GMP-ECM 6.2.1 / Oct 26, 2009
(26·10¹⁹²-11)/3 = 8(6)₁₉₁3_<193> = 19 · 31 · C191
C191 = P39 · P153
P39 = 101077267653156631307592584180426757637_<39>
P153 = 145573828899862454232548939907903440117030008911903381461583149437913645824448129191836349310485548267196198682523833675203109703598164258322341355722791_<153>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=97527106 Step 1 took 69743ms Step 2 took 21801ms ********** Factor found in step 2: 101077267653156631307592584180426757637 Found probable prime factor of 39 digits: 101077267653156631307592584180426757637 Probable prime cofactor 145573828899862454232548939907903440117030008911903381461583149437913645824448129191836349310485548267196198682523833675203109703598164258322341355722791 has 153 digits
(26·10¹⁸⁹-11)/3 = 8(6)₁₈₈3_<190> = 71 · C189
C189 = P39 · P150
P39 = 141538917737574835614928365545711650133_<39>
P150 = 862418122525500258553228011718122233569703757701307710205000528958821534542694199458423775010924655490594982609345756497272737613083229460774392256541_<150>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=4145718496 Step 1 took 70088ms Step 2 took 21780ms ********** Factor found in step 2: 141538917737574835614928365545711650133 Found probable prime factor of 39 digits: 141538917737574835614928365545711650133 Probable prime cofactor 862418122525500258553228011718122233569703757701307710205000528958821534542694199458423775010924655490594982609345756497272737613083229460774392256541 has 150 digits
Oct 26, 2009: Factorizations of 677...779 and Factorizations of 688...881 have been extended up to n=150. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.
Oct 25, 2009 (8th): By Jo Yeong Uk / GMP-ECM v6.2.3, YAFU v1.10, GGNFS, Msieve v1.39 / Oct 25, 2009
(83·10¹⁴¹+7)/9 = 9(2)₁₄₀3_<142> = 61 · 91303 · 45529459 · 61880267 · C120
C120 = P32 · P35 · P54
P32 = 90583254195064513964951551233389_<32>
P35 = 32008672599379556241790724929001261_<35>
P54 = 202703127076465420436501533853575825089948645698619413_<54>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 587727526365835134078809853742617748922618069947582969642059147943446920904864207550850301733379285639847576970969808477 (120 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=8461231021 Step 1 took 4243ms Step 2 took 4087ms ********** Factor found in step 2: 90583254195064513964951551233389 Found probable prime factor of 32 digits: 90583254195064513964951551233389 Composite cofactor 6488258029461010918009232216393658197894504657730103080991528610887031948984672636079793 has 88 digits 10/24/09 23:23:31 v1.10 @ 조영욱-PC, starting SIQS on c88: 6488258029461010918009232216393658197894504657730103080991528610887031948984672636079793 10/24/09 23:23:31 v1.10 @ 조영욱-PC, random seeds: 170176739, 2015898184 10/24/09 23:23:31 v1.10 @ 조영욱-PC, ==== sieve params ==== 10/24/09 23:23:31 v1.10 @ 조영욱-PC, n = 88 digits, 292 bits 10/24/09 23:23:31 v1.10 @ 조영욱-PC, factor base: 61677 primes (max prime = 1636883) 10/24/09 23:23:31 v1.10 @ 조영욱-PC, single large prime cutoff: 180057130 (110 * pmax) 10/24/09 23:23:31 v1.10 @ 조영욱-PC, double large prime range from 43 to 50 bits 10/24/09 23:23:31 v1.10 @ 조영욱-PC, double large prime cutoff: 724000026774137 10/24/09 23:23:31 v1.10 @ 조영욱-PC, using 15 large prime slices of factor base 10/24/09 23:23:31 v1.10 @ 조영욱-PC, buckets hold 1024 elements 10/24/09 23:23:31 v1.10 @ 조영욱-PC, sieve interval: 9 blocks of size 65536 10/24/09 23:23:31 v1.10 @ 조영욱-PC, polynomial A has ~ 11 factors 10/24/09 23:23:31 v1.10 @ 조영욱-PC, using multiplier of 1 10/24/09 23:23:31 v1.10 @ 조영욱-PC, using small prime variation correction of 18 bits 10/24/09 23:23:31 v1.10 @ 조영욱-PC, using SSE2 for trial division and x128 sieve scanning 10/24/09 23:23:31 v1.10 @ 조영욱-PC, trial factoring cutoff at 99 bits 10/24/09 23:23:31 v1.10 @ 조영욱-PC, ==== sieving started ==== 10/24/09 23:59:49 v1.10 @ 조영욱-PC, sieve time = 1044.0410, relation time = 341.2810, poly_time = 792.4710 10/24/09 23:59:49 v1.10 @ 조영욱-PC, 61780 relations found: 20672 full + 41108 from 551741 partial, using 422103 polys (412 A polys) 10/24/09 23:59:49 v1.10 @ 조영욱-PC, on average, sieving found 1.36 rels/poly and 262.74 rels/sec 10/24/09 23:59:49 v1.10 @ 조영욱-PC, trial division touched 11670223 sieve locations out of 497932959744 10/24/09 23:59:49 v1.10 @ 조영욱-PC, ==== post processing stage (msieve-1.38) ==== 10/24/09 23:59:50 v1.10 @ 조영욱-PC, begin with 572413 relations 10/24/09 23:59:50 v1.10 @ 조영욱-PC, reduce to 125508 relations in 9 passes 10/24/09 23:59:51 v1.10 @ 조영욱-PC, recovered 125508 relations 10/24/09 23:59:51 v1.10 @ 조영욱-PC, recovered 108512 polynomials 10/24/09 23:59:51 v1.10 @ 조영욱-PC, attempting to build 61780 cycles 10/24/09 23:59:51 v1.10 @ 조영욱-PC, found 61780 cycles in 4 passes 10/24/09 23:59:51 v1.10 @ 조영욱-PC, distribution of cycle lengths: 10/24/09 23:59:51 v1.10 @ 조영욱-PC, length 1 : 20672 10/24/09 23:59:51 v1.10 @ 조영욱-PC, length 2 : 17282 10/24/09 23:59:51 v1.10 @ 조영욱-PC, length 3 : 11476 10/24/09 23:59:51 v1.10 @ 조영욱-PC, length 4 : 6357 10/24/09 23:59:51 v1.10 @ 조영욱-PC, length 5 : 3343 10/24/09 23:59:51 v1.10 @ 조영욱-PC, length 6 : 1500 10/24/09 23:59:51 v1.10 @ 조영욱-PC, length 7 : 675 10/24/09 23:59:51 v1.10 @ 조영욱-PC, length 9+: 475 10/24/09 23:59:51 v1.10 @ 조영욱-PC, largest cycle: 15 relations 10/24/09 23:59:51 v1.10 @ 조영욱-PC, matrix is 61677 x 61780 (13.0 MB) with weight 2901214 (46.96/col) 10/24/09 23:59:51 v1.10 @ 조영욱-PC, sparse part has weight 2901214 (46.96/col) 10/24/09 23:59:51 v1.10 @ 조영욱-PC, filtering completed in 3 passes 10/24/09 23:59:51 v1.10 @ 조영욱-PC, matrix is 55117 x 55181 (11.8 MB) with weight 2649715 (48.02/col) 10/24/09 23:59:51 v1.10 @ 조영욱-PC, sparse part has weight 2649715 (48.02/col) 10/24/09 23:59:52 v1.10 @ 조영욱-PC, saving the first 48 matrix rows for later 10/24/09 23:59:52 v1.10 @ 조영욱-PC, matrix is 55069 x 55181 (8.3 MB) with weight 2124201 (38.50/col) 10/24/09 23:59:52 v1.10 @ 조영욱-PC, sparse part has weight 1633043 (29.59/col) 10/24/09 23:59:52 v1.10 @ 조영욱-PC, matrix includes 64 packed rows 10/24/09 23:59:52 v1.10 @ 조영욱-PC, using block size 22072 for processor cache size 4096 kB 10/24/09 23:59:52 v1.10 @ 조영욱-PC, commencing Lanczos iteration 10/24/09 23:59:52 v1.10 @ 조영욱-PC, memory use: 7.6 MB 10/25/09 00:00:04 v1.10 @ 조영욱-PC, lanczos halted after 872 iterations (dim = 55067) 10/25/09 00:00:04 v1.10 @ 조영욱-PC, recovered 15 nontrivial dependencies 10/25/09 00:00:04 v1.10 @ 조영욱-PC, prp35 = 32008672599379556241790724929001261 10/25/09 00:00:05 v1.10 @ 조영욱-PC, prp54 = 202703127076465420436501533853575825089948645698619413 10/25/09 00:00:05 v1.10 @ 조영욱-PC, Lanczos elapsed time = 14.2900 seconds. 10/25/09 00:00:05 v1.10 @ 조영욱-PC, Sqrt elapsed time = 0.9510 seconds. 10/25/09 00:00:05 v1.10 @ 조영욱-PC, SIQS elapsed time = 2193.8590 seconds. 10/25/09 00:00:05 v1.10 @ 조영욱-PC, 10/25/09 00:00:05 v1.10 @ 조영욱-PC,
(2·10¹⁹¹+1)/3 = (6)₁₉₀7_<191> = 107 · 434363 · C184
C184 = P50 · P51 · P84
P50 = 15883788275518933823378174648633065329129145471009_<50>
P51 = 129154159023019835829280546025015851553267122632403_<51>
P84 = 699213257067203864864521928555707071916884215419505461497175542943038439663014948481_<84>

Number: 66667_191 N=1434406152231100789889456270633080821191497646465831588396179221102111192683398311573427864141340128230028944236263102878843823887829783153004453694834093105998031722221970005807121587 ( 184 digits) SNFS difficulty: 191 digits. Divisors found: r1=15883788275518933823378174648633065329129145471009 r2=129154159023019835829280546025015851553267122632403 r3=699213257067203864864521928555707071916884215419505461497175542943038439663014948481 Version: Total time: 149.38 hours. Scaled time: 353.14 units (timescale=2.364). Factorization parameters were as follows: n: 1434406152231100789889456270633080821191497646465831588396179221102111192683398311573427864141340128230028944236263102878843823887829783153004453694834093105998031722221970005807121587 m: 100000000000000000000000000000000000000 deg: 5 c5: 20 c0: 1 skew: 0.55 type: snfs lss: 1 rlim: 10000000 alim: 10000000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5 Factor base limits: 10000000/10000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [5000000, 8700001) Primes: rational ideals reading, algebraic ideals reading, Relations: 21632821 Max relations in full relation-set: Initial matrix: Pruned matrix : 1981244 x 1981491 Total sieving time: 133.97 hours. Total relation processing time: 4.32 hours. Matrix solve time: 10.51 hours. Time per square root: 0.59 hours. Prototype def-par.txt line would be: snfs,191,5,0,0,0,0,0,0,0,0,10000000,10000000,28,28,55,55,2.5,2.5,100000 total time: 149.38 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
(64·10¹⁴⁶+71)/9 = 7(1)₁₄₅9_<147> = 29 · 43 · 2942688563887_<13> · C132
C132 = P38 · P94
P38 = 20922248714492232747363242068574188327_<38>
P94 = 9262289457946675998505921238040544871349507594919771113867620230027339113642857153369700991273_<94>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 193787923704779801177073863032680063432689263509288681043015945411329156407124011875072237800285489154167790197935985497233285470271 (132 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=5589003022 Step 1 took 3281ms Step 2 took 2185ms ********** Factor found in step 2: 20922248714492232747363242068574188327 Found probable prime factor of 38 digits: 20922248714492232747363242068574188327 Probable prime cofactor 9262289457946675998505921238040544871349507594919771113867620230027339113642857153369700991273 has 94 digits
(26·10¹⁴⁹-11)/3 = 8(6)₁₄₈3_<150> = 7 · 367 · 437964631187_<12> · 2462434045223432635184577368617_<31> · C105
C105 = P32 · P74
P32 = 14879455248887629252872247910309_<32>
P74 = 21023126856417165892087401739868084915754062458746846717606000991769788457_<74>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 312812675251746883894906550322388849288538455287149121253041175155208857123669318024554523653217239503213 (105 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=7586851862 Step 1 took 2674ms Step 2 took 1850ms ********** Factor found in step 2: 14879455248887629252872247910309 Found probable prime factor of 32 digits: 14879455248887629252872247910309 Probable prime cofactor 21023126856417165892087401739868084915754062458746846717606000991769788457 has 74 digits
(64·10¹⁴⁷+71)/9 = 7(1)₁₄₆9_<148> = 3³ · 7 · 23 · 1361 · 34037098252908254717_<20> · C122
C122 = P31 · P43 · P49
P31 = 9092679240857687203699489343863_<31>
P43 = 1133692009344949981305377259795459982489171_<43>
P49 = 3425706994020588576485113095334514017387044260077_<49>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 35313207866128717054296738530445351859223418556327577583962195210110904762886801944682119343082073509336326076720727163121 (122 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=7176917761 Step 1 took 4196ms Step 2 took 16ms ********** Factor found in step 2: 9092679240857687203699489343863 Found probable prime factor of 31 digits: 9092679240857687203699489343863 Composite cofactor 3883696645478249614182960181405500086959054640731065811210010188998322859496291566360126167 has 91 digits 10/25/09 09:34:43 v1.10 @ 조영욱-PC, starting SIQS on c91: 3883696645478249614182960181405500086959054640731065811210010188998322859496291566360126167 10/25/09 09:34:43 v1.10 @ 조영욱-PC, random seeds: 2850916953, 456782072 10/25/09 09:34:44 v1.10 @ 조영욱-PC, ==== sieve params ==== 10/25/09 09:34:44 v1.10 @ 조영욱-PC, n = 91 digits, 304 bits 10/25/09 09:34:44 v1.10 @ 조영욱-PC, factor base: 68495 primes (max prime = 1822187) 10/25/09 09:34:44 v1.10 @ 조영욱-PC, single large prime cutoff: 218662440 (120 * pmax) 10/25/09 09:34:44 v1.10 @ 조영욱-PC, double large prime range from 43 to 50 bits 10/25/09 09:34:44 v1.10 @ 조영욱-PC, double large prime cutoff: 1027054623429564 10/25/09 09:34:44 v1.10 @ 조영욱-PC, using 16 large prime slices of factor base 10/25/09 09:34:44 v1.10 @ 조영욱-PC, buckets hold 1024 elements 10/25/09 09:34:44 v1.10 @ 조영욱-PC, sieve interval: 11 blocks of size 65536 10/25/09 09:34:44 v1.10 @ 조영욱-PC, polynomial A has ~ 12 factors 10/25/09 09:34:44 v1.10 @ 조영욱-PC, using multiplier of 7 10/25/09 09:34:44 v1.10 @ 조영욱-PC, using small prime variation correction of 21 bits 10/25/09 09:34:44 v1.10 @ 조영욱-PC, using SSE2 for trial division and x128 sieve scanning 10/25/09 09:34:44 v1.10 @ 조영욱-PC, trial factoring cutoff at 96 bits 10/25/09 09:34:44 v1.10 @ 조영욱-PC, ==== sieving started ==== 10/25/09 10:24:05 v1.10 @ 조영욱-PC, sieve time = 1336.7250, relation time = 691.6450, poly_time = 932.2880 10/25/09 10:24:05 v1.10 @ 조영욱-PC, 68584 relations found: 19869 full + 48715 from 829684 partial, using 424594 polys (207 A polys) 10/25/09 10:24:05 v1.10 @ 조영욱-PC, on average, sieving found 2.00 rels/poly and 286.83 rels/sec 10/25/09 10:24:05 v1.10 @ 조영욱-PC, trial division touched 25510065 sieve locations out of 612176232448 10/25/09 10:24:05 v1.10 @ 조영욱-PC, ==== post processing stage (msieve-1.38) ==== 10/25/09 10:24:06 v1.10 @ 조영욱-PC, begin with 849553 relations 10/25/09 10:24:06 v1.10 @ 조영욱-PC, reduce to 159157 relations in 9 passes 10/25/09 10:24:07 v1.10 @ 조영욱-PC, recovered 159157 relations 10/25/09 10:24:07 v1.10 @ 조영욱-PC, recovered 132584 polynomials 10/25/09 10:24:08 v1.10 @ 조영욱-PC, attempting to build 68584 cycles 10/25/09 10:24:08 v1.10 @ 조영욱-PC, found 68584 cycles in 5 passes 10/25/09 10:24:08 v1.10 @ 조영욱-PC, distribution of cycle lengths: 10/25/09 10:24:08 v1.10 @ 조영욱-PC, length 1 : 19869 10/25/09 10:24:08 v1.10 @ 조영욱-PC, length 2 : 14935 10/25/09 10:24:08 v1.10 @ 조영욱-PC, length 3 : 12558 10/25/09 10:24:08 v1.10 @ 조영욱-PC, length 4 : 8791 10/25/09 10:24:08 v1.10 @ 조영욱-PC, length 5 : 5600 10/25/09 10:24:08 v1.10 @ 조영욱-PC, length 6 : 3169 10/25/09 10:24:08 v1.10 @ 조영욱-PC, length 7 : 1793 10/25/09 10:24:08 v1.10 @ 조영욱-PC, length 9+: 1869 10/25/09 10:24:08 v1.10 @ 조영욱-PC, largest cycle: 16 relations 10/25/09 10:24:08 v1.10 @ 조영욱-PC, matrix is 68495 x 68584 (16.9 MB) with weight 3885812 (56.66/col) 10/25/09 10:24:08 v1.10 @ 조영욱-PC, sparse part has weight 3885812 (56.66/col) 10/25/09 10:24:08 v1.10 @ 조영욱-PC, filtering completed in 3 passes 10/25/09 10:24:08 v1.10 @ 조영욱-PC, matrix is 63408 x 63471 (15.8 MB) with weight 3643439 (57.40/col) 10/25/09 10:24:08 v1.10 @ 조영욱-PC, sparse part has weight 3643439 (57.40/col) 10/25/09 10:24:08 v1.10 @ 조영욱-PC, saving the first 48 matrix rows for later 10/25/09 10:24:08 v1.10 @ 조영욱-PC, matrix is 63360 x 63471 (10.5 MB) with weight 2826606 (44.53/col) 10/25/09 10:24:08 v1.10 @ 조영욱-PC, sparse part has weight 2120045 (33.40/col) 10/25/09 10:24:08 v1.10 @ 조영욱-PC, matrix includes 64 packed rows 10/25/09 10:24:08 v1.10 @ 조영욱-PC, using block size 25388 for processor cache size 4096 kB 10/25/09 10:24:09 v1.10 @ 조영욱-PC, commencing Lanczos iteration 10/25/09 10:24:09 v1.10 @ 조영욱-PC, memory use: 9.4 MB 10/25/09 10:24:26 v1.10 @ 조영욱-PC, lanczos halted after 1004 iterations (dim = 63356) 10/25/09 10:24:26 v1.10 @ 조영욱-PC, recovered 15 nontrivial dependencies 10/25/09 10:24:29 v1.10 @ 조영욱-PC, prp49 = 3425706994020588576485113095334514017387044260077 10/25/09 10:24:30 v1.10 @ 조영욱-PC, prp43 = 1133692009344949981305377259795459982489171 10/25/09 10:24:30 v1.10 @ 조영욱-PC, Lanczos elapsed time = 20.9670 seconds. 10/25/09 10:24:30 v1.10 @ 조영욱-PC, Sqrt elapsed time = 3.5410 seconds. 10/25/09 10:24:30 v1.10 @ 조영욱-PC, SIQS elapsed time = 2986.4140 seconds. 10/25/09 10:24:30 v1.10 @ 조영욱-PC, 10/25/09 10:24:30 v1.10 @ 조영욱-PC,
(83·10¹⁴⁴+7)/9 = 9(2)₁₄₃3_<145> = 89 · 607 · 530743 · 26578672453_<11> · C125
C125 = P37 · P88
P37 = 7620243200305720178433627196673681023_<37>
P88 = 1588073113575697728528935879433186144051276413419026749657921230265554117895252647777853_<88>

Number: 92223_144 N=12101503345313544296726077856879492583269902651699773591285503600604622679901120704345584900671105410790856437888630685783619 ( 125 digits) SNFS difficulty: 146 digits. Divisors found: r1=7620243200305720178433627196673681023 r2=1588073113575697728528935879433186144051276413419026749657921230265554117895252647777853 Version: Total time: 7.02 hours. Scaled time: 16.72 units (timescale=2.383). Factorization parameters were as follows: n: 12101503345313544296726077856879492583269902651699773591285503600604622679901120704345584900671105410790856437888630685783619 m: 100000000000000000000000000000 deg: 5 c5: 83 c0: 70 skew: 0.97 type: snfs lss: 1 rlim: 2550000 alim: 2550000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 2550000/2550000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [1275000, 1950001) Primes: rational ideals reading, algebraic ideals reading, Relations: 4760461 Max relations in full relation-set: Initial matrix: Pruned matrix : 349434 x 349682 Total sieving time: 6.52 hours. Total relation processing time: 0.21 hours. Matrix solve time: 0.25 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,2550000,2550000,26,26,49,49,2.3,2.3,75000 total time: 7.02 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
(64·10¹⁴⁵+17)/9 = 7(1)₁₄₄3_<146> = 73 · 7109 · 9487363 · 211475533 · 146365173826136249057_<21> · C105
C105 = P49 · P57
P49 = 1169813637472724608879846874031360720284904573943_<49>
P57 = 398883444547249357116524080979030956658275082357933999821_<57>

Number: 71113_145 N=466619293193467609106637409577082544935587703521242296864100906176497819573361078885346853164715843264203 ( 105 digits) Divisors found: r1=1169813637472724608879846874031360720284904573943 r2=398883444547249357116524080979030956658275082357933999821 Version: Total time: 4.96 hours. Scaled time: 11.85 units (timescale=2.387). Factorization parameters were as follows: name: 71113_145 n: 466619293193467609106637409577082544935587703521242296864100906176497819573361078885346853164715843264203 skew: 6309.61 # norm 1.33e+14 c5: 31200 c4: -790565510 c3: -11376259783517 c2: 23289595609209357 c1: 16856853205610039493 c0: 20770263123537894491952 # alpha -4.99 Y1: 71362036229 Y0: -108383474337977239085 # Murphy_E 1.96e-09 # M 165076693542715147816953182526660278637643445471452452355295693622258007479330605559673783801438412873209 type: gnfs rlim: 2000000 alim: 2000000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1000000, 1800001) Primes: rational ideals reading, algebraic ideals reading, Relations: 7220317 Max relations in full relation-set: Initial matrix: Pruned matrix : 288024 x 288272 Polynomial selection time: 0.33 hours. Total sieving time: 3.86 hours. Total relation processing time: 0.53 hours. Matrix solve time: 0.18 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: gnfs,104,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2000000,2000000,27,27,50,50,2.6,2.6,50000 total time: 4.96 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
(59·10¹⁵³+13)/9 = 6(5)₁₅₂7_<154> = 61 · 14431 · C148
C148 = P36 · C113
P36 = 448464904859558179943943527591218691_<36>
C113 = [16605607864965677941097681100617903499359254644723048816511846628405008244182350794304630346346316241452961808797_<113>]

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 7447032351296963794422021303813801976341409324366096615273307980605908223025744390838433603837316927647284313432212252034333595998999825688954624727 (148 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3255258886 Step 1 took 4664ms Step 2 took 4586ms ********** Factor found in step 2: 448464904859558179943943527591218691 Found probable prime factor of 36 digits: 448464904859558179943943527591218691 Composite cofactor 16605607864965677941097681100617903499359254644723048816511846628405008244182350794304630346346316241452961808797 has 113 digits
Oct 25, 2009 (7th): By Sinkiti Sibata / GGNFS, Msieve / Oct 25, 2009
(26·10¹²⁸-11)/3 = 8(6)₁₂₇3_<129> = 534716673012120673637_<21> · C109
C109 = P53 · P56
P53 = 28231457338923355714210349805249384803656629093653461_<53>
P56 = 57410994463621940343419240971956483368602008129962515759_<56>

Number: 86663_128 N=1620796040984907771562505445804590777389195101791022914125100946213000619690680554239828560158443812097391899 ( 109 digits) SNFS difficulty: 130 digits. Divisors found: r1=28231457338923355714210349805249384803656629093653461 (pp53) r2=57410994463621940343419240971956483368602008129962515759 (pp56) Version: GGNFS-0.77.1-20060513-k8 Total time: 4.82 hours. Scaled time: 9.40 units (timescale=1.949). Factorization parameters were as follows: name: 86663_128 n: 1620796040984907771562505445804590777389195101791022914125100946213000619690680554239828560158443812097391899 m: 50000000000000000000000000 deg: 5 c5: 208 c0: -275 skew: 1.06 type: snfs lss: 1 rlim: 1060000 alim: 1060000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1060000/1060000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [530000, 980001) Primes: RFBsize:82832, AFBsize:83234, largePrimes:2781623 encountered Relations: rels:2702185, finalFF:229580 Max relations in full relation-set: 28 Initial matrix: 166133 x 229580 with sparse part having weight 17710428. Pruned matrix : 146994 x 147888 with weight 8493934. Total sieving time: 4.56 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.13 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,130,5,0,0,0,0,0,0,0,0,1060000,1060000,26,26,47,47,2.3,2.3,50000 total time: 4.82 hours. --------- CPU info (if available) ----------
(64·10¹³⁹+17)/9 = 7(1)₁₃₈3_<140> = 113 · 2066992703_<10> · 732894075941_<12> · 3316020366531589_<16> · C102
C102 = P41 · P61
P41 = 35340792430636249735607064473287711611151_<41>
P61 = 3544748225760749980193652509393545530287763093943914933592433_<61>

Number: 71113_139 N=125274211265476789012584372600934384359407136184462238841338702440456197293391775672309177070812020383 ( 102 digits) SNFS difficulty: 141 digits. Divisors found: r1=35340792430636249735607064473287711611151 (pp41) r2=3544748225760749980193652509393545530287763093943914933592433 (pp61) Version: GGNFS-0.77.1-20060513-k8 Total time: 8.57 hours. Scaled time: 16.96 units (timescale=1.979). Factorization parameters were as follows: name: 71113_139 n: 125274211265476789012584372600934384359407136184462238841338702440456197293391775672309177070812020383 m: 20000000000000000000000000000 deg: 5 c5: 1 c0: 85 skew: 2.43 type: snfs lss: 1 rlim: 1600000 alim: 1600000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1600000/1600000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [800000, 1500001) Primes: RFBsize:121127, AFBsize:121640, largePrimes:3807169 encountered Relations: rels:4056948, finalFF:533305 Max relations in full relation-set: 28 Initial matrix: 242831 x 533305 with sparse part having weight 45727150. Pruned matrix : 171742 x 173020 with weight 14020652. Total sieving time: 8.12 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.29 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,141,5,0,0,0,0,0,0,0,0,1600000,1600000,26,26,48,48,2.3,2.3,100000 total time: 8.57 hours. --------- CPU info (if available) ----------
(59·10¹⁶²+13)/9 = 6(5)₁₆₁7_<163> = 73² · 97 · 727 · 110119 · 187420399057_<12> · 2334523065937_<13> · 382716642977363_<15> · 12076827793624644509443_<23> · C89
C89 = P29 · P61
P29 = 69516819691144244489845582123_<29>
P61 = 1126834753234250582167665892728317395683413561745942050448631_<61>

Sun Oct 25 15:43:55 2009 Msieve v. 1.42 Sun Oct 25 15:43:55 2009 random seeds: eca55479 eedbe34a Sun Oct 25 15:43:55 2009 factoring 78333968362300416510181956690557714648145208117374814352621832119111721264997885503423613 (89 digits) Sun Oct 25 15:43:56 2009 no P-1/P+1/ECM available, skipping Sun Oct 25 15:43:56 2009 commencing quadratic sieve (89-digit input) Sun Oct 25 15:43:56 2009 using multiplier of 1 Sun Oct 25 15:43:56 2009 using 64kb Pentium 4 sieve core Sun Oct 25 15:43:56 2009 sieve interval: 17 blocks of size 65536 Sun Oct 25 15:43:56 2009 processing polynomials in batches of 6 Sun Oct 25 15:43:56 2009 using a sieve bound of 1565017 (59333 primes) Sun Oct 25 15:43:56 2009 using large prime bound of 125201360 (26 bits) Sun Oct 25 15:43:56 2009 using double large prime bound of 376440425084800 (42-49 bits) Sun Oct 25 15:43:56 2009 using trial factoring cutoff of 49 bits Sun Oct 25 15:43:56 2009 polynomial 'A' values have 11 factors Sun Oct 25 17:47:06 2009 59646 relations (15545 full + 44101 combined from 638233 partial), need 59429 Sun Oct 25 17:47:08 2009 begin with 653778 relations Sun Oct 25 17:47:09 2009 reduce to 147069 relations in 10 passes Sun Oct 25 17:47:09 2009 attempting to read 147069 relations Sun Oct 25 17:47:12 2009 recovered 147069 relations Sun Oct 25 17:47:12 2009 recovered 125914 polynomials Sun Oct 25 17:47:13 2009 attempting to build 59646 cycles Sun Oct 25 17:47:13 2009 found 59646 cycles in 5 passes Sun Oct 25 17:47:13 2009 distribution of cycle lengths: Sun Oct 25 17:47:13 2009 length 1 : 15545 Sun Oct 25 17:47:13 2009 length 2 : 11194 Sun Oct 25 17:47:13 2009 length 3 : 10420 Sun Oct 25 17:47:13 2009 length 4 : 8120 Sun Oct 25 17:47:13 2009 length 5 : 5800 Sun Oct 25 17:47:13 2009 length 6 : 3610 Sun Oct 25 17:47:13 2009 length 7 : 2239 Sun Oct 25 17:47:13 2009 length 9+: 2718 Sun Oct 25 17:47:13 2009 largest cycle: 18 relations Sun Oct 25 17:47:13 2009 matrix is 59333 x 59646 (14.8 MB) with weight 3630587 (60.87/col) Sun Oct 25 17:47:13 2009 sparse part has weight 3630587 (60.87/col) Sun Oct 25 17:47:14 2009 filtering completed in 3 passes Sun Oct 25 17:47:14 2009 matrix is 55723 x 55787 (13.9 MB) with weight 3413972 (61.20/col) Sun Oct 25 17:47:15 2009 sparse part has weight 3413972 (61.20/col) Sun Oct 25 17:47:15 2009 saving the first 48 matrix rows for later Sun Oct 25 17:47:15 2009 matrix is 55675 x 55787 (10.3 MB) with weight 2849057 (51.07/col) Sun Oct 25 17:47:15 2009 sparse part has weight 2368968 (42.46/col) Sun Oct 25 17:47:15 2009 matrix includes 64 packed rows Sun Oct 25 17:47:15 2009 using block size 21845 for processor cache size 512 kB Sun Oct 25 17:47:15 2009 commencing Lanczos iteration Sun Oct 25 17:47:15 2009 memory use: 9.7 MB Sun Oct 25 17:47:48 2009 lanczos halted after 881 iterations (dim = 55671) Sun Oct 25 17:47:48 2009 recovered 14 nontrivial dependencies Sun Oct 25 17:47:51 2009 prp29 factor: 69516819691144244489845582123 Sun Oct 25 17:47:51 2009 prp61 factor: 1126834753234250582167665892728317395683413561745942050448631 Sun Oct 25 17:47:51 2009 elapsed time 02:03:56
(26·10¹³⁹-11)/3 = 8(6)₁₃₈3_<140> = 1693 · 6888904706941_<13> · C124
C124 = P61 · P63
P61 = 8870595788892487911104375936030780894093930167133280256610899_<61>
P63 = 837707045164910241217663948652115615923423788814338069923561749_<63>

Number: 86663_139 N=7430960587165421962000123662758431206353926455170965852483838812840294402028743639310757689822470021911230605916761692902351 ( 124 digits) SNFS difficulty: 141 digits. Divisors found: r1=8870595788892487911104375936030780894093930167133280256610899 (pp61) r2=837707045164910241217663948652115615923423788814338069923561749 (pp63) Version: Msieve-1.40 Total time: 6.51 hours. Scaled time: 13.48 units (timescale=2.071). Factorization parameters were as follows: name: 86663_139 n: 7430960587165421962000123662758431206353926455170965852483838812840294402028743639310757689822470021911230605916761692902351 m: 10000000000000000000000000000 deg: 5 c5: 13 c0: -55 skew: 1.33 type: snfs lss: 1 rlim: 1570000 alim: 1570000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1570000/1570000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [785000, 1585001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 229759 x 229996 Total sieving time: 6.20 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.18 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,141.000,5,0,0,0,0,0,0,0,0,1570000,1570000,26,26,48,48,2.3,2.3,100000 total time: 6.51 hours. --------- CPU info (if available) ----------
(64·10¹⁴¹+17)/9 = 7(1)₁₄₀3_<142> = 3 · 3631 · 23774027 · 38210935379_<11> · C120
C120 = P47 · P74
P47 = 23562641469567864876337026588185070376527483949_<47>
P74 = 30498295302175290423634367739758902230843046755702055066361643029047633073_<74>

SNFS difficulty: 142 digits. Divisors found: r1=23562641469567864876337026588185070376527483949 (pp47) r2=30498295302175290423634367739758902230843046755702055066361643029047633073 (pp74) Version: GGNFS-0.77.1-20060513-k8 Total time: 10.53 hours. Scaled time: 20.20 units (timescale=1.919). Factorization parameters were as follows: name: 71113_141 n: 718620397638162294733305621236272925576662114980663962005049956604711481492309440291240165113252665825820512650449045277 m: 20000000000000000000000000000 deg: 5 c5: 20 c0: 17 skew: 0.97 type: snfs lss: 1 rlim: 1680000 alim: 1680000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1680000/1680000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [840000, 1740001) Primes: RFBsize:126753, AFBsize:126821, largePrimes:3769249 encountered Relations: rels:3815360, finalFF:333077 Max relations in full relation-set: 28 Initial matrix: 253640 x 333077 with sparse part having weight 30096722. Pruned matrix : 227339 x 228671 with weight 17309106. Total sieving time: 9.84 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.49 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,142,5,0,0,0,0,0,0,0,0,1680000,1680000,26,26,48,48,2.3,2.3,100000 total time: 10.53 hours. --------- CPU info (if available) ----------
Oct 25, 2009 (6th): By Norbert Schneider / Msieve / Oct 25, 2009
(26·10¹⁴⁷-11)/3 = 8(6)₁₄₆3_<148> = 31 · 79 · 167 · 1353459067381824712130681_<25> · 21398446694347252792235023_<26> · C93
C93 = P42 · P52
P42 = 126483774862839140088316862326098266953543_<42>
P52 = 5784750647104411502104764644569097235027045860205329_<52>

Sat Oct 24 19:10:22 2009 Sat Oct 24 19:10:22 2009 Sat Oct 24 19:10:22 2009 Msieve v. 1.43 Sat Oct 24 19:10:22 2009 random seeds: b616bf80 3a42ab57 Sat Oct 24 19:10:22 2009 factoring 731677098486017412808124512800179508883325488052549521445809992284550135852428581537284030647 (93 digits) Sat Oct 24 19:10:24 2009 searching for 15-digit factors Sat Oct 24 19:10:24 2009 commencing quadratic sieve (93-digit input) Sat Oct 24 19:10:25 2009 using multiplier of 47 Sat Oct 24 19:10:25 2009 using 64kb Pentium 4 sieve core Sat Oct 24 19:10:25 2009 sieve interval: 18 blocks of size 65536 Sat Oct 24 19:10:25 2009 processing polynomials in batches of 6 Sat Oct 24 19:10:25 2009 using a sieve bound of 1956901 (72705 primes) Sat Oct 24 19:10:25 2009 using large prime bound of 244612625 (27 bits) Sat Oct 24 19:10:25 2009 using double large prime bound of 1256787622996125 (42-51 bits) Sat Oct 24 19:10:25 2009 using trial factoring cutoff of 51 bits Sat Oct 24 19:10:25 2009 polynomial 'A' values have 12 factors Sat Oct 24 23:59:39 2009 73218 relations (18983 full + 54235 combined from 989961 partial), need 72801 Sat Oct 24 23:59:45 2009 begin with 1008944 relations Sat Oct 24 23:59:47 2009 reduce to 185654 relations in 13 passes Sat Oct 24 23:59:47 2009 attempting to read 185654 relations Sat Oct 24 23:59:53 2009 recovered 185654 relations Sat Oct 24 23:59:53 2009 recovered 166490 polynomials Sat Oct 24 23:59:53 2009 attempting to build 73218 cycles Sat Oct 24 23:59:54 2009 found 73218 cycles in 6 passes Sat Oct 24 23:59:54 2009 distribution of cycle lengths: Sat Oct 24 23:59:54 2009 length 1 : 18983 Sat Oct 24 23:59:54 2009 length 2 : 13497 Sat Oct 24 23:59:54 2009 length 3 : 12531 Sat Oct 24 23:59:54 2009 length 4 : 9663 Sat Oct 24 23:59:54 2009 length 5 : 7152 Sat Oct 24 23:59:54 2009 length 6 : 4604 Sat Oct 24 23:59:54 2009 length 7 : 2958 Sat Oct 24 23:59:54 2009 length 9+: 3830 Sat Oct 24 23:59:54 2009 largest cycle: 21 relations Sat Oct 24 23:59:54 2009 matrix is 72705 x 73218 (19.0 MB) with weight 4700937 (64.20/col) Sat Oct 24 23:59:54 2009 sparse part has weight 4700937 (64.20/col) Sat Oct 24 23:59:58 2009 filtering completed in 3 passes Sat Oct 24 23:59:58 2009 matrix is 68396 x 68460 (17.8 MB) with weight 4402031 (64.30/col) Sat Oct 24 23:59:58 2009 sparse part has weight 4402031 (64.30/col) Sat Oct 24 23:59:58 2009 saving the first 48 matrix rows for later Sat Oct 24 23:59:58 2009 matrix is 68348 x 68460 (11.8 MB) with weight 3524777 (51.49/col) Sat Oct 24 23:59:58 2009 sparse part has weight 2669452 (38.99/col) Sat Oct 24 23:59:58 2009 matrix includes 64 packed rows Sat Oct 24 23:59:59 2009 using block size 10922 for processor cache size 256 kB Sun Oct 25 00:00:00 2009 commencing Lanczos iteration Sun Oct 25 00:00:00 2009 memory use: 11.6 MB Sun Oct 25 00:00:23 2009 linear algebra at 35.2%, ETA 0h 0m Sun Oct 25 00:01:04 2009 lanczos halted after 1082 iterations (dim = 68345) Sun Oct 25 00:01:04 2009 recovered 16 nontrivial dependencies Sun Oct 25 00:01:05 2009 prp42 factor: 126483774862839140088316862326098266953543 Sun Oct 25 00:01:05 2009 prp52 factor: 5784750647104411502104764644569097235027045860205329 Sun Oct 25 00:01:05 2009 elapsed time 04:50:43
Oct 25, 2009 (5th): By Dmitry Domanov / GGNFS/msieve, ECMNET, GMP-ECM / Oct 25, 2009
(64·10¹⁵⁰+17)/9 = 7(1)₁₄₉3_<151> = 3 · 163 · 593 · C146
C146 = P45 · P102
P45 = 181460493643859860267546457615776892302547113_<45>
P102 = 135142461223855023769374585953390591400230384542853999743362412572020686220483774158288305519116127913_<102>

Number: s146 N=24523017725926922173521041707139225218245278456950417140363239536622253182532101204961466292537377485494060256886274122123861930812137207816865169 ( 146 digits) SNFS difficulty: 151 digits. Divisors found: r1=181460493643859860267546457615776892302547113 (pp45) r2=135142461223855023769374585953390591400230384542853999743362412572020686220483774158288305519116127913 (pp102) Version: Msieve-1.40 Total time: 11.57 hours. Scaled time: 21.45 units (timescale=1.855). Factorization parameters were as follows: n: 24523017725926922173521041707139225218245278456950417140363239536622253182532101204961466292537377485494060256886274122123861930812137207816865169 m: 2000000000000000000000000000000 deg: 5 c5: 2 c0: 17 skew: 1.53 type: snfs lss: 1 rlim: 2400000 alim: 2400000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1200000, 1900001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 385402 x 385626 Total sieving time: 11.29 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.19 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,151.000,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,49,49,2.4,2.4,100000 total time: 11.57 hours. --------- CPU info (if available) ----------
(64·10¹⁵⁰+71)/9 = 7(1)₁₄₉9_<151> = 3 · 37589 · 1608992995552909_<16> · 38743674467950353459894799_<26> · C106
C106 = P47 · P59
P47 = 60033171818637036837946345942978850104908263861_<47>
P59 = 16850360145293193596749837297116847910388052640299429895407_<59>

Number: gnfs106 N=1011580565808300035324835095269093337415387040964529896988277350606665747712644305132003455465229187986427 ( 106 digits) Divisors found: r1=60033171818637036837946345942978850104908263861 (pp47) r2=16850360145293193596749837297116847910388052640299429895407 (pp59) Version: Msieve-1.40 Total time: 7.46 hours. Scaled time: 14.39 units (timescale=1.928). Factorization parameters were as follows: name: gnfs106 n: 1011580565808300035324835095269093337415387040964529896988277350606665747712644305132003455465229187986427 skew: 12656.69 # norm 7.40e+014 c5: 92400 c4: 839948774 c3: -73701608093115 c2: -18833223482297583 c1: 3377810069304610720235 c0: 488844492386143255374089 # alpha -6.62 Y1: 273354832543 Y0: -101827148467019791260 # Murphy_E 1.89e-009 # M 301070719605173866416940685340759894911051254330603743674021012391945810541977611780615421200839662171667 type: gnfs rlim: 2500000 alim: 2500000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 150000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1250000, 2150001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 241887 x 242112 Polynomial selection time: 0.85 hours. Total sieving time: 6.35 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.16 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: gnfs,105,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 7.46 hours. --------- CPU info (if available) ----------
(83·10¹⁵⁷+7)/9 = 9(2)₁₅₆3_<158> = 3³ · 23 · 139 · 677 · C151
C151 = P36 · P40 · P76
P36 = 626045116755851438475264246925740973_<36>
P40 = 1012848459600439964833165666804565900201_<40>
P76 = 2488802357902899188563060987762312568445426174233937076223149292666541768377_<76>

Number: s151 N=1578121780566208685648783175796566047694410946908300383814237710890474095105303759855938548409399934460792588239638370389847815575334517088184990675021 ( 151 digits) SNFS difficulty: 161 digits. Divisors found: r1=626045116755851438475264246925740973 (pp36) r2=1012848459600439964833165666804565900201 (pp40) r3=2488802357902899188563060987762312568445426174233937076223149292666541768377 (pp76) Version: Msieve-1.40 Total time: 25.44 hours. Scaled time: 49.04 units (timescale=1.928). Factorization parameters were as follows: n: 1578121780566208685648783175796566047694410946908300383814237710890474095105303759855938548409399934460792588239638370389847815575334517088184990675021 m: 50000000000000000000000000000000 deg: 5 c5: 332 c0: 875 skew: 1.21 type: snfs lss: 1 rlim: 3400000 alim: 3400000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4Factor base limits: 3400000/3400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1700000, 3200001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 703919 x 704146 Total sieving time: 24.62 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.59 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: snfs,161.000,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000 total time: 25.44 hours. --------- CPU info (if available) ----------
(26·10¹⁹⁴-11)/3 = 8(6)₁₉₃3_<195> = C195
C195 = P39 · C157
P39 = 195721309769165290517468167522075066993_<39>
C157 = [4428064923992271188897172141909552065313113376249145079122632080472355721315498754192989009423534511274168794443365639986065578670493920034925645440231447191_<157>]

Factor=195721309769165290517468167522075066993 Method=ECM B1=11000000 Sigma=1337364280
Oct 25, 2009 (4th): By Robert Backstrom / GGNFS, Msieve / Oct 25, 2009
(64·10¹⁴⁶+17)/9 = 7(1)₁₄₅3_<147> = 131 · 409831 · C140
C140 = P46 · P94
P46 = 2851884250413709181276276969836114316460554033_<46>
P94 = 4644398416732077928294402657397906910999332994134532480822741775205785263948309822994189042901_<94>

Number: n N=13245286697324579779982501279220476135398858805552173350901633259539081117631248358192387495398840924415131962718930283162354169988465569733 ( 140 digits) SNFS difficulty: 147 digits. Divisors found: Sun Oct 25 04:44:32 2009 prp46 factor: 2851884250413709181276276969836114316460554033 Sun Oct 25 04:44:32 2009 prp94 factor: 4644398416732077928294402657397906910999332994134532480822741775205785263948309822994189042901 Sun Oct 25 04:44:32 2009 elapsed time 00:02:10 (Msieve 1.42 - dependency 1) Version: GGNFS-0.77.1-20051202-athlon Total time: 7.35 hours. Scaled time: 13.44 units (timescale=1.829). Factorization parameters were as follows: name: KA_7_1_145_3 n: 13245286697324579779982501279220476135398858805552173350901633259539081117631248358192387495398840924415131962718930283162354169988465569733 m: 200000000000000000000000000000 deg: 5 c5: 20 c0: 17 skew: 0.97 type: snfs lss: 1 rlim: 2000000 alim: 2000000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 qintsize: 20000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved special-q in [1000000, 2300323) Primes: RFBsize:148933, AFBsize:148990, largePrimes:3965971 encountered Relations: rels:3886206, finalFF:306420 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 553406 hash collisions in 4547224 relations Msieve: matrix is 338967 x 339192 (89.4 MB) Total sieving time: 7.26 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,147,5,0,0,0,0,0,0,0,0,2000000,2000000,26,26,49,49,2.3,2.3,100000 total time: 7.35 hours. --------- CPU info (if available) ----------
(83·10¹³⁸+7)/9 = 9(2)₁₃₇3_<139> = 29 · 296315088385031_<15> · C124
C124 = P50 · P74
P50 = 93988310201234862601570372294932527271313227418747_<50>
P74 = 11418524212125215153704901048888926793883689926626226465167573286606626391_<74>

Number: n N=1073207795689535631622836147825278952552729693717888979960708463097569132782518985104571996377844886200285553772238738352077 ( 124 digits) SNFS difficulty: 141 digits. Divisors found: Sun Oct 25 18:47:01 2009 prp50 factor: 93988310201234862601570372294932527271313227418747 Sun Oct 25 18:47:01 2009 prp74 factor: 11418524212125215153704901048888926793883689926626226465167573286606626391 Sun Oct 25 18:47:01 2009 elapsed time 00:20:23 (Msieve 1.42 - dependency 2) Version: GGNFS-0.77.1-20051202-athlon Total time: 5.21 hours. Scaled time: 9.50 units (timescale=1.823). Factorization parameters were as follows: name: KA_9_2_137_3 n: 1073207795689535631622836147825278952552729693717888979960708463097569132782518985104571996377844886200285553772238738352077 m: 5000000000000000000000000000 deg: 5 c5: 664 c0: 175 skew: 0.77 type: snfs lss: 1 rlim: 1590000 alim: 1590000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 qintsize: 20000 Factor base limits: 1590000/1590000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved special-q in [795000, 1787953) Primes: RFBsize:120451, AFBsize:120228, largePrimes:3468598 encountered Relations: rels:3326883, finalFF:241527 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 497871 hash collisions in 3752395 relations Msieve: matrix is 266381 x 266606 (71.1 MB) Total sieving time: 5.14 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,141,5,0,0,0,0,0,0,0,0,1590000,1590000,26,26,48,48,2.3,2.3,100000 total time: 5.21 hours. --------- CPU info (if available) ----------
Oct 25, 2009 (3rd): By Serge Batalov / Msieve / Oct 25, 2009
(26·10¹¹⁹-11)/3 = 8(6)₁₁₈3_<120> = 7 · 17 · 71 · 3803 · C113
C113 = P55 · P59
P55 = 1274995380145892465903774193098344924077906451577513651_<55>
P59 = 21154942370976421697486933878627177564197928329200354011079_<59>

SNFS difficulty: 121 digits. Divisors found: r1=1274995380145892465903774193098344924077906451577513651 (pp55) r2=21154942370976421697486933878627177564197928329200354011079 (pp59) Version: Msieve v. 1.44 SVN130 Total time: 0.74 hours. Scaled time: 1.77 units (timescale=2.400). Factorization parameters were as follows: n: 26972453790247530461781583895312188568657048061416609249055660677236196149119949520845251137975605926059727739429 m: 1000000000000000000000000 deg: 5 c5: 13 c0: -55 skew: 1.33 type: snfs lss: 1 rlim: 730000 alim: 730000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 name: 86663_119 Factor base limits: 730000/730000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [456250, 706251) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 76157 x 76382 Total sieving time: 0.70 hours. Total relation processing time: 0.01 hours. Matrix solve time: 0.02 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,121.000,5,0,0,0,0,0,0,0,0,730000,730000,25,25,46,46,2.2,2.2,50000 total time: 0.74 hours.
(83·10¹¹⁸+7)/9 = 9(2)₁₁₇3_<119> = 3 · 1092919 · C113
C113 = P42 · P71
P42 = 705070381600235455186991830596638083559201_<42>
P71 = 39892741314093663141511170138983554044263787963680068665654734350406339_<71>

SNFS difficulty: 121 digits. Divisors found: r1=705070381600235455186991830596638083559201 (pp42) r2=39892741314093663141511170138983554044263787963680068665654734350406339 (pp71) Version: Msieve v. 1.44 SVN130 Total time: 1.05 hours. Scaled time: 2.52 units (timescale=2.400). Factorization parameters were as follows: name: 92223_118 n: 28127190341407497482192862179851151586476894207842246992449340473301992865656778535958054293813851475489712175139 m: 500000000000000000000000 deg: 5 c5: 664 c0: 175 skew: 0.77 type: snfs lss: 1 rlim: 740000 alim: 740000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 740000/740000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [462500, 812501) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 88790 x 89015 Total sieving time: 0.96 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.06 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,121.000,5,0,0,0,0,0,0,0,0,740000,740000,25,25,46,46,2.2,2.2,50000 total time: 1.05 hours.
Oct 25, 2009 (2nd): By Erik Branger / GGNFS, Msieve / Oct 25, 2009
(64·10¹³⁵+71)/9 = 7(1)₁₃₄9_<136> = 3 · 7 · 17 · 47 · 59 · 71705902740581_<14> · C117
C117 = P44 · P73
P44 = 49396726635866252941349225764082311779594253_<44>
P73 = 2027992294691125275972524809223849871442123743225447567390794349798850103_<73>

Number: 71119_135 N=1001761810005006313080634948875632238963927787480139812249508104174234067865331438566434001609614270508832793072 58059 ( 117 digits) SNFS difficulty: 136 digits. Divisors found: r1=49396726635866252941349225764082311779594253 (pp44) r2=2027992294691125275972524809223849871442123743225447567390794349798850103 (pp73) Version: Msieve-1.40 Total time: 4.15 hours. Scaled time: 4.18 units (timescale=1.006). Factorization parameters were as follows: n: 100176181000500631308063494887563223896392778748013981224950810417423406786533143856643400160961427050883279307258 059 m: 2000000000000000000000000000 deg: 5 c5: 2 c0: 71 skew: 2.04 type: snfs lss: 1 rlim: 1330000 alim: 1330000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1330000/1330000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [665000, 1265001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 183913 x 184139 Total sieving time: 3.98 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.09 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,136.000,5,0,0,0,0,0,0,0,0,1330000,1330000,26,26,48,48,2.3,2.3,75000 total time: 4.15 hours. --------- CPU info (if available) ----------
Oct 25, 2009: Factorizations of 655...557 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.
Oct 24, 2009 (12th): By Dmitry Domanov / GGNFS/msieve, ECMNET, GMP-ECM / Oct 24, 2009
(83·10¹⁵³+7)/9 = 9(2)₁₅₂3_<154> = 19 · C153
C153 = P41 · P50 · P63
P41 = 11845787618552744408592793547872783337647_<41>
P50 = 99267096564836654377879865186188878175450767609761_<50>
P63 = 412774367410497933703892824746397001142527586353054293958148251_<63>

Number: s153 N=485380116959064327485380116959064327485380116959064327485380116959064327485380116959064327485380116959064327485380116959064327485380116959064327485380117 ( 153 digits) SNFS difficulty: 156 digits. Divisors found: r1=11845787618552744408592793547872783337647 (pp41) r2=99267096564836654377879865186188878175450767609761 (pp50) r3=412774367410497933703892824746397001142527586353054293958148251 (pp63) Version: Msieve-1.40 Total time: 19.76 hours. Scaled time: 37.09 units (timescale=1.877). Factorization parameters were as follows: n: 485380116959064327485380116959064327485380116959064327485380116959064327485380116959064327485380116959064327485380116959064327485380116959064327485380117 m: 5000000000000000000000000000000 deg: 5 c5: 664 c0: 175 skew: 0.77 type: snfs lss: 1 rlim: 2800000 alim: 2800000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1400000, 2600001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 496610 x 496839 Total sieving time: 19.17 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.30 hours. Time per square root: 0.22 hours. Prototype def-par.txt line would be: snfs,156.000,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000 total time: 19.76 hours. --------- CPU info (if available) ----------
(64·10¹⁷⁰+17)/9 = 7(1)₁₆₉3_<171> = C171
C171 = P41 · C131
P41 = 20144781073759431713450953582651849027061_<41>
C131 = [35300016838475530194639813738214629072622370366721985133667932037689576825363959054040956101074677617174755632664566964527186992133_<131>]

Factor=20144781073759431713450953582651849027061 Method=ECM B1=11000000 Sigma=2496299565
(64·10¹⁴⁷+17)/9 = 7(1)₁₄₆3_<148> = 3 · 57503 · 216157 · C138
C138 = P48 · P91
P48 = 107549954987785579928593402880636566882663688597_<48>
P91 = 1773152830631860446188329106257338288543867985415407300744686996376641282910154550813699133_<91>

Number: s138 N=190702507120921179029693498224047177003466422091042164816733207692270771454237644049874031134578027075937711938152210610862622491960886401 ( 138 digits) SNFS difficulty: 149 digits. Divisors found: r1=107549954987785579928593402880636566882663688597 (pp48) r2=1773152830631860446188329106257338288543867985415407300744686996376641282910154550813699133 (pp91) Version: Msieve-1.40 Total time: 6.95 hours. Scaled time: 13.17 units (timescale=1.894). Factorization parameters were as follows: n: 190702507120921179029693498224047177003466422091042164816733207692270771454237644049874031134578027075937711938152210610862622491960886401 m: 400000000000000000000000000000 deg: 5 c5: 25 c0: 68 skew: 1.22 type: snfs lss: 1 rlim: 2200000 alim: 2200000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3Factor base limits: 2200000/2200000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [1100000, 2300001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 324891 x 325117 Total sieving time: 6.76 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.13 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,149.000,5,0,0,0,0,0,0,0,0,2200000,2200000,26,26,49,49,2.3,2.3,100000 total time: 6.95 hours. --------- CPU info (if available) ----------
Oct 24, 2009 (11th): By Erik Branger / GGNFS, Msieve / Oct 24, 2009
(26·10¹³⁴-11)/3 = 8(6)₁₃₃3_<135> = 79 · 971 · C131
C131 = P40 · P91
P40 = 5793892158320044697483839891106768191867_<40>
P91 = 1950003382206205302748093895603935525675119062485432522884303420606445893015445347133372321_<91>

Number: 86663_134 N=11298109304862097885080846662929599742750741981601463539697645213295267395829259495843599403807462835738526987272245325407275113307 ( 131 digits) SNFS difficulty: 136 digits. Divisors found: r1=5793892158320044697483839891106768191867 (pp40) r2=1950003382206205302748093895603935525675119062485432522884303420606445893015445347133372321 (pp91) Version: Msieve-1.40 Total time: 3.59 hours. Scaled time: 3.70 units (timescale=1.029). Factorization parameters were as follows: n: 11298109304862097885080846662929599742750741981601463539697645213295267395829259495843599403807462835738526987272245325407275113307 m: 1000000000000000000000000000 deg: 5 c5: 13 c0: -55 skew: 1.33 type: snfs lss: 1 rlim: 1300000 alim: 1300000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [650000, 1175001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 190282 x 190507 Total sieving time: 3.43 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.10 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,136.000,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,48,48,2.3,2.3,75000 total time: 3.59 hours. --------- CPU info (if available) ----------
(83·10¹²²+7)/9 = 9(2)₁₂₁3_<123> = 13 · 108887 · 128563 · 1114283 · C106
C106 = P50 · P57
P50 = 15088320696223135169809198089153969811751774911547_<50>
P57 = 301414255803061414574888662754994760101373439276969078791_<57>

Number: 92223_122 N=4547834953970025762840857831440101814378063031264673061402797428646893129342321038178952983343358098699677 ( 106 digits) SNFS difficulty: 126 digits. Divisors found: r1=15088320696223135169809198089153969811751774911547 (pp50) r2=301414255803061414574888662754994760101373439276969078791 (pp57) Version: Msieve v. 1.41 Total time: 3.72 hours. Scaled time: 2.90 units (timescale=0.780). Factorization parameters were as follows: n: 4547834953970025762840857831440101814378063031264673061402797428646893129342321038178952983343358098699677 m: 5000000000000000000000000 deg: 5 c5: 332 c0: 875 skew: 1.21 type: snfs lss: 1 rlim: 880000 alim: 880000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 880000/880000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [440000, 790001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 114621 x 114866 Total sieving time: 3.38 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.09 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: snfs,126.000,5,0,0,0,0,0,0,0,0,880000,880000,26,26,46,46,2.3,2.3,50000 total time: 3.72 hours. --------- CPU info (if available) ----------
(61·10¹³⁵-43)/9 = 6(7)₁₃₄3_<136> = 13 · 113 · 2237 · 2689 · 48222969881785793_<17> · C110
C110 = P36 · P74
P36 = 344359163910943223401461453853061057_<36>
P74 = 46189487683276597744389391866230132568115599033739994894011952870193891269_<74>

Number: 67773_135 N=15905773360087939094211704956938899126912493543414565319868815848987679577477410100590419453658538537876211333 ( 110 digits) SNFS difficulty: 136 digits. Divisors found: r1=344359163910943223401461453853061057 (pp36) r2=46189487683276597744389391866230132568115599033739994894011952870193891269 (pp74) Version: Msieve-1.40 Total time: 4.16 hours. Scaled time: 4.09 units (timescale=0.982). Factorization parameters were as follows: n: 15905773360087939094211704956938899126912493543414565319868815848987679577477410100590419453658538537876211333 m: 1000000000000000000000000000 deg: 5 c5: 61 c0: -43 skew: 0.93 type: snfs lss: 1 rlim: 1330000 alim: 1330000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1330000/1330000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [665000, 1265001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 222182 x 222426 Total sieving time: 3.99 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.11 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,136.000,5,0,0,0,0,0,0,0,0,1330000,1330000,26,26,48,48,2.3,2.3,75000 total time: 4.16 hours. --------- CPU info (if available) ----------
Oct 24, 2009 (10th): By Sinkiti Sibata / GGNFS, Msieve / Oct 24, 2009
(26·10¹²²-11)/3 = 8(6)₁₂₁3_<123> = 29 · 173 · 694609010965955053_<18> · C102
C102 = P39 · P64
P39 = 120746948127208544826323464254407158937_<39>
P64 = 2059640468687729008837858895651778106818536471694582461670919699_<64>

Number: 86663_122 N=248695300833336709755409333590044888311569315534462185870771869373467855384404691791683714454457199963 ( 102 digits) SNFS difficulty: 124 digits. Divisors found: r1=120746948127208544826323464254407158937 (pp39) r2=2059640468687729008837858895651778106818536471694582461670919699 (pp64) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 3.28 hours. Scaled time: 1.54 units (timescale=0.469). Factorization parameters were as follows: name: 86663_122 n: 248695300833336709755409333590044888311569315534462185870771869373467855384404691791683714454457199963 m: 2000000000000000000000000 deg: 5 c5: 325 c0: -44 skew: 0.67 type: snfs lss: 1 rlim: 820000 alim: 820000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 820000/820000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [410000, 710001) Primes: RFBsize:65416, AFBsize:65484, largePrimes:1429398 encountered Relations: rels:1437565, finalFF:182524 Max relations in full relation-set: 28 Initial matrix: 130967 x 182524 with sparse part having weight 8950961. Pruned matrix : 108472 x 109190 with weight 4019574. Total sieving time: 3.09 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.10 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,124,5,0,0,0,0,0,0,0,0,820000,820000,25,25,46,46,2.2,2.2,50000 total time: 3.28 hours. --------- CPU info (if available) ----------
(61·10¹³²-43)/9 = 6(7)₁₃₁3_<133> = C133
C133 = P64 · P70
P64 = 4725606646772188984100152280396967524259863324041339868262971543_<64>
P70 = 1434266176683858768188100131193185398372991118836079821228326791155611_<70>

Number: 67773_132 N=6777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777773 ( 133 digits) SNFS difficulty: 134 digits. Divisors found: r1=4725606646772188984100152280396967524259863324041339868262971543 (pp64) r2=1434266176683858768188100131193185398372991118836079821228326791155611 (pp70) Version: Msieve-1.40 Total time: 5.14 hours. Scaled time: 10.57 units (timescale=2.058). Factorization parameters were as follows: name: 67773_132 n: 6777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777773 m: 200000000000000000000000000 deg: 5 c5: 1525 c0: -344 skew: 0.74 type: snfs lss: 1 rlim: 1230000 alim: 1230000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1230000/1230000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [615000, 1290001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 209854 x 210102 Total sieving time: 4.89 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.15 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,134.000,5,0,0,0,0,0,0,0,0,1230000,1230000,26,26,47,47,2.3,2.3,75000 total time: 5.14 hours. --------- CPU info (if available) ----------
Oct 24, 2009 (9th): By Norbert Schneider / Msieve / Oct 24, 2009
(26·10¹⁸⁴-11)/3 = 8(6)₁₈₃3_<185> = 997 · 3359 · 7535765227_<10> · 71533389013_<11> · 7870346972320838175697646839916923_<34> · 343812931207218909137926438686226411_<36> · C89
C89 = P39 · P50
P39 = 876770922639554917353142630986272212417_<39>
P50 = 20235248676411114188095713258897648593212272464731_<50>

Sat Oct 24 11:22:12 2009 Sat Oct 24 11:22:12 2009 Sat Oct 24 11:22:12 2009 Msieve v. 1.43 Sat Oct 24 11:22:12 2009 random seeds: 38021554 97df5c5b Sat Oct 24 11:22:12 2009 factoring 17741677651857805032606358886945695648559407609858617356573827167385163195236452972764827 (89 digits) Sat Oct 24 11:22:14 2009 searching for 15-digit factors Sat Oct 24 11:22:14 2009 commencing quadratic sieve (89-digit input) Sat Oct 24 11:22:15 2009 using multiplier of 3 Sat Oct 24 11:22:15 2009 using 64kb Pentium 4 sieve core Sat Oct 24 11:22:15 2009 sieve interval: 15 blocks of size 65536 Sat Oct 24 11:22:15 2009 processing polynomials in batches of 7 Sat Oct 24 11:22:15 2009 using a sieve bound of 1533841 (58667 primes) Sat Oct 24 11:22:15 2009 using large prime bound of 122707280 (26 bits) Sat Oct 24 11:22:15 2009 using double large prime bound of 363050102703040 (42-49 bits) Sat Oct 24 11:22:15 2009 using trial factoring cutoff of 49 bits Sat Oct 24 11:22:15 2009 polynomial 'A' values have 11 factors Sat Oct 24 13:21:58 2009 59137 relations (15514 full + 43623 combined from 623536 partial), need 58763 Sat Oct 24 13:22:00 2009 begin with 639050 relations Sat Oct 24 13:22:01 2009 reduce to 143799 relations in 11 passes Sat Oct 24 13:22:01 2009 attempting to read 143799 relations Sat Oct 24 13:22:03 2009 recovered 143799 relations Sat Oct 24 13:22:03 2009 recovered 121653 polynomials Sat Oct 24 13:22:03 2009 attempting to build 59137 cycles Sat Oct 24 13:22:03 2009 found 59137 cycles in 5 passes Sat Oct 24 13:22:03 2009 distribution of cycle lengths: Sat Oct 24 13:22:03 2009 length 1 : 15514 Sat Oct 24 13:22:03 2009 length 2 : 11441 Sat Oct 24 13:22:03 2009 length 3 : 10453 Sat Oct 24 13:22:03 2009 length 4 : 7982 Sat Oct 24 13:22:03 2009 length 5 : 5575 Sat Oct 24 13:22:03 2009 length 6 : 3626 Sat Oct 24 13:22:03 2009 length 7 : 2155 Sat Oct 24 13:22:03 2009 length 9+: 2391 Sat Oct 24 13:22:03 2009 largest cycle: 17 relations Sat Oct 24 13:22:04 2009 matrix is 58667 x 59137 (14.2 MB) with weight 3493263 (59.07/col) Sat Oct 24 13:22:04 2009 sparse part has weight 3493263 (59.07/col) Sat Oct 24 13:22:06 2009 filtering completed in 3 passes Sat Oct 24 13:22:06 2009 matrix is 54726 x 54790 (13.2 MB) with weight 3244734 (59.22/col) Sat Oct 24 13:22:06 2009 sparse part has weight 3244734 (59.22/col) Sat Oct 24 13:22:06 2009 saving the first 48 matrix rows for later Sat Oct 24 13:22:06 2009 matrix is 54678 x 54790 (8.9 MB) with weight 2562127 (46.76/col) Sat Oct 24 13:22:06 2009 sparse part has weight 2001405 (36.53/col) Sat Oct 24 13:22:06 2009 matrix includes 64 packed rows Sat Oct 24 13:22:06 2009 using block size 10922 for processor cache size 256 kB Sat Oct 24 13:22:07 2009 commencing Lanczos iteration Sat Oct 24 13:22:07 2009 memory use: 8.9 MB Sat Oct 24 13:22:36 2009 lanczos halted after 867 iterations (dim = 54676) Sat Oct 24 13:22:37 2009 recovered 16 nontrivial dependencies Sat Oct 24 13:22:38 2009 prp39 factor: 876770922639554917353142630986272212417 Sat Oct 24 13:22:38 2009 prp50 factor: 20235248676411114188095713258897648593212272464731 Sat Oct 24 13:22:38 2009 elapsed time 02:00:26
Oct 24, 2009 (8th): By Jo Yeong Uk / GMP-ECM / Oct 24, 2009
(26·10¹³³-11)/3 = 8(6)₁₃₂3_<134> = 8009 · 80177 · 32126005968869790559_<20> · C106
C106 = P45 · P61
P45 = 550163656152061301729216721644787738922797889_<45>
P61 = 7636166060905673296895325749165505687838183112138994178407041_<61>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 4201141039052149243603287764147523672856402177150099821931686403318057752296883188700119512080564817536449 (106 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3051414086 Step 1 took 3463ms Step 2 took 3744ms ********** Factor found in step 2: 550163656152061301729216721644787738922797889 Found probable prime factor of 45 digits: 550163656152061301729216721644787738922797889 Probable prime cofactor 7636166060905673296895325749165505687838183112138994178407041 has 61 digits
(26·10¹³⁷-11)/3 = 8(6)₁₃₆3_<138> = 7 · 23 · 1621 · 12781 · 818398784008789836734085037_<27> · C102
C102 = P34 · P69
P34 = 2800432686063638191873112356083593_<34>
P69 = 113367417640850910889863553364828353318982821587846623336743491667163_<69>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 317477821896066397184834973712219743381652191068754392191236772976186795003721381583904453464961156659 (102 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=6788081729 Step 1 took 3494ms Step 2 took 3666ms ********** Factor found in step 2: 2800432686063638191873112356083593 Found probable prime factor of 34 digits: 2800432686063638191873112356083593 Probable prime cofactor 113367417640850910889863553364828353318982821587846623336743491667163 has 69 digits
Oct 24, 2009 (7th): By Erik Branger / GGNFS, Msieve / Oct 24, 2009
(64·10¹³³+71)/9 = 7(1)₁₃₂9_<134> = 97 · 277 · 28460161 · 8090129964135488682227_<22> · C101
C101 = P43 · P58
P43 = 1664789434755203812778700766914906617226821_<43>
P58 = 6904524884467902638231307540947107049825316235236603917773_<58>

Number: 71119_133 N=11494580079666558542443783728928619354494775302497272662571411224326978098568361652889243341174189633 ( 101 digits) SNFS difficulty: 135 digits. Divisors found: r1=1664789434755203812778700766914906617226821 (pp43) r2=6904524884467902638231307540947107049825316235236603917773 (pp58) Version: Msieve-1.40 Total time: 4.57 hours. Scaled time: 4.67 units (timescale=1.022). Factorization parameters were as follows: n: 11494580079666558542443783728928619354494775302497272662571411224326978098568361652889243341174189633 m: 400000000000000000000000000 deg: 5 c5: 125 c0: 142 skew: 1.03 type: snfs lss: 1 rlim: 1250000 alim: 1250000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1250000/1250000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [625000, 1300001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 192195 x 192420 Total sieving time: 4.37 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.11 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,135.000,5,0,0,0,0,0,0,0,0,1250000,1250000,26,26,47,47,2.3,2.3,75000 total time: 4.57 hours. --------- CPU info (if available) ----------
(64·10¹³⁰+17)/9 = 7(1)₁₂₉3_<131> = 7 · 157 · 165063455625212909_<18> · C111
C111 = P54 · P57
P54 = 501311136493860382206840311242822408732912729612367501_<54>
P57 = 781954506321762288842405664687450652305558751607526123043_<57>

Number: 71113_130 N=392002502250658185901973161083526625449589937750275737553700107399876492854647059016885556452815419107060425543 ( 111 digits) SNFS difficulty: 131 digits. Divisors found: r1=501311136493860382206840311242822408732912729612367501 (pp54) r2=781954506321762288842405664687450652305558751607526123043 (pp57) Version: Msieve v. 1.41 Total time: 4.37 hours. Scaled time: 3.45 units (timescale=0.789). Factorization parameters were as follows: n: 392002502250658185901973161083526625449589937750275737553700107399876492854647059016885556452815419107060425543 m: 200000000000000000000000000 deg: 5 c5: 2 c0: 17 skew: 1.53 type: snfs lss: 1 rlim: 1100000 alim: 1100000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1100000/1100000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [550000, 950001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 145871 x 146108 Total sieving time: 4.17 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.12 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,131.000,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000 total time: 4.37 hours. --------- CPU info (if available) ----------
(26·10¹⁰⁷-11)/3 = 8(6)₁₀₆3_<108> = 7 · 131289139 · 697721177 · C91
C91 = P28 · P63
P28 = 3978386986036076319565900111_<28>
P63 = 339731895873013988365966755540530078047599588313131089726670973_<63>

Number: 86663_107 N=1351584953282562236353361499271620221383262966791354356378814555478909569263862450281178003 ( 91 digits) SNFS difficulty: 109 digits. Divisors found: r1=3978386986036076319565900111 (pp28) r2=339731895873013988365966755540530078047599588313131089726670973 (pp63) Version: Msieve-1.40 Total time: 0.60 hours. Scaled time: 0.55 units (timescale=0.922). Factorization parameters were as follows: n: 1351584953282562236353361499271620221383262966791354356378814555478909569263862450281178003 m: 2000000000000000000000 deg: 5 c5: 325 c0: -44 skew: 0.67 type: snfs lss: 1 rlim: 460000 alim: 460000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 Factor base limits: 460000/460000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [230000, 330001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 44372 x 44597 Total sieving time: 0.58 hours. Total relation processing time: 0.01 hours. Matrix solve time: 0.01 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,109.000,5,0,0,0,0,0,0,0,0,460000,460000,25,25,44,44,2.2,2.2,50000 total time: 0.60 hours. --------- CPU info (if available) ----------
(26·10¹¹⁰-11)/3 = 8(6)₁₀₉3_<111> = 5700415541281_<13> · C99
C99 = P47 · P53
P47 = 12272738724182301305612091265295950998101974637_<47>
P53 = 12388082508652856169851007015980590350203785032347779_<53>

Number: 86663_110 N=152035699922309336604290501684473783819776715715277959163551715561100466551758956332833140021281223 ( 99 digits) SNFS difficulty: 111 digits. Divisors found: r1=12272738724182301305612091265295950998101974637 (pp47) r2=12388082508652856169851007015980590350203785032347779 (pp53) Version: Msieve-1.40 Total time: 0.82 hours. Scaled time: 0.75 units (timescale=0.920). Factorization parameters were as follows: n: 152035699922309336604290501684473783819776715715277959163551715561100466551758956332833140021281223 m: 10000000000000000000000 deg: 5 c5: 26 c0: -11 skew: 0.84 type: snfs lss: 1 rlim: 500000 alim: 500000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 Factor base limits: 500000/500000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [250000, 400001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 51155 x 51381 Total sieving time: 0.79 hours. Total relation processing time: 0.01 hours. Matrix solve time: 0.01 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,111.000,5,0,0,0,0,0,0,0,0,500000,500000,25,25,44,44,2.2,2.2,50000 total time: 0.82 hours. --------- CPU info (if available) ----------
(83·10¹¹⁰+7)/9 = 9(2)₁₀₉3_<111> = 13 · 29 · 79 · 571 · 62260951271_<11> · C93
C93 = P42 · P52
P42 = 393854541172230339186777355842066105426479_<42>
P52 = 2211461708879282181705305020872043074904345739338579_<52>

Number: 92223_110 N=870994236670606108303870557022767515535183065838195376207590467620873957918857961332172833341 ( 93 digits) SNFS difficulty: 111 digits. Divisors found: r1=393854541172230339186777355842066105426479 (pp42) r2=2211461708879282181705305020872043074904345739338579 (pp52) Version: Msieve-1.40 Total time: 0.61 hours. Scaled time: 0.60 units (timescale=0.991). Factorization parameters were as follows: n: 870994236670606108303870557022767515535183065838195376207590467620873957918857961332172833341 m: 10000000000000000000000 deg: 5 c5: 83 c0: 7 skew: 0.61 type: snfs lss: 1 rlim: 510000 alim: 510000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 Factor base limits: 510000/510000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [255000, 355001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 56979 x 57211 Total sieving time: 0.57 hours. Total relation processing time: 0.01 hours. Matrix solve time: 0.01 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,111.000,5,0,0,0,0,0,0,0,0,510000,510000,25,25,44,44,2.2,2.2,50000 total time: 0.61 hours. --------- CPU info (if available) ----------
(26·10¹⁴⁶-11)/3 = 8(6)₁₄₅3_<147> = C147
C147 = P72 · P76
P72 = 131158134929014941897991043155494762191194655999220655657005466227475003_<72>
P76 = 6607799562991054291615354621323538605634856746762653073904905905353439897221_<76>

Number: 86663_146 N=866666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663 ( 147 digits) SNFS difficulty: 148 digits. Divisors found: r1=131158134929014941897991043155494762191194655999220655657005466227475003 (pp72) r2=6607799562991054291615354621323538605634856746762653073904905905353439897221 (pp76) Version: Msieve-1.40 Total time: 9.56 hours. Scaled time: 9.83 units (timescale=1.029). Factorization parameters were as follows: n: 866666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663 m: 200000000000000000000000000000 deg: 5 c5: 65 c0: -88 skew: 1.06 type: snfs lss: 1 rlim: 2100000 alim: 2100000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 2100000/2100000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [1050000, 2350001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 344320 x 344545 Total sieving time: 9.20 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.26 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,148.000,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,49,49,2.3,2.3,100000 total time: 9.56 hours. --------- CPU info (if available) ----------
(64·10¹⁴¹+71)/9 = 7(1)₁₄₀9_<142> = 3 · 7 · 57847 · 30874858832399_<14> · C123
C123 = P37 · P86
P37 = 6510739734848601425260429916535506287_<37>
P86 = 29120713619885368879626705765668284768909292908607215351267930881138585180884368345349_<86>

Number: 71119_141 N=189597387272134522772268193701446398461691904062379603481427004394227700656471441219573544266601776458865910529642176709163 ( 123 digits) SNFS difficulty: 142 digits. Divisors found: r1=6510739734848601425260429916535506287 (pp37) r2=29120713619885368879626705765668284768909292908607215351267930881138585180884368345349 (pp86) Version: Msieve v. 1.41 Total time: 10.10 hours. Scaled time: 7.97 units (timescale=0.789). Factorization parameters were as follows: n: 189597387272134522772268193701446398461691904062379603481427004394227700656471441219573544266601776458865910529642176709163 m: 20000000000000000000000000000 deg: 5 c5: 20 c0: 71 skew: 1.29 type: snfs lss: 1 rlim: 1680000 alim: 1680000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1680000/1680000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [840000, 1740001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 287547 x 287795 Total sieving time: 9.54 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.40 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,142.000,5,0,0,0,0,0,0,0,0,1680000,1680000,26,26,48,48,2.3,2.3,100000 total time: 10.10 hours. --------- CPU info (if available) ----------
(26·10¹²⁴-11)/3 = 8(6)₁₂₃3_<125> = 83 · 27431 · 381461 · 2016101 · C107
C107 = P45 · P63
P45 = 438878110517843642539991775562600262919496931_<45>
P63 = 112778421637215029419777137694092275643046196593126789882595041_<63>

Number: 86663_124 N=49495980595325626435872640529294835369469109074742694477217163577982039477317528441557433297428732515319171 ( 107 digits) SNFS difficulty: 126 digits. Divisors found: r1=438878110517843642539991775562600262919496931 (pp45) r2=112778421637215029419777137694092275643046196593126789882595041 (pp63) Version: Msieve-1.40 Total time: 1.72 hours. Scaled time: 1.70 units (timescale=0.994). Factorization parameters were as follows: n: 49495980595325626435872640529294835369469109074742694477217163577982039477317528441557433297428732515319171 m: 10000000000000000000000000 deg: 5 c5: 13 c0: -55 skew: 1.33 type: snfs lss: 1 rlim: 890000 alim: 890000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 890000/890000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [445000, 695001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 123067 x 123293 Total sieving time: 1.62 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.04 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,126.000,5,0,0,0,0,0,0,0,0,890000,890000,26,26,46,46,2.3,2.3,50000 total time: 1.72 hours. --------- CPU info (if available) ----------
Oct 24, 2009 (6th): By Sinkiti Sibata / Msieve, GGNFS / Oct 23, 2009
(64·10¹²⁹+17)/9 = 7(1)₁₂₈3_<130> = 3 · 73 · 12269 · 39990589935139_<14> · 95328430487254801_<17> · C93
C93 = P44 · P49
P44 = 90121920285179397280256156598295853120418907_<44>
P49 = 7703241133517384550461381620028772328027196622071_<49>

Fri Oct 23 19:53:21 2009 Msieve v. 1.42 Fri Oct 23 19:53:21 2009 random seeds: 2d359c10 ab5736ee Fri Oct 23 19:53:21 2009 factoring 694230883372368712626881565996878478687550383836869743633600004878384701569568055066881896397 (93 digits) Fri Oct 23 19:53:22 2009 searching for 15-digit factors Fri Oct 23 19:53:23 2009 commencing quadratic sieve (93-digit input) Fri Oct 23 19:53:23 2009 using multiplier of 5 Fri Oct 23 19:53:23 2009 using 32kb Intel Core sieve core Fri Oct 23 19:53:23 2009 sieve interval: 36 blocks of size 32768 Fri Oct 23 19:53:23 2009 processing polynomials in batches of 6 Fri Oct 23 19:53:23 2009 using a sieve bound of 1944721 (72941 primes) Fri Oct 23 19:53:23 2009 using large prime bound of 243090125 (27 bits) Fri Oct 23 19:53:23 2009 using double large prime bound of 1242742353333750 (42-51 bits) Fri Oct 23 19:53:23 2009 using trial factoring cutoff of 51 bits Fri Oct 23 19:53:23 2009 polynomial 'A' values have 12 factors Fri Oct 23 22:31:03 2009 73411 relations (18165 full + 55246 combined from 994698 partial), need 73037 Fri Oct 23 22:31:05 2009 begin with 1012863 relations Fri Oct 23 22:31:06 2009 reduce to 188691 relations in 10 passes Fri Oct 23 22:31:06 2009 attempting to read 188691 relations Fri Oct 23 22:31:09 2009 recovered 188691 relations Fri Oct 23 22:31:09 2009 recovered 170591 polynomials Fri Oct 23 22:31:09 2009 attempting to build 73411 cycles Fri Oct 23 22:31:09 2009 found 73411 cycles in 5 passes Fri Oct 23 22:31:09 2009 distribution of cycle lengths: Fri Oct 23 22:31:09 2009 length 1 : 18165 Fri Oct 23 22:31:09 2009 length 2 : 13171 Fri Oct 23 22:31:09 2009 length 3 : 12398 Fri Oct 23 22:31:09 2009 length 4 : 10001 Fri Oct 23 22:31:09 2009 length 5 : 7388 Fri Oct 23 22:31:09 2009 length 6 : 4931 Fri Oct 23 22:31:09 2009 length 7 : 3103 Fri Oct 23 22:31:09 2009 length 9+: 4254 Fri Oct 23 22:31:09 2009 largest cycle: 22 relations Fri Oct 23 22:31:09 2009 matrix is 72941 x 73411 (18.4 MB) with weight 4529616 (61.70/col) Fri Oct 23 22:31:09 2009 sparse part has weight 4529616 (61.70/col) Fri Oct 23 22:31:10 2009 filtering completed in 3 passes Fri Oct 23 22:31:10 2009 matrix is 69213 x 69277 (17.4 MB) with weight 4281226 (61.80/col) Fri Oct 23 22:31:10 2009 sparse part has weight 4281226 (61.80/col) Fri Oct 23 22:31:11 2009 saving the first 48 matrix rows for later Fri Oct 23 22:31:11 2009 matrix is 69165 x 69277 (10.2 MB) with weight 3257486 (47.02/col) Fri Oct 23 22:31:11 2009 sparse part has weight 2253122 (32.52/col) Fri Oct 23 22:31:11 2009 matrix includes 64 packed rows Fri Oct 23 22:31:11 2009 using block size 27710 for processor cache size 1024 kB Fri Oct 23 22:31:11 2009 commencing Lanczos iteration Fri Oct 23 22:31:11 2009 memory use: 10.9 MB Fri Oct 23 22:31:42 2009 lanczos halted after 1095 iterations (dim = 69159) Fri Oct 23 22:31:42 2009 recovered 13 nontrivial dependencies Fri Oct 23 22:31:43 2009 prp44 factor: 90121920285179397280256156598295853120418907 Fri Oct 23 22:31:43 2009 prp49 factor: 7703241133517384550461381620028772328027196622071 Fri Oct 23 22:31:43 2009 elapsed time 02:38:22
(64·10¹²⁰+71)/9 = 7(1)₁₁₉9_<121> = 3³ · 25056137 · 39405479110031809_<17> · C96
C96 = P31 · P66
P31 = 1909784723324945661063074631191_<31>
P66 = 139674960799589269574939897676758027913533545895886397551579842899_<66>

Number: 71119_120 N=266749106366066224179930490595843183605440843999355589847519042761546631831691215229244145262709 ( 96 digits) SNFS difficulty: 121 digits. Divisors found: r1=1909784723324945661063074631191 (pp31) r2=139674960799589269574939897676758027913533545895886397551579842899 (pp66) Version: Msieve v. 1.42 Total time: 0.05 hours. Scaled time: 0.04 units (timescale=0.854). Factorization parameters were as follows: name: 71119_120 n: 266749106366066224179930490595843183605440843999355589847519042761546631831691215229244145262709 m: 2000000000000000000000000 deg: 5 c5: 2 c0: 71 skew: 2.04 type: snfs lss: 1 rlim: 750000 alim: 750000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 750000/750000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [375000, 625001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 94388 x 94615 Total sieving time: 0.00 hours. Total relation processing time: 0.01 hours. Matrix solve time: 0.03 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,121.000,5,0,0,0,0,0,0,0,0,750000,750000,25,25,46,46,2.2,2.2,50000 total time: 0.05 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 5600+ stepping 02 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 5600+ stepping 02 Memory: 3886124k/4718592k available (3786k kernel code, 656964k absent, 175504k reserved, 2294k data, 1304k init) Calibrating delay loop (skipped), value calculated using timer frequency.. 5827.16 BogoMIPS (lpj=2913583) Calibrating delay using timer specific routine.. 5826.53 BogoMIPS (lpj=2913268) Total of 2 processors activated (11653.70 BogoMIPS). Total time: 42 min.
By Sinkiti Sibata / Msieve, GGNFS / Oct 24, 2009
(64·10¹²⁸+71)/9 = 7(1)₁₂₇9_<129> = 4493 · 35149 · C121
C121 = P33 · P33 · P56
P33 = 219246084445885541879554806930967_<33>
P33 = 226366253431612444268772260693243_<33>
P56 = 90728669742939326666422767939725447916165155744870994707_<56>

Number: 71119_128 N=4502856141598834885410504283773545671340260559585847498662674592011490095616482702936322973148554888563657439779014792567 ( 121 digits) SNFS difficulty: 130 digits. Divisors found: r1=219246084445885541879554806930967 (pp33) r2=226366253431612444268772260693243 (pp33) r3=90728669742939326666422767939725447916165155744870994707 (pp56) Version: Msieve-1.40 Total time: 3.48 hours. Scaled time: 6.96 units (timescale=1.999). Factorization parameters were as follows: name: 71119_128 n: 4502856141598834885410504283773545671340260559585847498662674592011490095616482702936322973148554888563657439779014792567 m: 40000000000000000000000000 deg: 5 c5: 125 c0: 142 skew: 1.03 type: snfs lss: 1 rlim: 1030000 alim: 1030000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1030000/1030000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [515000, 965001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 170055 x 170303 Total sieving time: 3.22 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.10 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: snfs,130.000,5,0,0,0,0,0,0,0,0,1030000,1030000,26,26,47,47,2.3,2.3,50000 total time: 3.48 hours. --------- CPU info (if available) ----------
(7·10¹⁷¹+11)/9 = (7)₁₇₀9_<171> = 79 · 38849977 · 203457481442417_<15> · 81709955186191980351449_<23> · C125
C125 = P44 · P81
P44 = 98257468015187235416827038555249763862904983_<44>
P81 = 155139886054848009277581492355401445786172323675067944033931354665035918101197867_<81>

Number: 77779_171 N=15243652391914020488510365474725098887583903365784101043635177021944272391291910540061456099835261086105261271359058703271261 ( 125 digits) SNFS difficulty: 171 digits. Divisors found: r1=98257468015187235416827038555249763862904983 (pp44) r2=155139886054848009277581492355401445786172323675067944033931354665035918101197867 (pp81) Version: Msieve-1.40 Total time: 59.76 hours. Scaled time: 198.54 units (timescale=3.322). Factorization parameters were as follows: name: 77779_171 n: 15243652391914020488510365474725098887583903365784101043635177021944272391291910540061456099835261086105261271359058703271261 m: 10000000000000000000000000000000000 deg: 5 c5: 70 c0: 11 skew: 0.69 type: snfs lss: 1 rlim: 5100000 alim: 5100000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 5100000/5100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2550000, 5550001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 950870 x 951118 Total sieving time: 57.71 hours. Total relation processing time: 0.10 hours. Matrix solve time: 1.71 hours. Time per square root: 0.25 hours. Prototype def-par.txt line would be: snfs,171.000,5,0,0,0,0,0,0,0,0,5100000,5100000,27,27,52,52,2.4,2.4,100000 total time: 59.76 hours. --------- CPU info (if available) ----------
(83·10¹¹⁷+7)/9 = 9(2)₁₁₆3_<118> = 19 · 16547 · C113
C113 = P38 · P75
P38 = 36779934795762142506535701356535567163_<38>
P75 = 797538689045240465818445964027040354448230908021748469854654299849630902597_<75>

Number: 92223_117 N=29333420980181563273426005738748070797448487155319050431218959144199209976755914483535645584418934970633004622311 ( 113 digits) SNFS difficulty: 121 digits. Divisors found: r1=36779934795762142506535701356535567163 (pp38) r2=797538689045240465818445964027040354448230908021748469854654299849630902597 (pp75) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 3.04 hours. Scaled time: 1.43 units (timescale=0.470). Factorization parameters were as follows: name: 92223_117 n: 29333420980181563273426005738748070797448487155319050431218959144199209976755914483535645584418934970633004622311 m: 500000000000000000000000 deg: 5 c5: 332 c0: 875 skew: 1.21 type: snfs lss: 1 rlim: 730000 alim: 730000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 730000/730000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [365000, 665001) Primes: RFBsize:58789, AFBsize:58546, largePrimes:1331675 encountered Relations: rels:1305723, finalFF:150232 Max relations in full relation-set: 28 Initial matrix: 117402 x 150232 with sparse part having weight 7226670. Pruned matrix : 103906 x 104557 with weight 3808187. Total sieving time: 2.87 hours. Total relation processing time: 0.06 hours. Matrix solve t