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2007-09-28, 22:34
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#1 |
Jul 2003
So Cal
24·7·19 Posts |
222-digit SNFS completed with msieve
The NFSNet factorization of 5^317-1 (SNFS difficulty of 222 digits) has been completed with msieve. Approximately 52 million relations were converted from CWI to GGNFS format, then fed to msieve running on a 1.8 GHz single-core Opteron 144 system with 3 GB of memory in 64-bit Linux.
The filtering took about 4 hours to complete, and used 2.6 GB of memory. It produced a final 4945096 x 4945296 matrix with weight 430746398. After setting aside the dense rows due to the quadratic characters and small primes, Block Lanczos was started on a 4945048 x 4945296 matrix with weight 325847903 (a bit less than 66 nonzero entries per column). Although the calendar time was a bit longer due to concurrently running processes, the runtime was just over 6 days, and used 1.4 GB of memory. Each square root run took about 2 1/4 hours and used about 1 GB of memory. The factors were found on the 5th dependency. The log file is included below. Greg Code:
Thu Sep 20 21:37:23 2007 Msieve v. 1.26 Thu Sep 20 21:37:23 2007 random seeds: 185f937d 2ecbaf6a Thu Sep 20 21:37:23 2007 factoring 92434965030908060747429142932658760565993426346095034973091641083459922025698557036123601926456020340672166067090025586894033416571549180375782645725393227577888065349349466348014027068797915321 (194 digits) Thu Sep 20 21:37:24 2007 commencing number field sieve (194-digit input) Thu Sep 20 21:37:24 2007 R0: -11102230246251565404236316680908203125 Thu Sep 20 21:37:24 2007 R1: 1 Thu Sep 20 21:37:24 2007 A0: -5 Thu Sep 20 21:37:24 2007 A1: 0 Thu Sep 20 21:37:24 2007 A2: 0 Thu Sep 20 21:37:24 2007 A3: 0 Thu Sep 20 21:37:24 2007 A4: 0 Thu Sep 20 21:37:24 2007 A5: 0 Thu Sep 20 21:37:24 2007 A6: 1 Thu Sep 20 21:37:24 2007 size score = 0.000000e+00, Murphy alpha = 0.000000, combined = 0.000000e+00 Thu Sep 20 21:40:16 2007 restarting with 51844324 relations Thu Sep 20 21:40:17 2007 generating factor base Thu Sep 20 21:41:07 2007 factor base complete: Thu Sep 20 21:41:07 2007 3001134 rational roots (max prime = 49999991) Thu Sep 20 21:41:07 2007 3000510 algebraic roots (max prime = 49999991) Thu Sep 20 21:41:10 2007 added 249974 free relations Thu Sep 20 21:41:10 2007 Thu Sep 20 21:41:10 2007 commencing relation filtering Thu Sep 20 21:41:10 2007 commencing duplicate removal, pass 1 Thu Sep 20 21:41:52 2007 error -10 reading relation 3160814 Thu Sep 20 21:42:08 2007 error -14 reading relation 4783231 Thu Sep 20 21:42:20 2007 error -10 reading relation 6034590 Thu Sep 20 21:42:25 2007 error -14 reading relation 6540043 Thu Sep 20 21:42:50 2007 error -10 reading relation 9049115 Thu Sep 20 21:43:05 2007 error -14 reading relation 10593905 Thu Sep 20 21:43:22 2007 error -14 reading relation 12326630 Thu Sep 20 21:43:24 2007 error -14 reading relation 12496884 Thu Sep 20 21:43:35 2007 error -14 reading relation 13555646 Thu Sep 20 21:45:35 2007 error -14 reading relation 25738563 Thu Sep 20 21:46:13 2007 error -10 reading relation 29463484 Thu Sep 20 21:46:20 2007 error -10 reading relation 30128793 Thu Sep 20 21:46:38 2007 error -14 reading relation 31846875 Thu Sep 20 21:47:00 2007 error -14 reading relation 34015236 Thu Sep 20 21:47:09 2007 error -10 reading relation 34841978 Thu Sep 20 21:47:59 2007 error -14 reading relation 39683392 Thu Sep 20 21:49:00 2007 error -10 reading relation 45489637 Thu Sep 20 21:49:35 2007 error -10 reading relation 48792568 Thu Sep 20 21:50:22 2007 found 4760720 hash collisions in 52094280 relations Thu Sep 20 21:50:22 2007 commencing duplicate removal, pass 2 Thu Sep 20 21:54:12 2007 found 22210 duplicates and 52072070 unique relations Thu Sep 20 21:54:12 2007 memory use: 153.2 MB Thu Sep 20 21:54:36 2007 ignoring smallest 1879449 rational and 1878692 algebraic ideals Thu Sep 20 21:54:36 2007 filtering rational ideals above 30369958 Thu Sep 20 21:54:36 2007 filtering algebraic ideals above 30369958 Thu Sep 20 21:54:36 2007 need 6388839 more relations than ideals Thu Sep 20 21:54:36 2007 commencing singleton removal, pass 1 Thu Sep 20 22:04:29 2007 relations with 0 large ideals: 735111 Thu Sep 20 22:04:29 2007 relations with 1 large ideals: 3882198 Thu Sep 20 22:04:29 2007 relations with 2 large ideals: 11251525 Thu Sep 20 22:04:29 2007 relations with 3 large ideals: 16987860 Thu Sep 20 22:04:29 2007 relations with 4 large ideals: 13436084 Thu Sep 20 22:04:29 2007 relations with 5 large ideals: 4730400 Thu Sep 20 22:04:29 2007 relations with 6 large ideals: 862680 Thu Sep 20 22:04:29 2007 relations with 7+ large ideals: 186212 Thu Sep 20 22:04:29 2007 52072070 relations and about 36660563 large ideals Thu Sep 20 22:04:29 2007 commencing singleton removal, pass 2 Thu Sep 20 22:14:33 2007 found 8069780 singletons Thu Sep 20 22:14:33 2007 current dataset: 44002290 relations and about 28067837 large ideals Thu Sep 20 22:14:33 2007 commencing singleton removal, pass 3 Thu Sep 20 22:23:21 2007 found 1192843 singletons Thu Sep 20 22:23:21 2007 current dataset: 42809447 relations and about 26861055 large ideals Thu Sep 20 22:23:21 2007 commencing singleton removal, pass 4 Thu Sep 20 22:32:08 2007 found 157916 singletons Thu Sep 20 22:32:08 2007 current dataset: 42651531 relations and about 26702860 large ideals Thu Sep 20 22:32:08 2007 commencing singleton removal, final pass Thu Sep 20 22:43:05 2007 memory use: 1307.2 MB Thu Sep 20 22:43:05 2007 commencing in-memory singleton removal Thu Sep 20 22:43:12 2007 begin with 42651531 relations and 32313095 unique ideals Thu Sep 20 22:44:29 2007 reduce to 37883734 relations and 27412452 ideals in 11 passes Thu Sep 20 22:44:29 2007 max relations containing the same ideal: 34 Thu Sep 20 22:44:58 2007 removing 2292623 relations and 1892623 ideals in 400000 cliques Thu Sep 20 22:45:01 2007 commencing in-memory singleton removal Thu Sep 20 22:45:06 2007 begin with 35591111 relations and 27412452 unique ideals Thu Sep 20 22:45:50 2007 reduce to 35517064 relations and 25444911 ideals in 7 passes Thu Sep 20 22:45:50 2007 max relations containing the same ideal: 34 Thu Sep 20 22:46:17 2007 removing 1750869 relations and 1350869 ideals in 400000 cliques Thu Sep 20 22:46:18 2007 commencing in-memory singleton removal Thu Sep 20 22:46:24 2007 begin with 33766195 relations and 25444911 unique ideals Thu Sep 20 22:46:59 2007 reduce to 33715677 relations and 24042952 ideals in 6 passes Thu Sep 20 22:46:59 2007 max relations containing the same ideal: 33 Thu Sep 20 22:47:24 2007 removing 1582346 relations and 1182346 ideals in 400000 cliques Thu Sep 20 22:47:25 2007 commencing in-memory singleton removal Thu Sep 20 22:47:30 2007 begin with 32133331 relations and 24042952 unique ideals Thu Sep 20 22:48:03 2007 reduce to 32089451 relations and 22816264 ideals in 6 passes Thu Sep 20 22:48:03 2007 max relations containing the same ideal: 32 Thu Sep 20 22:48:27 2007 removing 1479818 relations and 1079818 ideals in 400000 cliques Thu Sep 20 22:48:28 2007 commencing in-memory singleton removal Thu Sep 20 22:48:33 2007 begin with 30609633 relations and 22816264 unique ideals Thu Sep 20 22:49:04 2007 reduce to 30565346 relations and 21691669 ideals in 6 passes Thu Sep 20 22:49:04 2007 max relations containing the same ideal: 32 Thu Sep 20 22:49:26 2007 removing 1418795 relations and 1018795 ideals in 400000 cliques Thu Sep 20 22:49:28 2007 commencing in-memory singleton removal Thu Sep 20 22:49:32 2007 begin with 29146551 relations and 21691669 unique ideals Thu Sep 20 22:50:01 2007 reduce to 29105194 relations and 20631076 ideals in 6 passes Thu Sep 20 22:50:01 2007 max relations containing the same ideal: 30 Thu Sep 20 22:50:22 2007 removing 1371958 relations and 971958 ideals in 400000 cliques Thu Sep 20 22:50:24 2007 commencing in-memory singleton removal Thu Sep 20 22:50:28 2007 begin with 27733236 relations and 20631076 unique ideals Thu Sep 20 22:50:55 2007 reduce to 27690569 relations and 19615900 ideals in 6 passes Thu Sep 20 22:50:55 2007 max relations containing the same ideal: 27 Thu Sep 20 22:51:15 2007 removing 1347454 relations and 947454 ideals in 400000 cliques Thu Sep 20 22:51:17 2007 commencing in-memory singleton removal Thu Sep 20 22:51:21 2007 begin with 26343115 relations and 19615900 unique ideals Thu Sep 20 22:51:47 2007 reduce to 26300744 relations and 18625562 ideals in 6 passes Thu Sep 20 22:51:47 2007 max relations containing the same ideal: 27 Thu Sep 20 22:52:05 2007 removing 1318817 relations and 918817 ideals in 400000 cliques Thu Sep 20 22:52:07 2007 commencing in-memory singleton removal Thu Sep 20 22:52:10 2007 begin with 24981927 relations and 18625562 unique ideals Thu Sep 20 22:52:31 2007 reduce to 24936715 relations and 17660938 ideals in 5 passes Thu Sep 20 22:52:31 2007 max relations containing the same ideal: 26 Thu Sep 20 22:52:48 2007 removing 1302589 relations and 902589 ideals in 400000 cliques Thu Sep 20 22:52:50 2007 commencing in-memory singleton removal Thu Sep 20 22:52:53 2007 begin with 23634126 relations and 17660938 unique ideals Thu Sep 20 22:53:12 2007 reduce to 23589136 relations and 16712723 ideals in 5 passes Thu Sep 20 22:53:12 2007 max relations containing the same ideal: 26 Thu Sep 20 22:53:29 2007 removing 1288692 relations and 888692 ideals in 400000 cliques Thu Sep 20 22:53:30 2007 commencing in-memory singleton removal Thu Sep 20 22:53:33 2007 begin with 22300444 relations and 16712723 unique ideals Thu Sep 20 22:53:51 2007 reduce to 22254654 relations and 15777554 ideals in 5 passes Thu Sep 20 22:53:51 2007 max relations containing the same ideal: 24 Thu Sep 20 22:54:06 2007 removing 360589 relations and 272329 ideals in 88260 cliques Thu Sep 20 22:54:07 2007 commencing in-memory singleton removal Thu Sep 20 22:54:10 2007 begin with 21894065 relations and 15777554 unique ideals Thu Sep 20 22:54:27 2007 reduce to 21890629 relations and 15501781 ideals in 5 passes Thu Sep 20 22:54:27 2007 max relations containing the same ideal: 24 Thu Sep 20 22:54:32 2007 dataset has 70.0% excess relations Thu Sep 20 22:54:53 2007 ignoring smallest 1702465 rational and 1701110 algebraic ideals Thu Sep 20 22:54:53 2007 filtering rational ideals above 27332962 Thu Sep 20 22:54:53 2007 filtering algebraic ideals above 27332962 Thu Sep 20 22:54:53 2007 need 5749963 more relations than ideals Thu Sep 20 22:54:53 2007 commencing singleton removal, final pass Thu Sep 20 23:00:55 2007 memory use: 666.1 MB Thu Sep 20 23:00:55 2007 commencing in-memory singleton removal Thu Sep 20 23:00:58 2007 begin with 21890629 relations and 15856322 unique ideals Thu Sep 20 23:01:11 2007 reduce to 21890195 relations and 15855888 ideals in 4 passes Thu Sep 20 23:01:11 2007 max relations containing the same ideal: 26 Thu Sep 20 23:01:26 2007 removing 485218 relations and 343046 ideals in 142172 cliques Thu Sep 20 23:01:27 2007 commencing in-memory singleton removal Thu Sep 20 23:01:30 2007 begin with 21404977 relations and 15855888 unique ideals Thu Sep 20 23:01:46 2007 reduce to 21397794 relations and 15505621 ideals in 5 passes Thu Sep 20 23:01:46 2007 max relations containing the same ideal: 26 Thu Sep 20 23:02:00 2007 removing 475245 relations and 333073 ideals in 142172 cliques Thu Sep 20 23:02:01 2007 commencing in-memory singleton removal Thu Sep 20 23:02:04 2007 begin with 20922549 relations and 15505621 unique ideals Thu Sep 20 23:02:20 2007 reduce to 20914831 relations and 15164774 ideals in 5 passes Thu Sep 20 23:02:20 2007 max relations containing the same ideal: 26 Thu Sep 20 23:02:24 2007 dataset has 53.0% excess relations Thu Sep 20 23:02:43 2007 ignoring smallest 1524588 rational and 1522788 algebraic ideals Thu Sep 20 23:02:43 2007 filtering rational ideals above 24295966 Thu Sep 20 23:02:43 2007 filtering algebraic ideals above 24295966 Thu Sep 20 23:02:43 2007 need 4600045 more relations than ideals Thu Sep 20 23:02:43 2007 commencing singleton removal, final pass Thu Sep 20 23:08:44 2007 memory use: 666.1 MB Thu Sep 20 23:08:44 2007 commencing in-memory singleton removal Thu Sep 20 23:08:47 2007 begin with 20914831 relations and 15520961 unique ideals Thu Sep 20 23:09:00 2007 reduce to 20914571 relations and 15520701 ideals in 4 passes Thu Sep 20 23:09:00 2007 max relations containing the same ideal: 26 Thu Sep 20 23:09:15 2007 removing 1189323 relations and 792411 ideals in 396912 cliques Thu Sep 20 23:09:16 2007 commencing in-memory singleton removal Thu Sep 20 23:09:19 2007 begin with 19725248 relations and 15520701 unique ideals Thu Sep 20 23:09:35 2007 reduce to 19680890 relations and 14683241 ideals in 5 passes Thu Sep 20 23:09:35 2007 max relations containing the same ideal: 26 Thu Sep 20 23:09:49 2007 removing 1254272 relations and 857360 ideals in 396912 cliques Thu Sep 20 23:09:50 2007 commencing in-memory singleton removal Thu Sep 20 23:09:53 2007 begin with 18426618 relations and 14683241 unique ideals Thu Sep 20 23:10:10 2007 reduce to 18370924 relations and 13769218 ideals in 6 passes Thu Sep 20 23:10:10 2007 max relations containing the same ideal: 25 Thu Sep 20 23:10:24 2007 removing 10903 relations and 9243 ideals in 1660 cliques Thu Sep 20 23:10:24 2007 commencing in-memory singleton removal Thu Sep 20 23:10:27 2007 begin with 18360021 relations and 13769218 unique ideals Thu Sep 20 23:10:33 2007 reduce to 18360020 relations and 13759974 ideals in 2 passes Thu Sep 20 23:10:33 2007 max relations containing the same ideal: 25 Thu Sep 20 23:10:36 2007 dataset has 22.4% excess relations Thu Sep 20 23:10:53 2007 ignoring smallest 1345248 rational and 1344070 algebraic ideals Thu Sep 20 23:10:53 2007 filtering rational ideals above 21258970 Thu Sep 20 23:10:53 2007 filtering algebraic ideals above 21258970 Thu Sep 20 23:10:53 2007 need 4058792 more relations than ideals Thu Sep 20 23:10:53 2007 commencing singleton removal, final pass Thu Sep 20 23:16:45 2007 memory use: 666.1 MB Thu Sep 20 23:16:45 2007 commencing in-memory singleton removal Thu Sep 20 23:16:48 2007 begin with 18360020 relations and 14118010 unique ideals Thu Sep 20 23:17:00 2007 reduce to 18359713 relations and 14117703 ideals in 4 passes Thu Sep 20 23:17:00 2007 max relations containing the same ideal: 26 Thu Sep 20 23:17:13 2007 removing 372116 relations and 280507 ideals in 91609 cliques Thu Sep 20 23:17:13 2007 commencing in-memory singleton removal Thu Sep 20 23:17:16 2007 begin with 17987597 relations and 14117703 unique ideals Thu Sep 20 23:17:31 2007 reduce to 17982812 relations and 13832393 ideals in 5 passes Thu Sep 20 23:17:31 2007 max relations containing the same ideal: 26 Thu Sep 20 23:17:43 2007 removing 331205 relations and 239596 ideals in 91609 cliques Thu Sep 20 23:17:44 2007 commencing in-memory singleton removal Thu Sep 20 23:17:47 2007 begin with 17651607 relations and 13832393 unique ideals Thu Sep 20 23:18:01 2007 reduce to 17647274 relations and 13588433 ideals in 5 passes Thu Sep 20 23:18:01 2007 max relations containing the same ideal: 26 Thu Sep 20 23:18:04 2007 dataset has 8.0% excess relations Thu Sep 20 23:18:08 2007 relations with 0 large ideals: 384429 Thu Sep 20 23:18:08 2007 relations with 1 large ideals: 1663187 Thu Sep 20 23:18:08 2007 relations with 2 large ideals: 4123656 Thu Sep 20 23:18:08 2007 relations with 3 large ideals: 5304246 Thu Sep 20 23:18:08 2007 relations with 4 large ideals: 3877465 Thu Sep 20 23:18:08 2007 relations with 5 large ideals: 1662316 Thu Sep 20 23:18:08 2007 relations with 6 large ideals: 428657 Thu Sep 20 23:18:08 2007 relations with 7+ large ideals: 203318 Thu Sep 20 23:18:08 2007 commencing 2-way merge Thu Sep 20 23:18:24 2007 merged 4644428 relations Thu Sep 20 23:18:30 2007 reduce to 13002846 relation sets and 8944005 unique ideals Thu Sep 20 23:18:30 2007 commencing full merge Fri Sep 21 00:13:30 2007 found 6370042 cycles, need 5002205 Fri Sep 21 00:13:37 2007 weight of 5002205 cycles is about 325153895 (65.00/cycle) Fri Sep 21 00:13:37 2007 distribution of cycle lengths: Fri Sep 21 00:13:38 2007 1 relations: 631929 Fri Sep 21 00:13:38 2007 2 relations: 538402 Fri Sep 21 00:13:38 2007 3 relations: 592440 Fri Sep 21 00:13:38 2007 4 relations: 609638 Fri Sep 21 00:13:38 2007 5 relations: 609540 Fri Sep 21 00:13:38 2007 6 relations: 577173 Fri Sep 21 00:13:38 2007 7 relations: 522464 Fri Sep 21 00:13:38 2007 8 relations: 448822 Fri Sep 21 00:13:38 2007 9 relations: 347298 Fri Sep 21 00:13:38 2007 10+ relations: 124499 Fri Sep 21 00:13:38 2007 heaviest cycle: 12 relations Fri Sep 21 00:13:38 2007 commencing cycle optimization Fri Sep 21 00:41:57 2007 start with 24058516 relations Fri Sep 21 00:45:26 2007 pruned 453322 relations Fri Sep 21 00:45:29 2007 distribution of cycle lengths: Fri Sep 21 00:45:29 2007 1 relations: 631929 Fri Sep 21 00:45:29 2007 2 relations: 547975 Fri Sep 21 00:45:29 2007 3 relations: 611535 Fri Sep 21 00:45:29 2007 4 relations: 626972 Fri Sep 21 00:45:29 2007 5 relations: 634297 Fri Sep 21 00:45:29 2007 6 relations: 594660 Fri Sep 21 00:45:29 2007 7 relations: 531619 Fri Sep 21 00:45:29 2007 8 relations: 432246 Fri Sep 21 00:45:29 2007 9 relations: 296907 Fri Sep 21 00:45:29 2007 10+ relations: 94065 Fri Sep 21 00:45:29 2007 heaviest cycle: 12 relations Fri Sep 21 00:45:33 2007 Fri Sep 21 00:45:36 2007 commencing linear algebra Fri Sep 21 00:45:43 2007 factor base loaded: Fri Sep 21 00:45:43 2007 3001134 rational ideals (max prime = 49999991) Fri Sep 21 00:45:43 2007 3000510 algebraic ideals (max prime = 49999991) Fri Sep 21 00:45:45 2007 read 5002205 cycles Fri Sep 21 00:46:13 2007 cycles contain 13690128 unique relations Fri Sep 21 00:50:46 2007 read 13690128 relations Fri Sep 21 00:51:20 2007 using 32 quadratic characters above 499999230 Fri Sep 21 01:04:20 2007 matrix is 4999317 x 5002205 with weight 434154071 (avg 86.79/col) Fri Sep 21 01:07:26 2007 filtering completed in 3 passes Fri Sep 21 01:07:28 2007 matrix is 4945096 x 4945296 with weight 430746398 (avg 87.10/col) Fri Sep 21 01:08:24 2007 saving the first 48 matrix rows for later Fri Sep 21 01:08:31 2007 matrix is 4945048 x 4945296 with weight 325847903 (avg 65.89/col) Fri Sep 21 01:08:31 2007 matrix includes 64 packed rows Fri Sep 21 01:08:31 2007 using block size 43690 for processor cache size 1024 kB Fri Sep 21 01:43:04 2007 commencing Lanczos iteration Fri Sep 28 00:41:31 2007 lanczos halted after 78195 iterations Fri Sep 28 00:41:59 2007 recovered 48 nontrivial dependencies Fri Sep 28 00:41:59 2007 Fri Sep 28 00:41:59 2007 commencing square root phase Fri Sep 28 00:41:59 2007 reading relations for dependency 1 Fri Sep 28 00:42:13 2007 read 2472515 cycles Fri Sep 28 00:42:24 2007 cycles contain 8318517 unique relations Fri Sep 28 00:45:52 2007 read 8318517 relations Fri Sep 28 00:47:26 2007 multiplying 11735358 relations Fri Sep 28 01:42:26 2007 multiply complete, coefficients have about 279.45 million bits Fri Sep 28 01:42:37 2007 initial square root is modulo 103387 Fri Sep 28 02:59:35 2007 reading relations for dependency 2 Fri Sep 28 02:59:47 2007 read 2474474 cycles Fri Sep 28 02:59:58 2007 cycles contain 8320724 unique relations Fri Sep 28 03:09:37 2007 read 8320724 relations Fri Sep 28 03:11:14 2007 multiplying 11741672 relations Fri Sep 28 04:13:00 2007 multiply complete, coefficients have about 279.61 million bits Fri Sep 28 04:13:11 2007 initial square root is modulo 104047 Fri Sep 28 05:31:22 2007 reading relations for dependency 3 Fri Sep 28 05:31:34 2007 read 2472103 cycles Fri Sep 28 05:31:45 2007 cycles contain 8317780 unique relations Fri Sep 28 05:35:11 2007 read 8317780 relations Fri Sep 28 05:36:45 2007 multiplying 11735928 relations Fri Sep 28 06:31:56 2007 multiply complete, coefficients have about 279.46 million bits Fri Sep 28 06:32:08 2007 initial square root is modulo 103423 Fri Sep 28 07:41:53 2007 reading relations for dependency 4 Fri Sep 28 07:42:05 2007 read 2474158 cycles Fri Sep 28 07:42:16 2007 cycles contain 8320758 unique relations Fri Sep 28 07:45:42 2007 read 8320758 relations Fri Sep 28 07:47:16 2007 multiplying 11739724 relations Fri Sep 28 08:42:23 2007 multiply complete, coefficients have about 279.55 million bits Fri Sep 28 08:42:34 2007 initial square root is modulo 103837 Fri Sep 28 09:54:04 2007 reading relations for dependency 5 Fri Sep 28 09:54:16 2007 read 2472509 cycles Fri Sep 28 09:54:27 2007 cycles contain 8317244 unique relations Fri Sep 28 09:57:52 2007 read 8317244 relations Fri Sep 28 09:59:26 2007 multiplying 11732942 relations Fri Sep 28 10:54:26 2007 multiply complete, coefficients have about 279.39 million bits Fri Sep 28 10:54:38 2007 initial square root is modulo 103123 Fri Sep 28 12:06:02 2007 prp85 factor: 1173266048118996938584719882501239841331337879112270918586790280760729499132694039331 Fri Sep 28 12:06:02 2007 prp110 factor: 78784317656768133239109671345422644991678073397834197717116145126532590520938482143011654153492533979880370291 |
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2007-10-01, 16:40
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#2 |
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∂2ω=0
Sep 2002
República de California
265778 Posts |
That's quite impressive -- how much time do you estimate Msieve would need to do, say, the [known] factorization of M727? It would be interesting to compare the cycle count for that vs. what was used by the group that first factored that number via SNFS.
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2007-10-01, 18:23
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#3 |
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Jul 2003
So Cal
85016 Posts |
I actually now have the relations used to complete the (also known) factorization of 6,283-, so I'm going to try that one next.
Greg |
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