Tue Jun 30 19:50:59 2020 Tue Jun 30 19:50:59 2020 Tue Jun 30 19:50:59 2020 Msieve v. 1.53 (SVN 988) Tue Jun 30 19:50:59 2020 random seeds: 2ffe32e0 f348638b Tue Jun 30 19:50:59 2020 factoring 96874325686775252769973276212681868909098177195374865793536132418859110270542167780904477023247812621341462402988819810738448209140631920956426161898740674768284803543 (167 digits) Tue Jun 30 19:51:00 2020 searching for 15-digit factors Tue Jun 30 19:51:01 2020 commencing number field sieve (167-digit input) Tue Jun 30 19:51:01 2020 R0: -616023373754325918537711709243680 Tue Jun 30 19:51:01 2020 R1: 196304087002083467 Tue Jun 30 19:51:01 2020 A0: -25221208896076750249720299722301880528711211 Tue Jun 30 19:51:01 2020 A1: 1800996207055266204271191163695570319 Tue Jun 30 19:51:01 2020 A2: -25525442410464940616895780986 Tue Jun 30 19:51:01 2020 A3: 27529896807329132711 Tue Jun 30 19:51:01 2020 A4: 786461923675 Tue Jun 30 19:51:01 2020 A5: 1092 Tue Jun 30 19:51:01 2020 skew 182206040.29, size 2.387e-016, alpha -7.415, combined = 4.739e-013 rroots = 3 Tue Jun 30 19:51:01 2020 Tue Jun 30 19:51:01 2020 commencing relation filtering Tue Jun 30 19:51:01 2020 setting target matrix density to 130.0 Tue Jun 30 19:51:01 2020 estimated available RAM is 12043.5 MB Tue Jun 30 19:51:01 2020 commencing duplicate removal, pass 1 Tue Jun 30 19:51:18 2020 error -9 reading relation 1415246 Tue Jun 30 19:51:55 2020 error -9 reading relation 4333571 Redacted thousands of relation errors Tue Jun 30 20:42:41 2020 error -15 reading relation 253315578 Tue Jun 30 20:42:58 2020 error -9 reading relation 254726312 Tue Jun 30 20:42:59 2020 skipped 389 relations with composite factors Tue Jun 30 20:42:59 2020 found 55280659 hash collisions in 254763835 relations Tue Jun 30 20:43:35 2020 added 122050 free relations Tue Jun 30 20:43:35 2020 commencing duplicate removal, pass 2 Tue Jun 30 20:47:13 2020 found 55723115 duplicates and 199162770 unique relations Tue Jun 30 20:47:13 2020 memory use: 1449.5 MB Tue Jun 30 20:47:13 2020 reading ideals above 150011904 Tue Jun 30 20:47:13 2020 commencing singleton removal, initial pass Tue Jun 30 21:17:46 2020 memory use: 3012.0 MB Tue Jun 30 21:17:46 2020 reading all ideals from disk Tue Jun 30 21:17:52 2020 memory use: 3318.0 MB Tue Jun 30 21:18:03 2020 commencing in-memory singleton removal Tue Jun 30 21:18:14 2020 begin with 199162770 relations and 158386500 unique ideals Tue Jun 30 21:19:42 2020 reduce to 133449762 relations and 86287227 ideals in 12 passes Tue Jun 30 21:19:42 2020 max relations containing the same ideal: 24 Tue Jun 30 21:19:54 2020 reading ideals above 720000 Tue Jun 30 21:19:55 2020 commencing singleton removal, initial pass Tue Jun 30 21:45:19 2020 memory use: 2756.0 MB Tue Jun 30 21:45:19 2020 reading all ideals from disk Tue Jun 30 21:45:31 2020 memory use: 5148.6 MB Tue Jun 30 21:45:55 2020 keeping 102490803 ideals with weight <= 200, target excess is 687379 Tue Jun 30 21:46:18 2020 commencing in-memory singleton removal Tue Jun 30 21:46:36 2020 begin with 133449762 relations and 102490803 unique ideals Tue Jun 30 21:48:32 2020 reduce to 133434849 relations and 102475890 ideals in 8 passes Tue Jun 30 21:48:32 2020 max relations containing the same ideal: 200 Tue Jun 30 21:49:54 2020 removing 10187977 relations and 8187977 ideals in 2000000 cliques Tue Jun 30 21:49:59 2020 commencing in-memory singleton removal Tue Jun 30 21:50:16 2020 begin with 123246872 relations and 102475890 unique ideals Tue Jun 30 21:52:03 2020 reduce to 122679006 relations and 93709418 ideals in 8 passes Tue Jun 30 21:52:03 2020 max relations containing the same ideal: 196 Tue Jun 30 21:53:19 2020 removing 7756782 relations and 5756782 ideals in 2000000 cliques Tue Jun 30 21:53:23 2020 commencing in-memory singleton removal Tue Jun 30 21:53:38 2020 begin with 114922224 relations and 93709418 unique ideals Tue Jun 30 21:55:17 2020 reduce to 114539370 relations and 87563522 ideals in 8 passes Tue Jun 30 21:55:17 2020 max relations containing the same ideal: 190 Tue Jun 30 21:56:29 2020 removing 7053740 relations and 5053740 ideals in 2000000 cliques Tue Jun 30 21:56:33 2020 commencing in-memory singleton removal Tue Jun 30 21:56:48 2020 begin with 107485630 relations and 87563522 unique ideals Tue Jun 30 21:58:08 2020 reduce to 107150983 relations and 82169620 ideals in 7 passes Tue Jun 30 21:58:08 2020 max relations containing the same ideal: 183 Tue Jun 30 21:59:16 2020 removing 6684877 relations and 4684877 ideals in 2000000 cliques Tue Jun 30 21:59:20 2020 commencing in-memory singleton removal Tue Jun 30 21:59:33 2020 begin with 100466106 relations and 82169620 unique ideals Tue Jun 30 22:00:49 2020 reduce to 100155919 relations and 77169110 ideals in 7 passes Tue Jun 30 22:00:49 2020 max relations containing the same ideal: 180 Tue Jun 30 22:01:53 2020 removing 6460195 relations and 4460195 ideals in 2000000 cliques Tue Jun 30 22:01:56 2020 commencing in-memory singleton removal Tue Jun 30 22:02:09 2020 begin with 93695724 relations and 77169110 unique ideals Tue Jun 30 22:03:09 2020 reduce to 93394906 relations and 72402744 ideals in 6 passes Tue Jun 30 22:03:09 2020 max relations containing the same ideal: 170 Tue Jun 30 22:04:09 2020 removing 6301998 relations and 4301998 ideals in 2000000 cliques Tue Jun 30 22:04:12 2020 commencing in-memory singleton removal Tue Jun 30 22:04:24 2020 begin with 87092908 relations and 72402744 unique ideals Tue Jun 30 22:05:29 2020 reduce to 86794208 relations and 67796222 ideals in 7 passes Tue Jun 30 22:05:29 2020 max relations containing the same ideal: 163 Tue Jun 30 22:06:25 2020 removing 6191413 relations and 4191413 ideals in 2000000 cliques Tue Jun 30 22:06:28 2020 commencing in-memory singleton removal Tue Jun 30 22:06:39 2020 begin with 80602795 relations and 67796222 unique ideals Tue Jun 30 22:07:48 2020 reduce to 80301661 relations and 63297434 ideals in 8 passes Tue Jun 30 22:07:48 2020 max relations containing the same ideal: 153 Tue Jun 30 22:08:40 2020 removing 6112651 relations and 4112651 ideals in 2000000 cliques Tue Jun 30 22:08:43 2020 commencing in-memory singleton removal Tue Jun 30 22:08:53 2020 begin with 74189010 relations and 63297434 unique ideals Tue Jun 30 22:09:40 2020 reduce to 73878737 relations and 58867999 ideals in 6 passes Tue Jun 30 22:09:40 2020 max relations containing the same ideal: 145 Tue Jun 30 22:10:29 2020 removing 6053771 relations and 4053771 ideals in 2000000 cliques Tue Jun 30 22:10:32 2020 commencing in-memory singleton removal Tue Jun 30 22:10:41 2020 begin with 67824966 relations and 58867999 unique ideals Tue Jun 30 22:11:31 2020 reduce to 67500277 relations and 54482044 ideals in 7 passes Tue Jun 30 22:11:31 2020 max relations containing the same ideal: 137 Tue Jun 30 22:12:15 2020 removing 6018777 relations and 4018777 ideals in 2000000 cliques Tue Jun 30 22:12:18 2020 commencing in-memory singleton removal Tue Jun 30 22:12:26 2020 begin with 61481500 relations and 54482044 unique ideals Tue Jun 30 22:13:04 2020 reduce to 61138897 relations and 50111922 ideals in 6 passes Tue Jun 30 22:13:04 2020 max relations containing the same ideal: 129 Tue Jun 30 22:13:45 2020 removing 5990968 relations and 3990968 ideals in 2000000 cliques Tue Jun 30 22:13:47 2020 commencing in-memory singleton removal Tue Jun 30 22:13:55 2020 begin with 55147929 relations and 50111922 unique ideals Tue Jun 30 22:14:34 2020 reduce to 54779724 relations and 45742740 ideals in 7 passes Tue Jun 30 22:14:34 2020 max relations containing the same ideal: 118 Tue Jun 30 22:15:11 2020 removing 5979553 relations and 3979553 ideals in 2000000 cliques Tue Jun 30 22:15:14 2020 commencing in-memory singleton removal Tue Jun 30 22:15:20 2020 begin with 48800171 relations and 45742740 unique ideals Tue Jun 30 22:15:55 2020 reduce to 48397625 relations and 41348272 ideals in 7 passes Tue Jun 30 22:15:55 2020 max relations containing the same ideal: 112 Tue Jun 30 22:16:29 2020 removing 5980775 relations and 3980775 ideals in 2000000 cliques Tue Jun 30 22:16:31 2020 commencing in-memory singleton removal Tue Jun 30 22:16:37 2020 begin with 42416850 relations and 41348272 unique ideals Tue Jun 30 22:17:06 2020 reduce to 41966831 relations and 36901877 ideals in 7 passes Tue Jun 30 22:17:06 2020 max relations containing the same ideal: 104 Tue Jun 30 22:17:36 2020 removing 6000576 relations and 4000576 ideals in 2000000 cliques Tue Jun 30 22:17:38 2020 commencing in-memory singleton removal Tue Jun 30 22:17:42 2020 begin with 35966255 relations and 36901877 unique ideals Tue Jun 30 22:18:11 2020 reduce to 35441507 relations and 32356118 ideals in 8 passes Tue Jun 30 22:18:11 2020 max relations containing the same ideal: 90 Tue Jun 30 22:18:36 2020 removing 6039539 relations and 4039539 ideals in 2000000 cliques Tue Jun 30 22:18:38 2020 commencing in-memory singleton removal Tue Jun 30 22:18:42 2020 begin with 29401968 relations and 32356118 unique ideals Tue Jun 30 22:19:05 2020 reduce to 28752575 relations and 27636711 ideals in 8 passes Tue Jun 30 22:19:05 2020 max relations containing the same ideal: 78 Tue Jun 30 22:19:25 2020 removing 1379970 relations and 1061466 ideals in 318504 cliques Tue Jun 30 22:19:27 2020 commencing in-memory singleton removal Tue Jun 30 22:19:30 2020 begin with 27372605 relations and 27636711 unique ideals Tue Jun 30 22:19:46 2020 reduce to 27326027 relations and 26528204 ideals in 6 passes Tue Jun 30 22:19:46 2020 max relations containing the same ideal: 74 Tue Jun 30 22:20:10 2020 relations with 0 large ideals: 2256 Tue Jun 30 22:20:10 2020 relations with 1 large ideals: 14154 Tue Jun 30 22:20:10 2020 relations with 2 large ideals: 197030 Tue Jun 30 22:20:10 2020 relations with 3 large ideals: 1162285 Tue Jun 30 22:20:10 2020 relations with 4 large ideals: 3608374 Tue Jun 30 22:20:10 2020 relations with 5 large ideals: 6576821 Tue Jun 30 22:20:10 2020 relations with 6 large ideals: 7471281 Tue Jun 30 22:20:10 2020 relations with 7+ large ideals: 8293826 Tue Jun 30 22:20:10 2020 commencing 2-way merge Tue Jun 30 22:20:35 2020 reduce to 18076479 relation sets and 17278656 unique ideals Tue Jun 30 22:20:35 2020 commencing full merge Tue Jun 30 22:29:46 2020 memory use: 2157.5 MB Tue Jun 30 22:29:51 2020 found 7976134 cycles, need 7924856 Tue Jun 30 22:29:52 2020 weight of 7924856 cycles is about 1030491681 (130.03/cycle) Tue Jun 30 22:29:52 2020 distribution of cycle lengths: Tue Jun 30 22:29:52 2020 1 relations: 192991 Tue Jun 30 22:29:52 2020 2 relations: 384095 Tue Jun 30 22:29:52 2020 3 relations: 490626 Tue Jun 30 22:29:52 2020 4 relations: 534398 Tue Jun 30 22:29:52 2020 5 relations: 578236 Tue Jun 30 22:29:52 2020 6 relations: 589410 Tue Jun 30 22:29:52 2020 7 relations: 587336 Tue Jun 30 22:29:52 2020 8 relations: 575794 Tue Jun 30 22:29:52 2020 9 relations: 546570 Tue Jun 30 22:29:52 2020 10+ relations: 3445400 Tue Jun 30 22:29:52 2020 heaviest cycle: 28 relations Tue Jun 30 22:30:02 2020 commencing cycle optimization Tue Jun 30 22:30:23 2020 start with 74069799 relations Tue Jun 30 22:34:57 2020 pruned 3812877 relations Tue Jun 30 22:34:57 2020 memory use: 1896.6 MB Tue Jun 30 22:34:57 2020 distribution of cycle lengths: Tue Jun 30 22:34:57 2020 1 relations: 192991 Tue Jun 30 22:34:57 2020 2 relations: 395702 Tue Jun 30 22:34:57 2020 3 relations: 513668 Tue Jun 30 22:34:57 2020 4 relations: 560704 Tue Jun 30 22:34:57 2020 5 relations: 611799 Tue Jun 30 22:34:57 2020 6 relations: 624338 Tue Jun 30 22:34:57 2020 7 relations: 624519 Tue Jun 30 22:34:57 2020 8 relations: 610377 Tue Jun 30 22:34:57 2020 9 relations: 579362 Tue Jun 30 22:34:57 2020 10+ relations: 3211396 Tue Jun 30 22:34:57 2020 heaviest cycle: 28 relations Tue Jun 30 22:35:18 2020 RelProcTime: 9857 Tue Jun 30 22:35:18 2020 Tue Jun 30 22:35:18 2020 commencing linear algebra Tue Jun 30 22:35:20 2020 read 7924856 cycles Tue Jun 30 22:35:45 2020 cycles contain 26950782 unique relations Tue Jun 30 22:40:03 2020 read 26950782 relations Tue Jun 30 22:41:21 2020 using 20 quadratic characters above 4294917295 Tue Jun 30 22:44:14 2020 building initial matrix Tue Jun 30 22:52:46 2020 memory use: 3759.8 MB Tue Jun 30 22:52:57 2020 read 7924856 cycles Tue Jun 30 22:52:59 2020 matrix is 7924677 x 7924856 (3981.6 MB) with weight 1224362371 (154.50/col) Tue Jun 30 22:52:59 2020 sparse part has weight 948663404 (119.71/col) Tue Jun 30 22:55:29 2020 filtering completed in 2 passes Tue Jun 30 22:55:31 2020 matrix is 7924573 x 7924752 (3981.6 MB) with weight 1224357416 (154.50/col) Tue Jun 30 22:55:31 2020 sparse part has weight 948662124 (119.71/col) Tue Jun 30 22:56:08 2020 matrix starts at (0, 0) Tue Jun 30 22:56:10 2020 matrix is 7924573 x 7924752 (3981.6 MB) with weight 1224357416 (154.50/col) Tue Jun 30 22:56:10 2020 sparse part has weight 948662124 (119.71/col) Tue Jun 30 22:56:10 2020 saving the first 48 matrix rows for later Tue Jun 30 22:56:13 2020 matrix includes 64 packed rows Tue Jun 30 22:56:15 2020 matrix is 7924525 x 7924752 (3896.2 MB) with weight 1057291396 (133.42/col) Tue Jun 30 22:56:15 2020 sparse part has weight 942105747 (118.88/col) Tue Jun 30 22:56:15 2020 using block size 8192 and superblock size 786432 for processor cache size 8192 kB Tue Jun 30 22:57:23 2020 commencing Lanczos iteration (6 threads) Tue Jun 30 22:57:23 2020 memory use: 3248.1 MB Tue Jun 30 22:58:13 2020 linear algebra at 0.0%, ETA 69h54m Tue Jun 30 22:58:29 2020 checkpointing every 120000 dimensions Fri Jul 03 19:42:46 2020 lanczos halted after 125324 iterations (dim = 7924523) Fri Jul 03 19:43:00 2020 recovered 31 nontrivial dependencies Fri Jul 03 19:43:06 2020 BLanczosTime: 248868 Fri Jul 03 19:43:06 2020 Fri Jul 03 19:43:06 2020 commencing square root phase Fri Jul 03 19:43:06 2020 handling dependencies 1 to 64 Fri Jul 03 19:43:06 2020 reading relations for dependency 1 Fri Jul 03 19:43:09 2020 read 3961996 cycles Fri Jul 03 19:43:21 2020 cycles contain 13476426 unique relations Fri Jul 03 19:46:10 2020 read 13476426 relations Fri Jul 03 19:47:58 2020 multiplying 13476426 relations Fri Jul 03 20:11:07 2020 multiply complete, coefficients have about 671.39 million bits Fri Jul 03 20:11:14 2020 initial square root is modulo 1055503 Fri Jul 03 20:32:12 2020 GCD is 1, no factor found Fri Jul 03 20:32:12 2020 reading relations for dependency 2 Fri Jul 03 20:32:15 2020 read 3963504 cycles Fri Jul 03 20:32:27 2020 cycles contain 13475150 unique relations Fri Jul 03 20:35:15 2020 read 13475150 relations Fri Jul 03 20:36:56 2020 multiplying 13475150 relations Fri Jul 03 20:55:46 2020 multiply complete, coefficients have about 671.33 million bits Fri Jul 03 20:55:52 2020 initial square root is modulo 1054091 Fri Jul 03 21:16:44 2020 GCD is N, no factor found Fri Jul 03 21:16:44 2020 reading relations for dependency 3 Fri Jul 03 21:16:46 2020 read 3963204 cycles Fri Jul 03 21:16:58 2020 cycles contain 13478964 unique relations Fri Jul 03 21:19:46 2020 read 13478964 relations Fri Jul 03 21:21:27 2020 multiplying 13478964 relations Fri Jul 03 21:40:13 2020 multiply complete, coefficients have about 671.51 million bits Fri Jul 03 21:40:19 2020 initial square root is modulo 1057993 Fri Jul 03 22:01:15 2020 sqrtTime: 8289 Fri Jul 03 22:01:15 2020 p68 factor: 11145127652535447057837225234214204718673343332450028289273655210223 Fri Jul 03 22:01:15 2020 p100 factor: 8692078611117293719729271904587718933154653064643143006914599848787160027197381167928016453464722841 Fri Jul 03 22:01:15 2020 elapsed time 74:10:16