Wed Feb 26 21:58:49 2020 Wed Feb 26 21:58:49 2020 Wed Feb 26 21:58:49 2020 Msieve v. 1.53 (SVN unknown) Wed Feb 26 21:58:49 2020 random seeds: 67556420 e60f80ee Wed Feb 26 21:58:49 2020 factoring 22374751540039781462568291271125232298542697565824272701720715043528012605300299373908242439771412635769025176916863233716325840088169109852313897061447505042949044189163144215461921260014892962392454425283837193 (212 digits) Wed Feb 26 21:58:50 2020 searching for 15-digit factors Wed Feb 26 21:58:51 2020 commencing number field sieve (212-digit input) Wed Feb 26 21:58:51 2020 R0: 969773729787523602876821942164080815560161 Wed Feb 26 21:58:51 2020 R1: -1 Wed Feb 26 21:58:51 2020 A0: 1 Wed Feb 26 21:58:51 2020 A1: 0 Wed Feb 26 21:58:51 2020 A2: 0 Wed Feb 26 21:58:51 2020 A3: 0 Wed Feb 26 21:58:51 2020 A4: 0 Wed Feb 26 21:58:51 2020 A5: 0 Wed Feb 26 21:58:51 2020 A6: 69 Wed Feb 26 21:58:51 2020 skew 0.49, size 2.455e-12, alpha -0.758, combined = 2.233e-13 rroots = 0 Wed Feb 26 21:58:51 2020 Wed Feb 26 21:58:51 2020 commencing relation filtering Wed Feb 26 21:58:51 2020 estimated available RAM is 32721.3 MB Wed Feb 26 21:58:51 2020 commencing duplicate removal, pass 1 Wed Feb 26 22:02:31 2020 error -9 reading relation 16487701 Wed Feb 26 22:02:32 2020 error -1 reading relation 16569324 Wed Feb 26 22:02:58 2020 error -9 reading relation 18500360 Wed Feb 26 22:02:58 2020 error -9 reading relation 18527407 Wed Feb 26 22:59:56 2020 error -15 reading relation 272408413 Wed Feb 26 22:59:56 2020 error -9 reading relation 272414052 Wed Feb 26 22:59:56 2020 error -9 reading relation 272416360 Wed Feb 26 22:59:57 2020 skipped 387 relations with b > 2^32 Wed Feb 26 22:59:57 2020 skipped 745 relations with composite factors Wed Feb 26 22:59:57 2020 found 58832393 hash collisions in 272535564 relations Wed Feb 26 23:00:26 2020 added 1218412 free relations Wed Feb 26 23:00:26 2020 commencing duplicate removal, pass 2 Wed Feb 26 23:05:29 2020 found 59339599 duplicates and 214414377 unique relations Wed Feb 26 23:05:29 2020 memory use: 1449.5 MB Wed Feb 26 23:05:29 2020 reading ideals above 199950336 Wed Feb 26 23:05:29 2020 commencing singleton removal, initial pass Wed Feb 26 23:40:48 2020 memory use: 3012.0 MB Wed Feb 26 23:40:49 2020 reading all ideals from disk Wed Feb 26 23:40:51 2020 memory use: 3634.3 MB Wed Feb 26 23:40:59 2020 commencing in-memory singleton removal Wed Feb 26 23:41:07 2020 begin with 214414377 relations and 162717649 unique ideals Wed Feb 26 23:42:34 2020 reduce to 157623357 relations and 101394396 ideals in 12 passes Wed Feb 26 23:42:34 2020 max relations containing the same ideal: 36 Wed Feb 26 23:42:47 2020 reading ideals above 720000 Wed Feb 26 23:42:48 2020 commencing singleton removal, initial pass Thu Feb 27 00:14:02 2020 memory use: 3012.0 MB Thu Feb 27 00:14:02 2020 reading all ideals from disk Thu Feb 27 00:14:30 2020 memory use: 6271.5 MB Thu Feb 27 00:14:49 2020 keeping 122756128 ideals with weight <= 200, target excess is 787345 Thu Feb 27 00:15:10 2020 commencing in-memory singleton removal Thu Feb 27 00:15:25 2020 begin with 157623357 relations and 122756128 unique ideals Thu Feb 27 00:16:56 2020 reduce to 157620655 relations and 122753426 ideals in 6 passes Thu Feb 27 00:16:56 2020 max relations containing the same ideal: 200 Thu Feb 27 00:18:06 2020 removing 10011408 relations and 8011408 ideals in 2000000 cliques Thu Feb 27 00:18:10 2020 commencing in-memory singleton removal Thu Feb 27 00:18:24 2020 begin with 147609247 relations and 122753426 unique ideals Thu Feb 27 00:20:17 2020 reduce to 147084203 relations and 114208029 ideals in 8 passes Thu Feb 27 00:20:17 2020 max relations containing the same ideal: 198 Thu Feb 27 00:21:23 2020 removing 7724861 relations and 5724861 ideals in 2000000 cliques Thu Feb 27 00:21:26 2020 commencing in-memory singleton removal Thu Feb 27 00:21:39 2020 begin with 139359342 relations and 114208029 unique ideals Thu Feb 27 00:23:13 2020 reduce to 139008930 relations and 108127759 ideals in 7 passes Thu Feb 27 00:23:13 2020 max relations containing the same ideal: 193 Thu Feb 27 00:24:16 2020 removing 7054084 relations and 5054084 ideals in 2000000 cliques Thu Feb 27 00:24:19 2020 commencing in-memory singleton removal Thu Feb 27 00:24:31 2020 begin with 131954846 relations and 108127759 unique ideals Thu Feb 27 00:25:47 2020 reduce to 131650474 relations and 102764894 ideals in 6 passes Thu Feb 27 00:25:47 2020 max relations containing the same ideal: 187 Thu Feb 27 00:26:46 2020 removing 6708741 relations and 4708741 ideals in 2000000 cliques Thu Feb 27 00:26:49 2020 commencing in-memory singleton removal Thu Feb 27 00:27:00 2020 begin with 124941733 relations and 102764894 unique ideals Thu Feb 27 00:28:23 2020 reduce to 124656826 relations and 97767128 ideals in 7 passes Thu Feb 27 00:28:23 2020 max relations containing the same ideal: 180 Thu Feb 27 00:29:20 2020 removing 6500575 relations and 4500575 ideals in 2000000 cliques Thu Feb 27 00:29:23 2020 commencing in-memory singleton removal Thu Feb 27 00:29:33 2020 begin with 118156251 relations and 97767128 unique ideals Thu Feb 27 00:30:51 2020 reduce to 117881162 relations and 92987418 ideals in 7 passes Thu Feb 27 00:30:51 2020 max relations containing the same ideal: 175 Thu Feb 27 00:31:45 2020 removing 6353302 relations and 4353302 ideals in 2000000 cliques Thu Feb 27 00:31:48 2020 commencing in-memory singleton removal Thu Feb 27 00:31:58 2020 begin with 111527860 relations and 92987418 unique ideals Thu Feb 27 00:33:11 2020 reduce to 111257595 relations and 88359591 ideals in 7 passes Thu Feb 27 00:33:11 2020 max relations containing the same ideal: 169 Thu Feb 27 00:34:02 2020 removing 6249577 relations and 4249577 ideals in 2000000 cliques Thu Feb 27 00:34:05 2020 commencing in-memory singleton removal Thu Feb 27 00:34:14 2020 begin with 105008018 relations and 88359591 unique ideals Thu Feb 27 00:35:13 2020 reduce to 104737952 relations and 83835473 ideals in 6 passes Thu Feb 27 00:35:13 2020 max relations containing the same ideal: 165 Thu Feb 27 00:36:01 2020 removing 6178425 relations and 4178425 ideals in 2000000 cliques Thu Feb 27 00:36:04 2020 commencing in-memory singleton removal Thu Feb 27 00:36:13 2020 begin with 98559527 relations and 83835473 unique ideals Thu Feb 27 00:37:17 2020 reduce to 98286005 relations and 79378879 ideals in 7 passes Thu Feb 27 00:37:17 2020 max relations containing the same ideal: 157 Thu Feb 27 00:38:02 2020 removing 6128051 relations and 4128051 ideals in 2000000 cliques Thu Feb 27 00:38:04 2020 commencing in-memory singleton removal Thu Feb 27 00:38:13 2020 begin with 92157954 relations and 79378879 unique ideals Thu Feb 27 00:39:04 2020 reduce to 91878247 relations and 74965995 ideals in 6 passes Thu Feb 27 00:39:04 2020 max relations containing the same ideal: 150 Thu Feb 27 00:39:47 2020 removing 6088197 relations and 4088197 ideals in 2000000 cliques Thu Feb 27 00:39:50 2020 commencing in-memory singleton removal Thu Feb 27 00:39:57 2020 begin with 85790050 relations and 74965995 unique ideals Thu Feb 27 00:40:44 2020 reduce to 85497258 relations and 70579370 ideals in 6 passes Thu Feb 27 00:40:44 2020 max relations containing the same ideal: 143 Thu Feb 27 00:41:25 2020 removing 6072034 relations and 4072034 ideals in 2000000 cliques Thu Feb 27 00:41:27 2020 commencing in-memory singleton removal Thu Feb 27 00:41:34 2020 begin with 79425224 relations and 70579370 unique ideals Thu Feb 27 00:42:17 2020 reduce to 79118224 relations and 66194050 ideals in 6 passes Thu Feb 27 00:42:17 2020 max relations containing the same ideal: 137 Thu Feb 27 00:42:54 2020 removing 6063418 relations and 4063418 ideals in 2000000 cliques Thu Feb 27 00:42:57 2020 commencing in-memory singleton removal Thu Feb 27 00:43:03 2020 begin with 73054806 relations and 66194050 unique ideals Thu Feb 27 00:43:50 2020 reduce to 72728306 relations and 61797003 ideals in 7 passes Thu Feb 27 00:43:50 2020 max relations containing the same ideal: 128 Thu Feb 27 00:44:24 2020 removing 6065839 relations and 4065839 ideals in 2000000 cliques Thu Feb 27 00:44:27 2020 commencing in-memory singleton removal Thu Feb 27 00:44:33 2020 begin with 66662467 relations and 61797003 unique ideals Thu Feb 27 00:45:14 2020 reduce to 66312424 relations and 57372635 ideals in 7 passes Thu Feb 27 00:45:14 2020 max relations containing the same ideal: 120 Thu Feb 27 00:45:47 2020 removing 6082551 relations and 4082551 ideals in 2000000 cliques Thu Feb 27 00:45:49 2020 commencing in-memory singleton removal Thu Feb 27 00:45:54 2020 begin with 60229873 relations and 57372635 unique ideals Thu Feb 27 00:46:32 2020 reduce to 59844765 relations and 52894909 ideals in 7 passes Thu Feb 27 00:46:32 2020 max relations containing the same ideal: 113 Thu Feb 27 00:47:01 2020 removing 6115290 relations and 4115290 ideals in 2000000 cliques Thu Feb 27 00:47:03 2020 commencing in-memory singleton removal Thu Feb 27 00:47:08 2020 begin with 53729475 relations and 52894909 unique ideals Thu Feb 27 00:47:41 2020 reduce to 53297926 relations and 48335664 ideals in 7 passes Thu Feb 27 00:47:41 2020 max relations containing the same ideal: 107 Thu Feb 27 00:48:07 2020 removing 6172475 relations and 4172475 ideals in 2000000 cliques Thu Feb 27 00:48:10 2020 commencing in-memory singleton removal Thu Feb 27 00:48:13 2020 begin with 47125451 relations and 48335664 unique ideals Thu Feb 27 00:48:46 2020 reduce to 46623628 relations and 43645269 ideals in 8 passes Thu Feb 27 00:48:46 2020 max relations containing the same ideal: 94 Thu Feb 27 00:49:09 2020 removing 6258613 relations and 4258613 ideals in 2000000 cliques Thu Feb 27 00:49:11 2020 commencing in-memory singleton removal Thu Feb 27 00:49:14 2020 begin with 40365015 relations and 43645269 unique ideals Thu Feb 27 00:49:42 2020 reduce to 39754294 relations and 38753587 ideals in 8 passes Thu Feb 27 00:49:42 2020 max relations containing the same ideal: 85 Thu Feb 27 00:50:02 2020 removing 480871 relations and 393485 ideals in 87386 cliques Thu Feb 27 00:50:02 2020 commencing in-memory singleton removal Thu Feb 27 00:50:06 2020 begin with 39273423 relations and 38753587 unique ideals Thu Feb 27 00:50:26 2020 reduce to 39269213 relations and 38355886 ideals in 6 passes Thu Feb 27 00:50:26 2020 max relations containing the same ideal: 84 Thu Feb 27 00:50:35 2020 relations with 0 large ideals: 29550 Thu Feb 27 00:50:35 2020 relations with 1 large ideals: 12366 Thu Feb 27 00:50:35 2020 relations with 2 large ideals: 175371 Thu Feb 27 00:50:35 2020 relations with 3 large ideals: 1117236 Thu Feb 27 00:50:35 2020 relations with 4 large ideals: 3881952 Thu Feb 27 00:50:35 2020 relations with 5 large ideals: 8070082 Thu Feb 27 00:50:35 2020 relations with 6 large ideals: 10487859 Thu Feb 27 00:50:35 2020 relations with 7+ large ideals: 15494797 Thu Feb 27 00:50:35 2020 commencing 2-way merge Thu Feb 27 00:51:01 2020 reduce to 26649201 relation sets and 25735874 unique ideals Thu Feb 27 00:51:01 2020 commencing full merge Thu Feb 27 00:57:49 2020 memory use: 3070.0 MB Thu Feb 27 00:57:52 2020 found 14265671 cycles, need 14140074 Thu Feb 27 00:57:54 2020 weight of 14140074 cycles is about 990126922 (70.02/cycle) Thu Feb 27 00:57:54 2020 distribution of cycle lengths: Thu Feb 27 00:57:54 2020 1 relations: 1467921 Thu Feb 27 00:57:54 2020 2 relations: 1703155 Thu Feb 27 00:57:54 2020 3 relations: 1797427 Thu Feb 27 00:57:54 2020 4 relations: 1731403 Thu Feb 27 00:57:54 2020 5 relations: 1625406 Thu Feb 27 00:57:54 2020 6 relations: 1423045 Thu Feb 27 00:57:54 2020 7 relations: 1194007 Thu Feb 27 00:57:54 2020 8 relations: 949355 Thu Feb 27 00:57:54 2020 9 relations: 717400 Thu Feb 27 00:57:54 2020 10+ relations: 1530955 Thu Feb 27 00:57:54 2020 heaviest cycle: 19 relations Thu Feb 27 00:57:56 2020 commencing cycle optimization Thu Feb 27 00:58:13 2020 start with 73911379 relations Thu Feb 27 01:00:14 2020 pruned 2048392 relations Thu Feb 27 01:00:14 2020 memory use: 2394.7 MB Thu Feb 27 01:00:14 2020 distribution of cycle lengths: Thu Feb 27 01:00:14 2020 1 relations: 1467921 Thu Feb 27 01:00:14 2020 2 relations: 1738891 Thu Feb 27 01:00:14 2020 3 relations: 1866026 Thu Feb 27 01:00:14 2020 4 relations: 1785449 Thu Feb 27 01:00:14 2020 5 relations: 1679742 Thu Feb 27 01:00:14 2020 6 relations: 1454491 Thu Feb 27 01:00:14 2020 7 relations: 1209219 Thu Feb 27 01:00:14 2020 8 relations: 937222 Thu Feb 27 01:00:14 2020 9 relations: 691849 Thu Feb 27 01:00:14 2020 10+ relations: 1309264 Thu Feb 27 01:00:14 2020 heaviest cycle: 18 relations Thu Feb 27 01:00:40 2020 RelProcTime: 10909 Thu Feb 27 01:00:40 2020 Thu Feb 27 01:00:40 2020 commencing linear algebra Thu Feb 27 01:00:42 2020 read 14140074 cycles Thu Feb 27 01:01:04 2020 cycles contain 38812809 unique relations Thu Feb 27 01:07:44 2020 read 38812809 relations Thu Feb 27 01:08:55 2020 using 20 quadratic characters above 4294917295 Thu Feb 27 01:11:36 2020 building initial matrix Thu Feb 27 01:18:03 2020 memory use: 5157.9 MB Thu Feb 27 01:18:12 2020 read 14140074 cycles Thu Feb 27 01:18:16 2020 matrix is 14139897 x 14140074 (4236.5 MB) with weight 1279799490 (90.51/col) Thu Feb 27 01:18:16 2020 sparse part has weight 955023805 (67.54/col) Thu Feb 27 01:20:26 2020 filtering completed in 2 passes Thu Feb 27 01:20:30 2020 matrix is 14137408 x 14137585 (4236.3 MB) with weight 1279726908 (90.52/col) Thu Feb 27 01:20:30 2020 sparse part has weight 955005523 (67.55/col) Thu Feb 27 01:21:02 2020 matrix starts at (0, 0) Thu Feb 27 01:21:06 2020 matrix is 14137408 x 14137585 (4236.3 MB) with weight 1279726908 (90.52/col) Thu Feb 27 01:21:06 2020 sparse part has weight 955005523 (67.55/col) Thu Feb 27 01:21:06 2020 saving the first 48 matrix rows for later Thu Feb 27 01:21:09 2020 matrix includes 64 packed rows Thu Feb 27 01:21:11 2020 matrix is 14137360 x 14137585 (4068.2 MB) with weight 1016291757 (71.89/col) Thu Feb 27 01:21:11 2020 sparse part has weight 925083801 (65.43/col) Thu Feb 27 01:21:11 2020 using block size 8192 and superblock size 589824 for processor cache size 6144 kB Thu Feb 27 01:22:20 2020 commencing Lanczos iteration (6 threads) Thu Feb 27 01:22:20 2020 memory use: 3401.8 MB Thu Feb 27 01:23:22 2020 linear algebra at 0.0%, ETA 152h37m Thu Feb 27 01:23:42 2020 checkpointing every 100000 dimensions Wed Mar 4 11:26:10 2020 lanczos halted after 223568 iterations (dim = 14137358) Wed Mar 4 11:26:47 2020 recovered 37 nontrivial dependencies Wed Mar 4 11:26:57 2020 BLanczosTime: 555977 Wed Mar 4 11:26:57 2020 Wed Mar 4 11:26:57 2020 commencing square root phase Wed Mar 4 11:26:57 2020 handling dependencies 1 to 64 Wed Mar 4 11:26:57 2020 reading relations for dependency 1 Wed Mar 4 11:27:00 2020 read 7068850 cycles Wed Mar 4 11:27:10 2020 cycles contain 19400466 unique relations Wed Mar 4 11:31:58 2020 read 19400466 relations Wed Mar 4 11:33:40 2020 multiplying 19400466 relations Wed Mar 4 11:51:27 2020 multiply complete, coefficients have about 596.23 million bits Wed Mar 4 11:51:31 2020 initial square root is modulo 223441 Wed Mar 4 12:11:03 2020 GCD is N, no factor found Wed Mar 4 12:11:03 2020 reading relations for dependency 2 Wed Mar 4 12:11:06 2020 read 7069714 cycles Wed Mar 4 12:11:16 2020 cycles contain 19408542 unique relations Wed Mar 4 12:15:20 2020 read 19408542 relations Wed Mar 4 12:17:01 2020 multiplying 19408542 relations Wed Mar 4 12:34:49 2020 multiply complete, coefficients have about 596.48 million bits Wed Mar 4 12:34:54 2020 initial square root is modulo 224569 Wed Mar 4 12:54:40 2020 found factor: 140608178586949720216684218782500821902572231132341968301792447362453 Wed Mar 4 12:54:40 2020 reading relations for dependency 3 Wed Mar 4 12:54:43 2020 read 7068456 cycles Wed Mar 4 12:54:53 2020 cycles contain 19405500 unique relations Wed Mar 4 12:59:16 2020 read 19405500 relations Wed Mar 4 13:01:00 2020 multiplying 19405500 relations Wed Mar 4 13:18:50 2020 multiply complete, coefficients have about 596.38 million bits Wed Mar 4 13:18:54 2020 initial square root is modulo 224149 Wed Mar 4 13:38:43 2020 found factor: 140608178586949720216684218782500821902572231132341968301792447362453 Wed Mar 4 13:38:43 2020 reading relations for dependency 4 Wed Mar 4 13:38:49 2020 read 7070921 cycles Wed Mar 4 13:39:00 2020 cycles contain 19409852 unique relations Wed Mar 4 13:43:11 2020 read 19409852 relations Wed Mar 4 13:44:54 2020 multiplying 19409852 relations Wed Mar 4 14:02:44 2020 multiply complete, coefficients have about 596.51 million bits Wed Mar 4 14:02:49 2020 initial square root is modulo 224869 Wed Mar 4 14:22:38 2020 found factor: 140608178586949720216684218782500821902572231132341968301792447362453 Wed Mar 4 14:22:38 2020 reading relations for dependency 5 Wed Mar 4 14:22:45 2020 read 7068572 cycles Wed Mar 4 14:22:56 2020 cycles contain 19405112 unique relations Wed Mar 4 14:27:07 2020 read 19405112 relations Wed Mar 4 14:28:51 2020 multiplying 19405112 relations Wed Mar 4 14:46:40 2020 multiply complete, coefficients have about 596.36 million bits Wed Mar 4 14:46:45 2020 initial square root is modulo 224047 Wed Mar 4 15:06:34 2020 sqrtTime: 13177 Wed Mar 4 15:06:34 2020 p67 factor: 1017427293854259988038024275612197407393617272662943703343053137541 Wed Mar 4 15:06:34 2020 p69 factor: 140608178586949720216684218782500821902572231132341968301792447362453 Wed Mar 4 15:06:34 2020 p78 factor: 156402703184321544600933789506075228059079503374185320610065913984660309569441 Wed Mar 4 15:06:34 2020 elapsed time 161:07:45