Thu Feb 18 18:35:39 2021 Thu Feb 18 18:35:39 2021 Thu Feb 18 18:35:39 2021 Msieve v. 1.53 (SVN unknown) Thu Feb 18 18:35:39 2021 random seeds: 6027114c 608eb80e Thu Feb 18 18:35:39 2021 factoring 840233298978916998934618564021480502696668410680123724501169618248420909684410765815715209220820290534329439226443752032650382301837447303628588010189231992455230000087942942140533038485352403548129763221369575285517973324842957407750179298876609383801 (252 digits) Thu Feb 18 18:35:40 2021 searching for 15-digit factors Thu Feb 18 18:35:41 2021 commencing number field sieve (252-digit input) Thu Feb 18 18:35:41 2021 R0: 971393965110385490392311061031893351773049 Thu Feb 18 18:35:41 2021 R1: -1 Thu Feb 18 18:35:41 2021 A0: -1 Thu Feb 18 18:35:41 2021 A1: 0 Thu Feb 18 18:35:41 2021 A2: 0 Thu Feb 18 18:35:41 2021 A3: 0 Thu Feb 18 18:35:41 2021 A4: 0 Thu Feb 18 18:35:41 2021 A5: 0 Thu Feb 18 18:35:41 2021 A6: 15803 Thu Feb 18 18:35:41 2021 skew 0.20, size 3.476e-13, alpha 3.268, combined = 5.595e-14 rroots = 2 Thu Feb 18 18:35:41 2021 Thu Feb 18 18:35:41 2021 commencing relation filtering Thu Feb 18 18:35:41 2021 setting target matrix density to 116.0 Thu Feb 18 18:35:41 2021 estimated available RAM is 32721.3 MB Thu Feb 18 18:35:41 2021 commencing duplicate removal, pass 1 Thu Feb 18 18:36:34 2021 error -9 reading relation 3879959 Thu Feb 18 18:37:02 2021 error -9 reading relation 6013782 Thu Feb 18 18:37:23 2021 error -9 reading relation 7554988 Thu Feb 18 18:37:59 2021 error -9 reading relation 10260248 Thu Feb 18 18:37:59 2021 error -9 reading relation 10270873 Thu Feb 18 18:38:24 2021 error -1 reading relation 12135934 Thu Feb 18 18:39:24 2021 error -9 reading relation 16596633 Thu Feb 18 18:39:26 2021 error -9 reading relation 16739426 Thu Feb 18 19:52:15 2021 error -1 reading relation 342069644 Thu Feb 18 19:52:15 2021 error -5 reading relation 342074634 Thu Feb 18 19:52:16 2021 error -9 reading relation 342099951 Thu Feb 18 19:52:24 2021 error -9 reading relation 342706485 Thu Feb 18 19:52:31 2021 error -15 reading relation 343225139 Thu Feb 18 19:52:37 2021 error -1 reading relation 343687834 Thu Feb 18 19:52:43 2021 error -9 reading relation 344109299 Thu Feb 18 19:53:09 2021 skipped 14746 relations with b > 2^32 Thu Feb 18 19:53:09 2021 skipped 451 relations with composite factors Thu Feb 18 19:53:09 2021 found 76767672 hash collisions in 346000674 relations Thu Feb 18 19:53:38 2021 added 1218444 free relations Thu Feb 18 19:53:38 2021 commencing duplicate removal, pass 2 Thu Feb 18 19:59:51 2021 found 75366039 duplicates and 271853079 unique relations Thu Feb 18 19:59:51 2021 memory use: 2387.0 MB Thu Feb 18 19:59:51 2021 reading ideals above 199950336 Thu Feb 18 19:59:51 2021 commencing singleton removal, initial pass Thu Feb 18 20:47:35 2021 memory use: 6024.0 MB Thu Feb 18 20:47:35 2021 reading all ideals from disk Thu Feb 18 20:47:45 2021 memory use: 5079.5 MB Thu Feb 18 20:47:58 2021 commencing in-memory singleton removal Thu Feb 18 20:48:10 2021 begin with 271853079 relations and 238191027 unique ideals Thu Feb 18 20:51:13 2021 reduce to 175198290 relations and 132013049 ideals in 19 passes Thu Feb 18 20:51:13 2021 max relations containing the same ideal: 37 Thu Feb 18 20:51:30 2021 reading ideals above 720000 Thu Feb 18 20:51:31 2021 commencing singleton removal, initial pass Thu Feb 18 21:30:35 2021 memory use: 3012.0 MB Thu Feb 18 21:30:35 2021 reading all ideals from disk Thu Feb 18 21:31:22 2021 memory use: 7358.9 MB Thu Feb 18 21:31:46 2021 keeping 153252295 ideals with weight <= 200, target excess is 907723 Thu Feb 18 21:32:14 2021 commencing in-memory singleton removal Thu Feb 18 21:32:33 2021 begin with 175198290 relations and 153252295 unique ideals Thu Feb 18 21:34:29 2021 reduce to 175197627 relations and 153251632 ideals in 6 passes Thu Feb 18 21:34:29 2021 max relations containing the same ideal: 200 Thu Feb 18 21:36:02 2021 removing 13288625 relations and 11288625 ideals in 2000000 cliques Thu Feb 18 21:36:07 2021 commencing in-memory singleton removal Thu Feb 18 21:36:23 2021 begin with 161909002 relations and 153251632 unique ideals Thu Feb 18 21:39:06 2021 reduce to 161048870 relations and 141089553 ideals in 9 passes Thu Feb 18 21:39:06 2021 max relations containing the same ideal: 197 Thu Feb 18 21:40:33 2021 removing 10146089 relations and 8146089 ideals in 2000000 cliques Thu Feb 18 21:40:37 2021 commencing in-memory singleton removal Thu Feb 18 21:40:52 2021 begin with 150902781 relations and 141089553 unique ideals Thu Feb 18 21:43:06 2021 reduce to 150338017 relations and 132371214 ideals in 8 passes Thu Feb 18 21:43:06 2021 max relations containing the same ideal: 192 Thu Feb 18 21:44:26 2021 removing 9201576 relations and 7201576 ideals in 2000000 cliques Thu Feb 18 21:44:30 2021 commencing in-memory singleton removal Thu Feb 18 21:44:45 2021 begin with 141136441 relations and 132371214 unique ideals Thu Feb 18 21:46:50 2021 reduce to 140639226 relations and 124665780 ideals in 8 passes Thu Feb 18 21:46:50 2021 max relations containing the same ideal: 184 Thu Feb 18 21:48:09 2021 removing 8724780 relations and 6724780 ideals in 2000000 cliques Thu Feb 18 21:48:13 2021 commencing in-memory singleton removal Thu Feb 18 21:48:26 2021 begin with 131914446 relations and 124665780 unique ideals Thu Feb 18 21:50:39 2021 reduce to 131436654 relations and 117456633 ideals in 9 passes Thu Feb 18 21:50:39 2021 max relations containing the same ideal: 176 Thu Feb 18 21:51:50 2021 removing 8445545 relations and 6445545 ideals in 2000000 cliques Thu Feb 18 21:51:54 2021 commencing in-memory singleton removal Thu Feb 18 21:52:06 2021 begin with 122991109 relations and 117456633 unique ideals Thu Feb 18 21:53:40 2021 reduce to 122514336 relations and 110527505 ideals in 7 passes Thu Feb 18 21:53:40 2021 max relations containing the same ideal: 168 Thu Feb 18 21:54:47 2021 removing 8276059 relations and 6276059 ideals in 2000000 cliques Thu Feb 18 21:54:51 2021 commencing in-memory singleton removal Thu Feb 18 21:55:02 2021 begin with 114238277 relations and 110527505 unique ideals Thu Feb 18 21:56:41 2021 reduce to 113752134 relations and 103758137 ideals in 8 passes Thu Feb 18 21:56:41 2021 max relations containing the same ideal: 161 Thu Feb 18 21:57:44 2021 removing 8182368 relations and 6182368 ideals in 2000000 cliques Thu Feb 18 21:57:47 2021 commencing in-memory singleton removal Thu Feb 18 21:57:57 2021 begin with 105569766 relations and 103758137 unique ideals Thu Feb 18 21:59:29 2021 reduce to 105060017 relations and 97057823 ideals in 8 passes Thu Feb 18 21:59:29 2021 max relations containing the same ideal: 152 Thu Feb 18 22:00:27 2021 removing 8137979 relations and 6137979 ideals in 2000000 cliques Thu Feb 18 22:00:30 2021 commencing in-memory singleton removal Thu Feb 18 22:00:40 2021 begin with 96922038 relations and 97057823 unique ideals Thu Feb 18 22:01:53 2021 reduce to 96379166 relations and 90367861 ideals in 7 passes Thu Feb 18 22:01:53 2021 max relations containing the same ideal: 145 Thu Feb 18 22:02:47 2021 removing 8145726 relations and 6145726 ideals in 2000000 cliques Thu Feb 18 22:02:50 2021 commencing in-memory singleton removal Thu Feb 18 22:02:59 2021 begin with 88233440 relations and 90367861 unique ideals Thu Feb 18 22:04:23 2021 reduce to 87641099 relations and 83619298 ideals in 9 passes Thu Feb 18 22:04:23 2021 max relations containing the same ideal: 137 Thu Feb 18 22:05:14 2021 removing 8194115 relations and 6194115 ideals in 2000000 cliques Thu Feb 18 22:05:17 2021 commencing in-memory singleton removal Thu Feb 18 22:05:25 2021 begin with 79446984 relations and 83619298 unique ideals Thu Feb 18 22:06:41 2021 reduce to 78786697 relations and 76751841 ideals in 9 passes Thu Feb 18 22:06:41 2021 max relations containing the same ideal: 125 Thu Feb 18 22:07:27 2021 removing 4721264 relations and 3739367 ideals in 981897 cliques Thu Feb 18 22:07:29 2021 commencing in-memory singleton removal Thu Feb 18 22:07:37 2021 begin with 74065433 relations and 76751841 unique ideals Thu Feb 18 22:08:41 2021 reduce to 73840034 relations and 72784645 ideals in 8 passes Thu Feb 18 22:08:41 2021 max relations containing the same ideal: 120 Thu Feb 18 22:09:37 2021 relations with 0 large ideals: 34370 Thu Feb 18 22:09:37 2021 relations with 1 large ideals: 6710 Thu Feb 18 22:09:37 2021 relations with 2 large ideals: 101090 Thu Feb 18 22:09:37 2021 relations with 3 large ideals: 819963 Thu Feb 18 22:09:37 2021 relations with 4 large ideals: 3687036 Thu Feb 18 22:09:37 2021 relations with 5 large ideals: 10044840 Thu Feb 18 22:09:37 2021 relations with 6 large ideals: 17379417 Thu Feb 18 22:09:37 2021 relations with 7+ large ideals: 41766608 Thu Feb 18 22:09:37 2021 commencing 2-way merge Thu Feb 18 22:10:36 2021 reduce to 47570452 relation sets and 46515063 unique ideals Thu Feb 18 22:10:36 2021 commencing full merge Thu Feb 18 22:35:17 2021 memory use: 6048.5 MB Thu Feb 18 22:35:24 2021 found 21324649 cycles, need 21315263 Thu Feb 18 22:35:26 2021 weight of 21315263 cycles is about 2472672222 (116.00/cycle) Thu Feb 18 22:35:26 2021 distribution of cycle lengths: Thu Feb 18 22:35:26 2021 1 relations: 1569956 Thu Feb 18 22:35:26 2021 2 relations: 1629560 Thu Feb 18 22:35:26 2021 3 relations: 1654565 Thu Feb 18 22:35:26 2021 4 relations: 1595967 Thu Feb 18 22:35:26 2021 5 relations: 1550631 Thu Feb 18 22:35:26 2021 6 relations: 1488445 Thu Feb 18 22:35:26 2021 7 relations: 1407994 Thu Feb 18 22:35:26 2021 8 relations: 1330427 Thu Feb 18 22:35:26 2021 9 relations: 1239376 Thu Feb 18 22:35:26 2021 10+ relations: 7848342 Thu Feb 18 22:35:26 2021 heaviest cycle: 28 relations Thu Feb 18 22:35:31 2021 commencing cycle optimization Thu Feb 18 22:36:12 2021 start with 178734783 relations Thu Feb 18 22:46:07 2021 pruned 7314340 relations Thu Feb 18 22:46:07 2021 memory use: 4878.4 MB Thu Feb 18 22:46:07 2021 distribution of cycle lengths: Thu Feb 18 22:46:07 2021 1 relations: 1569956 Thu Feb 18 22:46:07 2021 2 relations: 1667739 Thu Feb 18 22:46:07 2021 3 relations: 1720274 Thu Feb 18 22:46:07 2021 4 relations: 1655587 Thu Feb 18 22:46:07 2021 5 relations: 1617822 Thu Feb 18 22:46:07 2021 6 relations: 1547193 Thu Feb 18 22:46:07 2021 7 relations: 1466659 Thu Feb 18 22:46:07 2021 8 relations: 1378334 Thu Feb 18 22:46:07 2021 9 relations: 1281780 Thu Feb 18 22:46:07 2021 10+ relations: 7409919 Thu Feb 18 22:46:07 2021 heaviest cycle: 28 relations Thu Feb 18 22:47:44 2021 RelProcTime: 15123 Thu Feb 18 22:47:44 2021 Thu Feb 18 22:47:44 2021 commencing linear algebra Thu Feb 18 22:47:48 2021 read 21315263 cycles Thu Feb 18 22:48:41 2021 cycles contain 73152758 unique relations Thu Feb 18 23:01:23 2021 read 73152758 relations Thu Feb 18 23:05:05 2021 using 20 quadratic characters above 4294917295 Thu Feb 18 23:10:32 2021 building initial matrix Thu Feb 18 23:28:06 2021 memory use: 9291.5 MB Thu Feb 18 23:28:30 2021 read 21315263 cycles Thu Feb 18 23:28:37 2021 matrix is 21315086 x 21315263 (9721.0 MB) with weight 2743376546 (128.70/col) Thu Feb 18 23:28:37 2021 sparse part has weight 2335142056 (109.55/col) Thu Feb 18 23:34:40 2021 filtering completed in 2 passes Thu Feb 18 23:34:46 2021 matrix is 21314828 x 21315005 (9721.0 MB) with weight 2743369182 (128.71/col) Thu Feb 18 23:34:46 2021 sparse part has weight 2335139777 (109.55/col) Thu Feb 18 23:37:09 2021 matrix starts at (0, 0) Thu Feb 18 23:37:15 2021 matrix is 21314828 x 21315005 (9721.0 MB) with weight 2743369182 (128.71/col) Thu Feb 18 23:37:15 2021 sparse part has weight 2335139777 (109.55/col) Thu Feb 18 23:37:15 2021 saving the first 48 matrix rows for later Thu Feb 18 23:37:23 2021 matrix includes 64 packed rows Thu Feb 18 23:37:27 2021 matrix is 21314780 x 21315005 (9337.1 MB) with weight 2367354577 (111.07/col) Thu Feb 18 23:37:27 2021 sparse part has weight 2234526912 (104.83/col) Thu Feb 18 23:37:27 2021 using block size 8192 and superblock size 589824 for processor cache size 6144 kB Thu Feb 18 23:40:28 2021 commencing Lanczos iteration (6 threads) Thu Feb 18 23:40:28 2021 memory use: 8099.5 MB Thu Feb 18 23:43:00 2021 linear algebra at 0.0%, ETA 564h46m Thu Feb 18 23:43:50 2021 checkpointing every 40000 dimensions Sun Mar 14 23:58:53 2021 lanczos halted after 337071 iterations (dim = 21314780) Sun Mar 14 23:59:43 2021 recovered 38 nontrivial dependencies Mon Mar 15 00:00:29 2021 BLanczosTime: 2074365 Mon Mar 15 00:00:29 2021 Mon Mar 15 00:00:29 2021 commencing square root phase Mon Mar 15 00:00:29 2021 handling dependencies 1 to 64 Mon Mar 15 00:00:29 2021 reading relations for dependency 1 Mon Mar 15 00:00:35 2021 read 10658135 cycles Mon Mar 15 00:01:02 2021 cycles contain 36582276 unique relations Mon Mar 15 00:08:18 2021 read 36582276 relations Mon Mar 15 00:12:06 2021 multiplying 36582276 relations Mon Mar 15 01:03:58 2021 multiply complete, coefficients have about 1422.91 million bits Mon Mar 15 01:04:07 2021 initial square root is modulo 2414239 Mon Mar 15 02:00:30 2021 found factor: 3667987513379661752230990409397303598089715955245110775300601829788474951 Mon Mar 15 02:00:30 2021 reading relations for dependency 2 Mon Mar 15 02:00:34 2021 read 10657801 cycles Mon Mar 15 02:00:59 2021 cycles contain 36574172 unique relations Mon Mar 15 02:08:17 2021 read 36574172 relations Mon Mar 15 02:12:08 2021 multiplying 36574172 relations Mon Mar 15 03:03:42 2021 multiply complete, coefficients have about 1422.58 million bits Mon Mar 15 03:03:52 2021 initial square root is modulo 2405983 Mon Mar 15 04:00:04 2021 found factor: 3667987513379661752230990409397303598089715955245110775300601829788474951 Mon Mar 15 04:00:04 2021 reading relations for dependency 3 Mon Mar 15 04:00:09 2021 read 10659388 cycles Mon Mar 15 04:00:34 2021 cycles contain 36576730 unique relations Mon Mar 15 04:07:55 2021 read 36576730 relations Mon Mar 15 04:11:38 2021 multiplying 36576730 relations Mon Mar 15 05:03:19 2021 multiply complete, coefficients have about 1422.68 million bits Mon Mar 15 05:03:29 2021 initial square root is modulo 2408503 Mon Mar 15 05:59:18 2021 found factor: 3667987513379661752230990409397303598089715955245110775300601829788474951 Mon Mar 15 05:59:18 2021 reading relations for dependency 4 Mon Mar 15 06:00:39 2021 read 10651763 cycles Mon Mar 15 06:01:04 2021 cycles contain 36568484 unique relations Mon Mar 15 06:08:18 2021 read 36568484 relations Mon Mar 15 06:12:11 2021 multiplying 36568484 relations Mon Mar 15 07:03:40 2021 multiply complete, coefficients have about 1422.36 million bits Mon Mar 15 07:03:50 2021 initial square root is modulo 2400571 Mon Mar 15 07:59:35 2021 sqrtTime: 28746 Mon Mar 15 07:59:35 2021 p63 factor: 673463212904697549042966290404684056989946041020357037381839399 Mon Mar 15 07:59:35 2021 p73 factor: 3667987513379661752230990409397303598089715955245110775300601829788474951 Mon Mar 15 07:59:35 2021 p117 factor: 340140356402296551478244448618534996651146282709955817744873664001135619446861145542115683455655564528678156479134249 Mon Mar 15 07:59:35 2021 elapsed time 588:23:56