Thu Sep 23 09:23:15 2021 Thu Sep 23 09:23:15 2021 Thu Sep 23 09:23:15 2021 Msieve v. 1.53 (SVN 988) Thu Sep 23 09:23:15 2021 random seeds: 46bfbfb8 01af0d69 Thu Sep 23 09:23:15 2021 factoring 26794745868028856768762552038954501484345325983054792228711288577054513254905253015077798155044319857597474642430116964867641350655002468386557565902048259156814533375073 (170 digits) Thu Sep 23 09:23:16 2021 searching for 15-digit factors Thu Sep 23 09:23:17 2021 commencing number field sieve (170-digit input) Thu Sep 23 09:23:17 2021 R0: 12765847665027705571158569756679998053 Thu Sep 23 09:23:17 2021 R1: -1 Thu Sep 23 09:23:17 2021 A0: 1 Thu Sep 23 09:23:17 2021 A1: 1 Thu Sep 23 09:23:17 2021 A2: 1 Thu Sep 23 09:23:17 2021 A3: 1 Thu Sep 23 09:23:17 2021 A4: 1 Thu Sep 23 09:23:17 2021 A5: 1 Thu Sep 23 09:23:17 2021 A6: 1 Thu Sep 23 09:23:17 2021 skew 1.00, size 4.866e-011, alpha 2.428, combined = 2.005e-012 rroots = 0 Thu Sep 23 09:23:17 2021 Thu Sep 23 09:23:17 2021 commencing relation filtering Thu Sep 23 09:23:17 2021 setting target matrix density to 100.0 Thu Sep 23 09:23:17 2021 estimated available RAM is 12041.5 MB Thu Sep 23 09:23:17 2021 commencing duplicate removal, pass 1 Thu Sep 23 09:29:02 2021 error -15 reading relation 26130689 Thu Sep 23 09:35:40 2021 error -9 reading relation 55975149 Thu Sep 23 09:37:22 2021 error -15 reading relation 63136191 Thu Sep 23 09:38:21 2021 error -15 reading relation 67416617 Thu Sep 23 09:39:05 2021 error -9 reading relation 70728025 Thu Sep 23 09:39:26 2021 error -15 reading relation 72276273 Thu Sep 23 09:39:59 2021 error -1 reading relation 74668408 Thu Sep 23 09:40:32 2021 error -15 reading relation 77139210 Thu Sep 23 09:40:58 2021 error -15 reading relation 79121009 Thu Sep 23 09:41:06 2021 error -9 reading relation 79733618 Thu Sep 23 09:43:29 2021 error -1 reading relation 90776993 Thu Sep 23 09:44:28 2021 error -1 reading relation 95299588 Thu Sep 23 09:45:23 2021 error -9 reading relation 99535460 Thu Sep 23 09:45:27 2021 error -15 reading relation 99760860 Thu Sep 23 09:45:40 2021 error -9 reading relation 100815613 Thu Sep 23 09:46:27 2021 error -9 reading relation 104411531 Thu Sep 23 09:47:14 2021 error -15 reading relation 108013532 Thu Sep 23 09:47:21 2021 error -9 reading relation 108557276 Thu Sep 23 09:47:26 2021 error -9 reading relation 108920009 Thu Sep 23 09:47:34 2021 error -15 reading relation 109606766 Thu Sep 23 09:47:46 2021 error -9 reading relation 110454349 Thu Sep 23 09:48:25 2021 error -15 reading relation 113354881 Thu Sep 23 09:48:44 2021 error -9 reading relation 114678238 Thu Sep 23 09:49:59 2021 error -9 reading relation 119768897 Thu Sep 23 09:50:28 2021 error -5 reading relation 121886510 Thu Sep 23 09:50:44 2021 error -5 reading relation 123078011 Thu Sep 23 09:51:00 2021 error -9 reading relation 124261878 Thu Sep 23 09:51:10 2021 error -15 reading relation 124991497 Thu Sep 23 09:51:42 2021 error -9 reading relation 127370827 Thu Sep 23 09:51:57 2021 error -1 reading relation 128508789 Thu Sep 23 09:52:08 2021 error -15 reading relation 129451909 Thu Sep 23 09:52:09 2021 error -15 reading relation 129482696 Thu Sep 23 09:52:09 2021 error -15 reading relation 129522760 Thu Sep 23 09:52:12 2021 error -15 reading relation 129735997 Thu Sep 23 09:52:13 2021 error -9 reading relation 129841561 Thu Sep 23 09:52:31 2021 skipped 10 relations with b > 2^32 Thu Sep 23 09:52:31 2021 skipped 21 relations with composite factors Thu Sep 23 09:52:31 2021 found 21206663 hash collisions in 131280109 relations Thu Sep 23 09:52:42 2021 added 2438534 free relations Thu Sep 23 09:52:42 2021 commencing duplicate removal, pass 2 Thu Sep 23 09:54:35 2021 found 18211854 duplicates and 115506789 unique relations Thu Sep 23 09:54:35 2021 memory use: 660.8 MB Thu Sep 23 09:54:36 2021 reading ideals above 69926912 Thu Sep 23 09:54:36 2021 commencing singleton removal, initial pass Thu Sep 23 10:15:20 2021 memory use: 2756.0 MB Thu Sep 23 10:15:20 2021 reading all ideals from disk Thu Sep 23 10:15:24 2021 memory use: 1981.5 MB Thu Sep 23 10:15:29 2021 commencing in-memory singleton removal Thu Sep 23 10:15:35 2021 begin with 115506789 relations and 85512654 unique ideals Thu Sep 23 10:16:21 2021 reduce to 85339492 relations and 52915594 ideals in 10 passes Thu Sep 23 10:16:21 2021 max relations containing the same ideal: 54 Thu Sep 23 10:16:29 2021 reading ideals above 720000 Thu Sep 23 10:16:29 2021 commencing singleton removal, initial pass Thu Sep 23 10:35:57 2021 memory use: 1506.0 MB Thu Sep 23 10:35:57 2021 reading all ideals from disk Thu Sep 23 10:36:04 2021 memory use: 3166.2 MB Thu Sep 23 10:36:17 2021 keeping 60709786 ideals with weight <= 200, target excess is 433726 Thu Sep 23 10:36:30 2021 commencing in-memory singleton removal Thu Sep 23 10:36:41 2021 begin with 85339494 relations and 60709786 unique ideals Thu Sep 23 10:37:11 2021 reduce to 85339440 relations and 60709728 ideals in 3 passes Thu Sep 23 10:37:11 2021 max relations containing the same ideal: 200 Thu Sep 23 10:37:58 2021 removing 7498625 relations and 5498625 ideals in 2000000 cliques Thu Sep 23 10:38:02 2021 commencing in-memory singleton removal Thu Sep 23 10:38:12 2021 begin with 77840815 relations and 60709728 unique ideals Thu Sep 23 10:39:08 2021 reduce to 77287892 relations and 54641870 ideals in 7 passes Thu Sep 23 10:39:08 2021 max relations containing the same ideal: 196 Thu Sep 23 10:39:51 2021 removing 6125871 relations and 4125871 ideals in 2000000 cliques Thu Sep 23 10:39:55 2021 commencing in-memory singleton removal Thu Sep 23 10:40:03 2021 begin with 71162021 relations and 54641870 unique ideals Thu Sep 23 10:40:54 2021 reduce to 70783154 relations and 50127086 ideals in 7 passes Thu Sep 23 10:40:54 2021 max relations containing the same ideal: 188 Thu Sep 23 10:41:34 2021 removing 5715451 relations and 3715451 ideals in 2000000 cliques Thu Sep 23 10:41:37 2021 commencing in-memory singleton removal Thu Sep 23 10:41:45 2021 begin with 65067703 relations and 50127086 unique ideals Thu Sep 23 10:42:29 2021 reduce to 64738728 relations and 46073887 ideals in 7 passes Thu Sep 23 10:42:29 2021 max relations containing the same ideal: 179 Thu Sep 23 10:43:06 2021 removing 5494606 relations and 3494606 ideals in 2000000 cliques Thu Sep 23 10:43:09 2021 commencing in-memory singleton removal Thu Sep 23 10:43:15 2021 begin with 59244122 relations and 46073887 unique ideals Thu Sep 23 10:43:55 2021 reduce to 58932304 relations and 42258638 ideals in 7 passes Thu Sep 23 10:43:55 2021 max relations containing the same ideal: 170 Thu Sep 23 10:44:28 2021 removing 5357698 relations and 3357698 ideals in 2000000 cliques Thu Sep 23 10:44:31 2021 commencing in-memory singleton removal Thu Sep 23 10:44:37 2021 begin with 53574606 relations and 42258638 unique ideals Thu Sep 23 10:45:12 2021 reduce to 53269552 relations and 38586626 ideals in 7 passes Thu Sep 23 10:45:12 2021 max relations containing the same ideal: 157 Thu Sep 23 10:45:42 2021 removing 5263275 relations and 3263275 ideals in 2000000 cliques Thu Sep 23 10:45:45 2021 commencing in-memory singleton removal Thu Sep 23 10:45:50 2021 begin with 48006277 relations and 38586626 unique ideals Thu Sep 23 10:46:17 2021 reduce to 47695723 relations and 35002455 ideals in 6 passes Thu Sep 23 10:46:17 2021 max relations containing the same ideal: 145 Thu Sep 23 10:46:45 2021 removing 5197988 relations and 3197988 ideals in 2000000 cliques Thu Sep 23 10:46:48 2021 commencing in-memory singleton removal Thu Sep 23 10:46:52 2021 begin with 42497735 relations and 35002455 unique ideals Thu Sep 23 10:47:18 2021 reduce to 42172685 relations and 31467665 ideals in 6 passes Thu Sep 23 10:47:18 2021 max relations containing the same ideal: 133 Thu Sep 23 10:47:43 2021 removing 5150343 relations and 3150343 ideals in 2000000 cliques Thu Sep 23 10:47:45 2021 commencing in-memory singleton removal Thu Sep 23 10:47:49 2021 begin with 37022342 relations and 31467665 unique ideals Thu Sep 23 10:48:10 2021 reduce to 36675820 relations and 27956924 ideals in 6 passes Thu Sep 23 10:48:10 2021 max relations containing the same ideal: 124 Thu Sep 23 10:48:32 2021 removing 5117905 relations and 3117905 ideals in 2000000 cliques Thu Sep 23 10:48:34 2021 commencing in-memory singleton removal Thu Sep 23 10:48:37 2021 begin with 31557915 relations and 27956924 unique ideals Thu Sep 23 10:48:54 2021 reduce to 31178612 relations and 24442559 ideals in 6 passes Thu Sep 23 10:48:54 2021 max relations containing the same ideal: 109 Thu Sep 23 10:49:13 2021 removing 5091905 relations and 3091905 ideals in 2000000 cliques Thu Sep 23 10:49:15 2021 commencing in-memory singleton removal Thu Sep 23 10:49:18 2021 begin with 26086707 relations and 24442559 unique ideals Thu Sep 23 10:49:32 2021 reduce to 25662548 relations and 20904340 ideals in 6 passes Thu Sep 23 10:49:32 2021 max relations containing the same ideal: 95 Thu Sep 23 10:49:47 2021 removing 5060502 relations and 3060502 ideals in 2000000 cliques Thu Sep 23 10:49:49 2021 commencing in-memory singleton removal Thu Sep 23 10:49:52 2021 begin with 20602046 relations and 20904340 unique ideals Thu Sep 23 10:50:04 2021 reduce to 20115954 relations and 17327384 ideals in 7 passes Thu Sep 23 10:50:04 2021 max relations containing the same ideal: 82 Thu Sep 23 10:50:17 2021 removing 5011943 relations and 3011943 ideals in 2000000 cliques Thu Sep 23 10:50:18 2021 commencing in-memory singleton removal Thu Sep 23 10:50:20 2021 begin with 15104011 relations and 17327384 unique ideals Thu Sep 23 10:50:31 2021 reduce to 14498863 relations and 13661760 ideals in 8 passes Thu Sep 23 10:50:31 2021 max relations containing the same ideal: 67 Thu Sep 23 10:50:39 2021 removing 1112250 relations and 778270 ideals in 333980 cliques Thu Sep 23 10:50:40 2021 commencing in-memory singleton removal Thu Sep 23 10:50:42 2021 begin with 13386613 relations and 13661760 unique ideals Thu Sep 23 10:50:49 2021 reduce to 13291354 relations and 12785768 ideals in 6 passes Thu Sep 23 10:50:49 2021 max relations containing the same ideal: 61 Thu Sep 23 10:50:59 2021 relations with 0 large ideals: 31905 Thu Sep 23 10:50:59 2021 relations with 1 large ideals: 11409 Thu Sep 23 10:50:59 2021 relations with 2 large ideals: 99165 Thu Sep 23 10:50:59 2021 relations with 3 large ideals: 573192 Thu Sep 23 10:50:59 2021 relations with 4 large ideals: 1749466 Thu Sep 23 10:50:59 2021 relations with 5 large ideals: 3130418 Thu Sep 23 10:50:59 2021 relations with 6 large ideals: 3462523 Thu Sep 23 10:50:59 2021 relations with 7+ large ideals: 4233276 Thu Sep 23 10:50:59 2021 commencing 2-way merge Thu Sep 23 10:51:10 2021 reduce to 9458866 relation sets and 8953280 unique ideals Thu Sep 23 10:51:10 2021 commencing full merge Thu Sep 23 10:55:52 2021 memory use: 1198.3 MB Thu Sep 23 10:55:54 2021 found 4490508 cycles, need 4435480 Thu Sep 23 10:55:55 2021 weight of 4435480 cycles is about 443785203 (100.05/cycle) Thu Sep 23 10:55:55 2021 distribution of cycle lengths: Thu Sep 23 10:55:55 2021 1 relations: 163457 Thu Sep 23 10:55:55 2021 2 relations: 274725 Thu Sep 23 10:55:55 2021 3 relations: 353543 Thu Sep 23 10:55:55 2021 4 relations: 390232 Thu Sep 23 10:55:55 2021 5 relations: 406521 Thu Sep 23 10:55:55 2021 6 relations: 399411 Thu Sep 23 10:55:55 2021 7 relations: 381641 Thu Sep 23 10:55:55 2021 8 relations: 347556 Thu Sep 23 10:55:55 2021 9 relations: 309638 Thu Sep 23 10:55:55 2021 10+ relations: 1408756 Thu Sep 23 10:55:55 2021 heaviest cycle: 27 relations Thu Sep 23 10:55:58 2021 commencing cycle optimization Thu Sep 23 10:56:08 2021 start with 34887908 relations Thu Sep 23 10:58:06 2021 pruned 1710783 relations Thu Sep 23 10:58:06 2021 memory use: 916.0 MB Thu Sep 23 10:58:06 2021 distribution of cycle lengths: Thu Sep 23 10:58:06 2021 1 relations: 163457 Thu Sep 23 10:58:06 2021 2 relations: 281797 Thu Sep 23 10:58:06 2021 3 relations: 369820 Thu Sep 23 10:58:06 2021 4 relations: 409610 Thu Sep 23 10:58:06 2021 5 relations: 430430 Thu Sep 23 10:58:06 2021 6 relations: 422667 Thu Sep 23 10:58:06 2021 7 relations: 403998 Thu Sep 23 10:58:06 2021 8 relations: 364035 Thu Sep 23 10:58:06 2021 9 relations: 321849 Thu Sep 23 10:58:06 2021 10+ relations: 1267817 Thu Sep 23 10:58:06 2021 heaviest cycle: 27 relations Thu Sep 23 10:58:14 2021 RelProcTime: 5697 Thu Sep 23 10:58:14 2021 Thu Sep 23 10:58:14 2021 commencing linear algebra Thu Sep 23 10:58:15 2021 read 4435480 cycles Thu Sep 23 10:58:27 2021 cycles contain 13061282 unique relations Thu Sep 23 11:01:04 2021 read 13061282 relations Thu Sep 23 11:01:36 2021 using 20 quadratic characters above 4294917295 Thu Sep 23 11:03:11 2021 building initial matrix Thu Sep 23 11:07:00 2021 memory use: 1614.6 MB Thu Sep 23 11:07:06 2021 read 4435480 cycles Thu Sep 23 11:07:07 2021 matrix is 4435302 x 4435480 (1769.9 MB) with weight 506956904 (114.30/col) Thu Sep 23 11:07:07 2021 sparse part has weight 415165626 (93.60/col) Thu Sep 23 11:08:09 2021 filtering completed in 2 passes Thu Sep 23 11:08:10 2021 matrix is 4435008 x 4435186 (1769.8 MB) with weight 506944913 (114.30/col) Thu Sep 23 11:08:10 2021 sparse part has weight 415159690 (93.61/col) Thu Sep 23 11:08:25 2021 matrix starts at (0, 0) Thu Sep 23 11:08:26 2021 matrix is 4435008 x 4435186 (1769.8 MB) with weight 506944913 (114.30/col) Thu Sep 23 11:08:26 2021 sparse part has weight 415159690 (93.61/col) Thu Sep 23 11:08:26 2021 saving the first 48 matrix rows for later Thu Sep 23 11:08:28 2021 matrix includes 64 packed rows Thu Sep 23 11:08:29 2021 matrix is 4434960 x 4435186 (1689.3 MB) with weight 428454815 (96.60/col) Thu Sep 23 11:08:29 2021 sparse part has weight 398482239 (89.85/col) Thu Sep 23 11:08:29 2021 using block size 8192 and superblock size 786432 for processor cache size 8192 kB Thu Sep 23 11:08:58 2021 commencing Lanczos iteration (6 threads) Thu Sep 23 11:08:58 2021 memory use: 1413.0 MB Thu Sep 23 11:09:16 2021 linear algebra at 0.0%, ETA 13h50m Thu Sep 23 11:09:22 2021 checkpointing every 320000 dimensions Fri Sep 24 01:01:21 2021 lanczos halted after 70136 iterations (dim = 4434960) Fri Sep 24 01:01:27 2021 recovered 40 nontrivial dependencies Fri Sep 24 01:01:29 2021 BLanczosTime: 50595 Fri Sep 24 01:01:29 2021 Fri Sep 24 01:01:29 2021 commencing square root phase Fri Sep 24 01:01:29 2021 handling dependencies 1 to 64 Fri Sep 24 01:01:29 2021 reading relations for dependency 1 Fri Sep 24 01:01:30 2021 read 2218639 cycles Fri Sep 24 01:01:36 2021 cycles contain 6529930 unique relations Fri Sep 24 01:03:21 2021 read 6529930 relations Fri Sep 24 01:04:03 2021 multiplying 6529930 relations Fri Sep 24 01:09:24 2021 multiply complete, coefficients have about 158.80 million bits Fri Sep 24 01:09:26 2021 initial square root is modulo 500197 Fri Sep 24 01:14:51 2021 GCD is N, no factor found Fri Sep 24 01:14:51 2021 reading relations for dependency 2 Fri Sep 24 01:14:53 2021 read 2215771 cycles Fri Sep 24 01:14:58 2021 cycles contain 6526472 unique relations Fri Sep 24 01:16:43 2021 read 6526472 relations Fri Sep 24 01:17:25 2021 multiplying 6526472 relations Fri Sep 24 01:22:53 2021 multiply complete, coefficients have about 158.72 million bits Fri Sep 24 01:22:54 2021 initial square root is modulo 496849 Fri Sep 24 01:28:24 2021 GCD is N, no factor found Fri Sep 24 01:28:24 2021 reading relations for dependency 3 Fri Sep 24 01:28:26 2021 read 2216978 cycles Fri Sep 24 01:28:31 2021 cycles contain 6529896 unique relations Fri Sep 24 01:30:17 2021 read 6529896 relations Fri Sep 24 01:31:01 2021 multiplying 6529896 relations Fri Sep 24 01:36:26 2021 multiply complete, coefficients have about 158.80 million bits Fri Sep 24 01:36:27 2021 initial square root is modulo 500069 Fri Sep 24 01:41:51 2021 sqrtTime: 2422 Fri Sep 24 01:41:51 2021 p75 factor: 640441129436406709412668323020706981303785602378972958134019631219424059713 Fri Sep 24 01:41:51 2021 p95 factor: 41837952992819880833424939694185688968895045237169683206391182979227790868155230450152954194721 Fri Sep 24 01:41:51 2021 elapsed time 16:18:36