Sun Feb 21 08:11:29 2021 Sun Feb 21 08:11:29 2021 Sun Feb 21 08:11:29 2021 Msieve v. 1.53 (SVN 988M) Sun Feb 21 08:11:29 2021 random seeds: 61a04fcd 9df9c042 Sun Feb 21 08:11:29 2021 factoring 4106609588424447396996222513379693412003124266674309491729863520838604405098468326525117796586140070117851619915391156765666063208322467227650127948824324948835330331474513772746013914096270530047953563697353232926629461 (220 digits) Sun Feb 21 08:11:30 2021 searching for 15-digit factors Sun Feb 21 08:11:31 2021 commencing number field sieve (220-digit input) Sun Feb 21 08:11:31 2021 R0: -411376139330301510538742295639337626245683966408394965837152256 Sun Feb 21 08:11:31 2021 R1: 834385168331080533771857328695283 Sun Feb 21 08:11:31 2021 A0: 9 Sun Feb 21 08:11:31 2021 A1: 18 Sun Feb 21 08:11:31 2021 A2: 18 Sun Feb 21 08:11:31 2021 A3: 12 Sun Feb 21 08:11:31 2021 A4: 4 Sun Feb 21 08:11:31 2021 skew 1.22, size 1.207e-25, alpha 1.559, combined = 2.910e-15 rroots = 0 Sun Feb 21 08:11:31 2021 Sun Feb 21 08:11:31 2021 commencing relation filtering Sun Feb 21 08:11:31 2021 setting target matrix density to 120.0 Sun Feb 21 08:11:31 2021 estimated available RAM is 32768.0 MB Sun Feb 21 08:11:31 2021 commencing duplicate removal, pass 1 Sun Feb 21 08:18:45 2021 error -5 reading relation 70107704 [4083 more error lines] Sun Feb 21 08:48:15 2021 error -15 reading relation 353497303 Sun Feb 21 08:49:40 2021 skipped 82202 relations with b > 2^32 Sun Feb 21 08:49:40 2021 skipped 8 relations with composite factors Sun Feb 21 08:49:40 2021 found 28099679 hash collisions in 367008278 relations Sun Feb 21 08:49:45 2021 added 3657369 free relations Sun Feb 21 08:49:45 2021 commencing duplicate removal, pass 2 Sun Feb 21 09:06:32 2021 found 1 duplicates and 370665646 unique relations Sun Feb 21 09:06:33 2021 memory use: 1321.5 MB Sun Feb 21 09:06:33 2021 reading ideals above 319881216 Sun Feb 21 09:06:33 2021 commencing singleton removal, initial pass Sun Feb 21 09:33:50 2021 memory use: 6024.0 MB Sun Feb 21 09:33:50 2021 reading all ideals from disk Sun Feb 21 09:36:29 2021 memory use: 6694.4 MB Sun Feb 21 09:36:43 2021 commencing in-memory singleton removal Sun Feb 21 09:36:57 2021 begin with 370665646 relations and 299989154 unique ideals Sun Feb 21 09:39:42 2021 reduce to 257525356 relations and 177764969 ideals in 13 passes Sun Feb 21 09:39:42 2021 max relations containing the same ideal: 48 Sun Feb 21 09:40:13 2021 reading ideals above 720000 Sun Feb 21 09:40:14 2021 commencing singleton removal, initial pass Sun Feb 21 10:07:37 2021 memory use: 5512.0 MB Sun Feb 21 10:07:38 2021 reading all ideals from disk Sun Feb 21 10:12:06 2021 memory use: 11312.5 MB Sun Feb 21 10:12:33 2021 keeping 210896358 ideals with weight <= 200, target excess is 1399296 Sun Feb 21 10:13:03 2021 commencing in-memory singleton removal Sun Feb 21 10:13:23 2021 begin with 257525356 relations and 210896358 unique ideals Sun Feb 21 10:16:20 2021 reduce to 257459323 relations and 210830316 ideals in 8 passes Sun Feb 21 10:16:20 2021 max relations containing the same ideal: 200 Sun Feb 21 10:18:02 2021 removing 12055373 relations and 10055373 ideals in 2000000 cliques Sun Feb 21 10:18:07 2021 commencing in-memory singleton removal Sun Feb 21 10:18:27 2021 begin with 245403950 relations and 210830316 unique ideals Sun Feb 21 10:21:36 2021 reduce to 244959436 relations and 200325769 ideals in 9 passes Sun Feb 21 10:21:36 2021 max relations containing the same ideal: 200 Sun Feb 21 10:23:13 2021 removing 9236046 relations and 7236046 ideals in 2000000 cliques Sun Feb 21 10:23:18 2021 commencing in-memory singleton removal Sun Feb 21 10:23:37 2021 begin with 235723390 relations and 200325769 unique ideals Sun Feb 21 10:25:57 2021 reduce to 235434806 relations and 192798412 ideals in 7 passes Sun Feb 21 10:25:57 2021 max relations containing the same ideal: 197 Sun Feb 21 10:27:31 2021 removing 8355852 relations and 6355852 ideals in 2000000 cliques Sun Feb 21 10:27:36 2021 commencing in-memory singleton removal Sun Feb 21 10:27:54 2021 begin with 227078954 relations and 192798412 unique ideals Sun Feb 21 10:29:49 2021 reduce to 226829472 relations and 186190973 ideals in 6 passes Sun Feb 21 10:29:49 2021 max relations containing the same ideal: 194 Sun Feb 21 10:31:20 2021 removing 7876962 relations and 5876962 ideals in 2000000 cliques Sun Feb 21 10:31:24 2021 commencing in-memory singleton removal Sun Feb 21 10:31:41 2021 begin with 218952510 relations and 186190973 unique ideals Sun Feb 21 10:33:51 2021 reduce to 218719233 relations and 180078629 ideals in 7 passes Sun Feb 21 10:33:51 2021 max relations containing the same ideal: 190 Sun Feb 21 10:35:20 2021 removing 7572613 relations and 5572613 ideals in 2000000 cliques Sun Feb 21 10:35:24 2021 commencing in-memory singleton removal Sun Feb 21 10:35:40 2021 begin with 211146620 relations and 180078629 unique ideals Sun Feb 21 10:37:28 2021 reduce to 210924909 relations and 174282428 ideals in 6 passes Sun Feb 21 10:37:28 2021 max relations containing the same ideal: 187 Sun Feb 21 10:38:53 2021 removing 7355769 relations and 5355769 ideals in 2000000 cliques Sun Feb 21 10:38:57 2021 commencing in-memory singleton removal Sun Feb 21 10:39:12 2021 begin with 203569140 relations and 174282428 unique ideals Sun Feb 21 10:40:56 2021 reduce to 203350696 relations and 168706275 ideals in 6 passes Sun Feb 21 10:40:56 2021 max relations containing the same ideal: 185 Sun Feb 21 10:42:18 2021 removing 7205997 relations and 5205997 ideals in 2000000 cliques Sun Feb 21 10:42:22 2021 commencing in-memory singleton removal Sun Feb 21 10:42:37 2021 begin with 196144699 relations and 168706275 unique ideals Sun Feb 21 10:44:16 2021 reduce to 195930119 relations and 163283695 ideals in 6 passes Sun Feb 21 10:44:16 2021 max relations containing the same ideal: 182 Sun Feb 21 10:45:36 2021 removing 7094444 relations and 5094444 ideals in 2000000 cliques Sun Feb 21 10:45:39 2021 commencing in-memory singleton removal Sun Feb 21 10:45:54 2021 begin with 188835675 relations and 163283695 unique ideals Sun Feb 21 10:47:29 2021 reduce to 188620089 relations and 157971586 ideals in 6 passes Sun Feb 21 10:47:29 2021 max relations containing the same ideal: 179 Sun Feb 21 10:48:46 2021 removing 7013191 relations and 5013191 ideals in 2000000 cliques Sun Feb 21 10:48:50 2021 commencing in-memory singleton removal Sun Feb 21 10:49:04 2021 begin with 181606898 relations and 157971586 unique ideals Sun Feb 21 10:50:35 2021 reduce to 181390592 relations and 152739952 ideals in 6 passes Sun Feb 21 10:50:35 2021 max relations containing the same ideal: 174 Sun Feb 21 10:51:49 2021 removing 6956273 relations and 4956273 ideals in 2000000 cliques Sun Feb 21 10:51:53 2021 commencing in-memory singleton removal Sun Feb 21 10:52:06 2021 begin with 174434319 relations and 152739952 unique ideals Sun Feb 21 10:53:34 2021 reduce to 174213832 relations and 147560941 ideals in 6 passes Sun Feb 21 10:53:34 2021 max relations containing the same ideal: 171 Sun Feb 21 10:54:46 2021 removing 6912532 relations and 4912532 ideals in 2000000 cliques Sun Feb 21 10:54:50 2021 commencing in-memory singleton removal Sun Feb 21 10:55:03 2021 begin with 167301300 relations and 147560941 unique ideals Sun Feb 21 10:56:27 2021 reduce to 167074956 relations and 142419678 ideals in 6 passes Sun Feb 21 10:56:27 2021 max relations containing the same ideal: 169 Sun Feb 21 10:57:35 2021 removing 6886635 relations and 4886635 ideals in 2000000 cliques Sun Feb 21 10:57:38 2021 commencing in-memory singleton removal Sun Feb 21 10:57:51 2021 begin with 160188321 relations and 142419678 unique ideals Sun Feb 21 10:59:11 2021 reduce to 159956320 relations and 137298516 ideals in 6 passes Sun Feb 21 10:59:11 2021 max relations containing the same ideal: 165 Sun Feb 21 11:00:16 2021 removing 6878098 relations and 4878098 ideals in 2000000 cliques Sun Feb 21 11:00:20 2021 commencing in-memory singleton removal Sun Feb 21 11:00:31 2021 begin with 153078222 relations and 137298516 unique ideals Sun Feb 21 11:02:12 2021 reduce to 152838733 relations and 132178169 ideals in 8 passes Sun Feb 21 11:02:12 2021 max relations containing the same ideal: 162 Sun Feb 21 11:03:15 2021 removing 6879344 relations and 4879344 ideals in 2000000 cliques Sun Feb 21 11:03:18 2021 commencing in-memory singleton removal Sun Feb 21 11:03:29 2021 begin with 145959389 relations and 132178169 unique ideals Sun Feb 21 11:04:53 2021 reduce to 145708679 relations and 127045185 ideals in 7 passes Sun Feb 21 11:04:53 2021 max relations containing the same ideal: 155 Sun Feb 21 11:05:54 2021 removing 6888612 relations and 4888612 ideals in 2000000 cliques Sun Feb 21 11:05:57 2021 commencing in-memory singleton removal Sun Feb 21 11:06:07 2021 begin with 138820067 relations and 127045185 unique ideals Sun Feb 21 11:07:27 2021 reduce to 138558276 relations and 121891488 ideals in 7 passes Sun Feb 21 11:07:27 2021 max relations containing the same ideal: 147 Sun Feb 21 11:08:24 2021 removing 6915824 relations and 4915824 ideals in 2000000 cliques Sun Feb 21 11:08:27 2021 commencing in-memory singleton removal Sun Feb 21 11:08:37 2021 begin with 131642452 relations and 121891488 unique ideals Sun Feb 21 11:10:03 2021 reduce to 131367250 relations and 116696956 ideals in 8 passes Sun Feb 21 11:10:03 2021 max relations containing the same ideal: 142 Sun Feb 21 11:10:58 2021 removing 6943377 relations and 4943377 ideals in 2000000 cliques Sun Feb 21 11:11:01 2021 commencing in-memory singleton removal Sun Feb 21 11:11:10 2021 begin with 124423873 relations and 116696956 unique ideals Sun Feb 21 11:12:31 2021 reduce to 124131500 relations and 111457263 ideals in 8 passes Sun Feb 21 11:12:31 2021 max relations containing the same ideal: 138 Sun Feb 21 11:13:23 2021 removing 6992056 relations and 4992056 ideals in 2000000 cliques Sun Feb 21 11:13:26 2021 commencing in-memory singleton removal Sun Feb 21 11:13:35 2021 begin with 117139444 relations and 111457263 unique ideals Sun Feb 21 11:14:41 2021 reduce to 116827382 relations and 106148776 ideals in 7 passes Sun Feb 21 11:14:41 2021 max relations containing the same ideal: 135 Sun Feb 21 11:15:30 2021 removing 7045158 relations and 5045158 ideals in 2000000 cliques Sun Feb 21 11:15:33 2021 commencing in-memory singleton removal Sun Feb 21 11:15:40 2021 begin with 109782224 relations and 106148776 unique ideals Sun Feb 21 11:16:43 2021 reduce to 109447642 relations and 100764032 ideals in 7 passes Sun Feb 21 11:16:43 2021 max relations containing the same ideal: 124 Sun Feb 21 11:17:29 2021 removing 7118901 relations and 5118901 ideals in 2000000 cliques Sun Feb 21 11:17:32 2021 commencing in-memory singleton removal Sun Feb 21 11:17:39 2021 begin with 102328741 relations and 100764032 unique ideals Sun Feb 21 11:18:53 2021 reduce to 101963723 relations and 95274408 ideals in 9 passes Sun Feb 21 11:18:53 2021 max relations containing the same ideal: 119 Sun Feb 21 11:19:37 2021 removing 7199434 relations and 5199434 ideals in 2000000 cliques Sun Feb 21 11:19:39 2021 commencing in-memory singleton removal Sun Feb 21 11:19:46 2021 begin with 94764289 relations and 95274408 unique ideals Sun Feb 21 11:20:39 2021 reduce to 94364086 relations and 89667962 ideals in 7 passes Sun Feb 21 11:20:39 2021 max relations containing the same ideal: 109 Sun Feb 21 11:21:19 2021 removing 7306673 relations and 5306673 ideals in 2000000 cliques Sun Feb 21 11:21:22 2021 commencing in-memory singleton removal Sun Feb 21 11:21:28 2021 begin with 87057413 relations and 89667962 unique ideals Sun Feb 21 11:22:30 2021 reduce to 86613644 relations and 83909477 ideals in 9 passes Sun Feb 21 11:22:30 2021 max relations containing the same ideal: 103 Sun Feb 21 11:23:07 2021 removing 4529790 relations and 3448807 ideals in 1080983 cliques Sun Feb 21 11:23:10 2021 commencing in-memory singleton removal Sun Feb 21 11:23:16 2021 begin with 82083854 relations and 83909477 unique ideals Sun Feb 21 11:23:54 2021 reduce to 81909142 relations and 80284265 ideals in 6 passes Sun Feb 21 11:23:54 2021 max relations containing the same ideal: 99 Sun Feb 21 11:24:38 2021 relations with 0 large ideals: 108420 Sun Feb 21 11:24:38 2021 relations with 1 large ideals: 13463 Sun Feb 21 11:24:38 2021 relations with 2 large ideals: 145029 Sun Feb 21 11:24:38 2021 relations with 3 large ideals: 1087805 Sun Feb 21 11:24:38 2021 relations with 4 large ideals: 4692879 Sun Feb 21 11:24:38 2021 relations with 5 large ideals: 14629497 Sun Feb 21 11:24:38 2021 relations with 6 large ideals: 19305801 Sun Feb 21 11:24:38 2021 relations with 7+ large ideals: 41926248 Sun Feb 21 11:24:38 2021 commencing 2-way merge Sun Feb 21 11:25:29 2021 reduce to 54483716 relation sets and 52858839 unique ideals Sun Feb 21 11:25:29 2021 commencing full merge Sun Feb 21 11:48:19 2021 memory use: 6903.4 MB Sun Feb 21 11:48:33 2021 found 24365302 cycles, need 24337039 Sun Feb 21 11:48:34 2021 weight of 24337039 cycles is about 2921098408 (120.03/cycle) Sun Feb 21 11:48:34 2021 distribution of cycle lengths: Sun Feb 21 11:48:34 2021 1 relations: 1366958 Sun Feb 21 11:48:34 2021 2 relations: 1522952 Sun Feb 21 11:48:34 2021 3 relations: 1623652 Sun Feb 21 11:48:34 2021 4 relations: 1663033 Sun Feb 21 11:48:34 2021 5 relations: 1676509 Sun Feb 21 11:48:34 2021 6 relations: 1658664 Sun Feb 21 11:48:34 2021 7 relations: 1628476 Sun Feb 21 11:48:34 2021 8 relations: 1572949 Sun Feb 21 11:48:34 2021 9 relations: 1496230 Sun Feb 21 11:48:34 2021 10+ relations: 10127616 Sun Feb 21 11:48:34 2021 heaviest cycle: 28 relations Sun Feb 21 11:48:46 2021 commencing cycle optimization Sun Feb 21 11:49:48 2021 start with 220454627 relations Sun Feb 21 12:00:18 2021 pruned 10698891 relations Sun Feb 21 12:00:18 2021 memory use: 5657.8 MB Sun Feb 21 12:00:18 2021 distribution of cycle lengths: Sun Feb 21 12:00:18 2021 1 relations: 1366958 Sun Feb 21 12:00:18 2021 2 relations: 1554212 Sun Feb 21 12:00:18 2021 3 relations: 1690214 Sun Feb 21 12:00:18 2021 4 relations: 1734396 Sun Feb 21 12:00:18 2021 5 relations: 1765282 Sun Feb 21 12:00:18 2021 6 relations: 1744742 Sun Feb 21 12:00:18 2021 7 relations: 1719492 Sun Feb 21 12:00:18 2021 8 relations: 1654465 Sun Feb 21 12:00:18 2021 9 relations: 1574651 Sun Feb 21 12:00:18 2021 10+ relations: 9532627 Sun Feb 21 12:00:18 2021 heaviest cycle: 28 relations Sun Feb 21 12:01:40 2021 RelProcTime: 13809 Sun Feb 21 12:01:40 2021 Sun Feb 21 12:01:40 2021 commencing linear algebra Sun Feb 21 12:01:44 2021 read 24337039 cycles Sun Feb 21 12:02:41 2021 cycles contain 81059334 unique relations Sun Feb 21 12:19:46 2021 read 81059334 relations Sun Feb 21 12:23:01 2021 using 20 quadratic characters above 4294917295 Sun Feb 21 12:27:34 2021 building initial matrix Sun Feb 21 12:42:13 2021 memory use: 10690.5 MB Sun Feb 21 12:47:03 2021 read 24337039 cycles Sun Feb 21 12:47:08 2021 matrix is 24336862 x 24337039 (11511.9 MB) with weight 3257233932 (133.84/col) Sun Feb 21 12:47:08 2021 sparse part has weight 2750066546 (113.00/col) Sun Feb 21 12:52:07 2021 filtering completed in 2 passes Sun Feb 21 12:52:11 2021 matrix is 24336687 x 24336864 (11511.9 MB) with weight 3257228968 (133.84/col) Sun Feb 21 12:52:11 2021 sparse part has weight 2750065144 (113.00/col) Sun Feb 21 12:59:37 2021 matrix starts at (0, 0) Sun Feb 21 12:59:39 2021 matrix is 24336687 x 24336864 (11511.9 MB) with weight 3257228968 (133.84/col) Sun Feb 21 12:59:39 2021 sparse part has weight 2750065144 (113.00/col) Sun Feb 21 12:59:39 2021 saving the first 48 matrix rows for later Sun Feb 21 12:59:42 2021 matrix includes 64 packed rows Sun Feb 21 12:59:45 2021 matrix is 24336639 x 24336864 (11033.6 MB) with weight 2818778073 (115.82/col) Sun Feb 21 12:59:45 2021 sparse part has weight 2649028187 (108.85/col) Sun Feb 21 12:59:45 2021 using block size 8192 and superblock size 2162688 for processor cache size 22528 kB Sun Feb 21 13:02:26 2021 commencing Lanczos iteration (16 threads) Sun Feb 21 13:02:26 2021 memory use: 9621.0 MB Sun Feb 21 13:03:01 2021 linear algebra at 0.0%, ETA 146h57m Sun Feb 21 13:03:13 2021 checkpointing every 170000 dimensions Sat Feb 27 21:58:11 2021 lanczos halted after 384859 iterations (dim = 24336639) Sat Feb 27 21:58:31 2021 recovered 39 nontrivial dependencies Sat Feb 27 21:58:45 2021 BLanczosTime: 554225 Sat Feb 27 21:58:45 2021 Sat Feb 27 21:58:45 2021 commencing square root phase Sat Feb 27 21:58:45 2021 handling dependencies 1 to 64 Sat Feb 27 21:58:45 2021 reading relations for dependency 1 Sat Feb 27 21:59:06 2021 read 12171717 cycles Sat Feb 27 21:59:33 2021 cycles contain 40539526 unique relations Sat Feb 27 22:17:06 2021 read 40539526 relations Sat Feb 27 22:20:28 2021 multiplying 40539526 relations Sat Feb 27 22:35:48 2021 multiply complete, coefficients have about 1220.35 million bits Sat Feb 27 22:35:51 2021 warning: no irreducible prime found, switching to small primes Sat Feb 27 22:35:52 2021 initial square root is modulo 53 Sat Feb 27 22:55:51 2021 Newton iteration failed to converge Sat Feb 27 22:55:51 2021 algebraic square root failed Sat Feb 27 22:55:51 2021 reading relations for dependency 2 Sat Feb 27 22:56:17 2021 read 12167963 cycles Sat Feb 27 22:56:46 2021 cycles contain 40524126 unique relations Sat Feb 27 23:13:37 2021 read 40524126 relations Sat Feb 27 23:17:15 2021 multiplying 40524126 relations Sat Feb 27 23:32:26 2021 multiply complete, coefficients have about 1219.89 million bits Sat Feb 27 23:32:29 2021 warning: no irreducible prime found, switching to small primes Sat Feb 27 23:32:30 2021 initial square root is modulo 53 Sat Feb 27 23:52:30 2021 GCD is N, no factor found Sat Feb 27 23:52:30 2021 reading relations for dependency 3 Sat Feb 27 23:52:56 2021 read 12169727 cycles Sat Feb 27 23:53:24 2021 cycles contain 40534686 unique relations Sun Feb 28 00:10:15 2021 read 40534686 relations Sun Feb 28 00:13:52 2021 multiplying 40534686 relations Sun Feb 28 00:28:59 2021 multiply complete, coefficients have about 1220.22 million bits Sun Feb 28 00:29:03 2021 warning: no irreducible prime found, switching to small primes Sun Feb 28 00:29:03 2021 initial square root is modulo 53 Sun Feb 28 00:49:07 2021 sqrtTime: 10222 Sun Feb 28 00:49:07 2021 p84 factor: 161289010875891408149774896723759782914182820797075070649700914143222073547620631141 Sun Feb 28 00:49:07 2021 p137 factor: 25461186513099763516889424900310819155839006551455787591490616227574623778042820495426387362343186856642399003119352921829574129988105521 Sun Feb 28 00:49:07 2021 elapsed time 160:37:38