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- Mon Sep 14 22:42:26 2020
- Mon Sep 14 22:42:26 2020
- Mon Sep 14 22:42:26 2020 Msieve v. 1.54 (SVN 1025)
- Mon Sep 14 22:42:26 2020 random seeds: 36b5114e 423448cb
- Mon Sep 14 22:42:26 2020 factoring 8234161389485425299752739910830700919519753294323225681792747992069869743569790470719989833079632210025773936402163484157349625695365042516910042936413359959104099161157908511584124476829547688516120943557774639173206762871 (223 digits)
- Mon Sep 14 22:42:27 2020 searching for 15-digit factors
- Mon Sep 14 22:42:28 2020 commencing number field sieve (223-digit input)
- Mon Sep 14 22:42:28 2020 R0: 716917930050061252587451465154207645335151330
- Mon Sep 14 22:42:28 2020 R1: -26775323154913765719823
- Mon Sep 14 22:42:28 2020 A0: 1
- Mon Sep 14 22:42:28 2020 A1: 3
- Mon Sep 14 22:42:28 2020 A2: -3
- Mon Sep 14 22:42:28 2020 A3: -4
- Mon Sep 14 22:42:28 2020 A4: 1
- Mon Sep 14 22:42:28 2020 A5: 1
- Mon Sep 14 22:42:28 2020 skew 1.00, size 2.842e-15, alpha 2.379, combined = 1.865e-12 rroots = 5
- Mon Sep 14 22:42:28 2020
- Mon Sep 14 22:42:28 2020 commencing relation filtering
- Mon Sep 14 22:42:28 2020 setting target matrix density to 124.0
- Mon Sep 14 22:42:28 2020 estimated available RAM is 16007.4 MB
- Mon Sep 14 22:42:28 2020 commencing duplicate removal, pass 1
- Mon Sep 14 22:51:00 2020 error -11 reading relation 77216017
- Mon Sep 14 22:52:39 2020 error -1 reading relation 92148200
- Mon Sep 14 22:54:56 2020 skipped 31 relations with b > 2^32
- Mon Sep 14 22:54:56 2020 found 5527491 hash collisions in 112740460 relations
- Mon Sep 14 22:55:03 2020 added 2926300 free relations
- Mon Sep 14 22:55:03 2020 commencing duplicate removal, pass 2
- Mon Sep 14 22:55:34 2020 found 0 duplicates and 115666760 unique relations
- Mon Sep 14 22:55:34 2020 memory use: 378.4 MB
- Mon Sep 14 22:55:34 2020 reading ideals above 71892992
- Mon Sep 14 22:55:34 2020 commencing singleton removal, initial pass
- Mon Sep 14 23:05:12 2020 memory use: 2756.0 MB
- Mon Sep 14 23:05:12 2020 reading all ideals from disk
- Mon Sep 14 23:05:13 2020 memory use: 1976.3 MB
- Mon Sep 14 23:05:17 2020 commencing in-memory singleton removal
- Mon Sep 14 23:05:20 2020 begin with 115666760 relations and 85369263 unique ideals
- Mon Sep 14 23:06:02 2020 reduce to 85708297 relations and 53005924 ideals in 12 passes
- Mon Sep 14 23:06:02 2020 max relations containing the same ideal: 59
- Mon Sep 14 23:06:06 2020 reading ideals above 720000
- Mon Sep 14 23:06:06 2020 commencing singleton removal, initial pass
- Mon Sep 14 23:14:47 2020 memory use: 1506.0 MB
- Mon Sep 14 23:14:47 2020 reading all ideals from disk
- Mon Sep 14 23:14:55 2020 memory use: 3176.3 MB
- Mon Sep 14 23:15:02 2020 keeping 61013418 ideals with weight <= 200, target excess is 437774
- Mon Sep 14 23:15:10 2020 commencing in-memory singleton removal
- Mon Sep 14 23:15:15 2020 begin with 85708297 relations and 61013418 unique ideals
- Mon Sep 14 23:15:48 2020 reduce to 85708211 relations and 61013332 ideals in 5 passes
- Mon Sep 14 23:15:48 2020 max relations containing the same ideal: 200
- Mon Sep 14 23:16:16 2020 removing 7503141 relations and 5503141 ideals in 2000000 cliques
- Mon Sep 14 23:16:18 2020 commencing in-memory singleton removal
- Mon Sep 14 23:16:24 2020 begin with 78205070 relations and 61013332 unique ideals
- Mon Sep 14 23:17:03 2020 reduce to 77647343 relations and 54936067 ideals in 7 passes
- Mon Sep 14 23:17:03 2020 max relations containing the same ideal: 195
- Mon Sep 14 23:17:27 2020 removing 6100600 relations and 4100600 ideals in 2000000 cliques
- Mon Sep 14 23:17:30 2020 commencing in-memory singleton removal
- Mon Sep 14 23:17:34 2020 begin with 71546743 relations and 54936067 unique ideals
- Mon Sep 14 23:18:06 2020 reduce to 71169993 relations and 50448689 ideals in 7 passes
- Mon Sep 14 23:18:06 2020 max relations containing the same ideal: 188
- Mon Sep 14 23:18:27 2020 removing 5701556 relations and 3701556 ideals in 2000000 cliques
- Mon Sep 14 23:18:29 2020 commencing in-memory singleton removal
- Mon Sep 14 23:18:33 2020 begin with 65468437 relations and 50448689 unique ideals
- Mon Sep 14 23:18:58 2020 reduce to 65140636 relations and 46410263 ideals in 6 passes
- Mon Sep 14 23:18:58 2020 max relations containing the same ideal: 178
- Mon Sep 14 23:19:18 2020 removing 5484936 relations and 3484936 ideals in 2000000 cliques
- Mon Sep 14 23:19:20 2020 commencing in-memory singleton removal
- Mon Sep 14 23:19:23 2020 begin with 59655700 relations and 46410263 unique ideals
- Mon Sep 14 23:19:46 2020 reduce to 59345543 relations and 42606303 ideals in 6 passes
- Mon Sep 14 23:19:46 2020 max relations containing the same ideal: 167
- Mon Sep 14 23:20:04 2020 removing 5351628 relations and 3351628 ideals in 2000000 cliques
- Mon Sep 14 23:20:06 2020 commencing in-memory singleton removal
- Mon Sep 14 23:20:09 2020 begin with 53993915 relations and 42606303 unique ideals
- Mon Sep 14 23:20:29 2020 reduce to 53687696 relations and 38939206 ideals in 6 passes
- Mon Sep 14 23:20:29 2020 max relations containing the same ideal: 156
- Mon Sep 14 23:20:46 2020 removing 5262752 relations and 3262752 ideals in 2000000 cliques
- Mon Sep 14 23:20:48 2020 commencing in-memory singleton removal
- Mon Sep 14 23:20:50 2020 begin with 48424944 relations and 38939206 unique ideals
- Mon Sep 14 23:21:11 2020 reduce to 48113418 relations and 35354970 ideals in 7 passes
- Mon Sep 14 23:21:11 2020 max relations containing the same ideal: 145
- Mon Sep 14 23:21:26 2020 removing 5198680 relations and 3198680 ideals in 2000000 cliques
- Mon Sep 14 23:21:28 2020 commencing in-memory singleton removal
- Mon Sep 14 23:21:30 2020 begin with 42914738 relations and 35354970 unique ideals
- Mon Sep 14 23:21:48 2020 reduce to 42587787 relations and 31817780 ideals in 7 passes
- Mon Sep 14 23:21:48 2020 max relations containing the same ideal: 136
- Mon Sep 14 23:22:02 2020 removing 5156064 relations and 3156064 ideals in 2000000 cliques
- Mon Sep 14 23:22:03 2020 commencing in-memory singleton removal
- Mon Sep 14 23:22:05 2020 begin with 37431723 relations and 31817780 unique ideals
- Mon Sep 14 23:22:19 2020 reduce to 37080702 relations and 28296800 ideals in 6 passes
- Mon Sep 14 23:22:19 2020 max relations containing the same ideal: 122
- Mon Sep 14 23:22:30 2020 removing 5131897 relations and 3131897 ideals in 2000000 cliques
- Mon Sep 14 23:22:32 2020 commencing in-memory singleton removal
- Mon Sep 14 23:22:34 2020 begin with 31948805 relations and 28296800 unique ideals
- Mon Sep 14 23:22:45 2020 reduce to 31561196 relations and 24760164 ideals in 6 passes
- Mon Sep 14 23:22:45 2020 max relations containing the same ideal: 110
- Mon Sep 14 23:22:55 2020 removing 5117206 relations and 3117206 ideals in 2000000 cliques
- Mon Sep 14 23:22:56 2020 commencing in-memory singleton removal
- Mon Sep 14 23:22:58 2020 begin with 26443990 relations and 24760164 unique ideals
- Mon Sep 14 23:23:09 2020 reduce to 26000562 relations and 21176458 ideals in 7 passes
- Mon Sep 14 23:23:09 2020 max relations containing the same ideal: 96
- Mon Sep 14 23:23:17 2020 removing 5110734 relations and 3110734 ideals in 2000000 cliques
- Mon Sep 14 23:23:18 2020 commencing in-memory singleton removal
- Mon Sep 14 23:23:19 2020 begin with 20889828 relations and 21176458 unique ideals
- Mon Sep 14 23:23:28 2020 reduce to 20363465 relations and 17506552 ideals in 7 passes
- Mon Sep 14 23:23:28 2020 max relations containing the same ideal: 83
- Mon Sep 14 23:23:34 2020 removing 5103135 relations and 3103135 ideals in 2000000 cliques
- Mon Sep 14 23:23:35 2020 commencing in-memory singleton removal
- Mon Sep 14 23:23:36 2020 begin with 15260330 relations and 17506552 unique ideals
- Mon Sep 14 23:23:42 2020 reduce to 14590059 relations and 13678824 ideals in 7 passes
- Mon Sep 14 23:23:42 2020 max relations containing the same ideal: 66
- Mon Sep 14 23:23:47 2020 removing 1352953 relations and 949536 ideals in 403417 cliques
- Mon Sep 14 23:23:47 2020 commencing in-memory singleton removal
- Mon Sep 14 23:23:48 2020 begin with 13237106 relations and 13678824 unique ideals
- Mon Sep 14 23:23:52 2020 reduce to 13105763 relations and 12594019 ideals in 6 passes
- Mon Sep 14 23:23:52 2020 max relations containing the same ideal: 65
- Mon Sep 14 23:23:58 2020 relations with 0 large ideals: 34720
- Mon Sep 14 23:23:58 2020 relations with 1 large ideals: 7766
- Mon Sep 14 23:23:58 2020 relations with 2 large ideals: 94466
- Mon Sep 14 23:23:58 2020 relations with 3 large ideals: 553726
- Mon Sep 14 23:23:58 2020 relations with 4 large ideals: 1710171
- Mon Sep 14 23:23:58 2020 relations with 5 large ideals: 3093542
- Mon Sep 14 23:23:58 2020 relations with 6 large ideals: 3875445
- Mon Sep 14 23:23:58 2020 relations with 7+ large ideals: 3735927
- Mon Sep 14 23:23:58 2020 commencing 2-way merge
- Mon Sep 14 23:24:04 2020 reduce to 9128925 relation sets and 8617181 unique ideals
- Mon Sep 14 23:24:04 2020 commencing full merge
- Mon Sep 14 23:27:02 2020 memory use: 1152.7 MB
- Mon Sep 14 23:27:02 2020 found 4031783 cycles, need 4031381
- Mon Sep 14 23:27:03 2020 weight of 4031381 cycles is about 500481945 (124.15/cycle)
- Mon Sep 14 23:27:03 2020 distribution of cycle lengths:
- Mon Sep 14 23:27:03 2020 1 relations: 102835
- Mon Sep 14 23:27:03 2020 2 relations: 171604
- Mon Sep 14 23:27:03 2020 3 relations: 230716
- Mon Sep 14 23:27:03 2020 4 relations: 260944
- Mon Sep 14 23:27:03 2020 5 relations: 280815
- Mon Sep 14 23:27:03 2020 6 relations: 288262
- Mon Sep 14 23:27:03 2020 7 relations: 288363
- Mon Sep 14 23:27:03 2020 8 relations: 281060
- Mon Sep 14 23:27:03 2020 9 relations: 267607
- Mon Sep 14 23:27:03 2020 10+ relations: 1859175
- Mon Sep 14 23:27:03 2020 heaviest cycle: 28 relations
- Mon Sep 14 23:27:04 2020 commencing cycle optimization
- Mon Sep 14 23:27:11 2020 start with 39909448 relations
- Mon Sep 14 23:28:35 2020 pruned 2335109 relations
- Mon Sep 14 23:28:35 2020 memory use: 954.4 MB
- Mon Sep 14 23:28:35 2020 distribution of cycle lengths:
- Mon Sep 14 23:28:35 2020 1 relations: 102835
- Mon Sep 14 23:28:35 2020 2 relations: 175979
- Mon Sep 14 23:28:35 2020 3 relations: 241432
- Mon Sep 14 23:28:35 2020 4 relations: 273900
- Mon Sep 14 23:28:35 2020 5 relations: 298512
- Mon Sep 14 23:28:35 2020 6 relations: 307218
- Mon Sep 14 23:28:35 2020 7 relations: 309088
- Mon Sep 14 23:28:35 2020 8 relations: 300579
- Mon Sep 14 23:28:35 2020 9 relations: 286097
- Mon Sep 14 23:28:35 2020 10+ relations: 1735741
- Mon Sep 14 23:28:35 2020 heaviest cycle: 28 relations
- Mon Sep 14 23:28:40 2020 RelProcTime: 2772
- Mon Sep 14 23:28:40 2020
- Mon Sep 14 23:28:40 2020 commencing linear algebra
- Mon Sep 14 23:28:41 2020 read 4031381 cycles
- Mon Sep 14 23:28:49 2020 cycles contain 12854807 unique relations
- Mon Sep 14 23:29:55 2020 read 12854807 relations
- Mon Sep 14 23:30:11 2020 using 20 quadratic characters above 4294917295
- Mon Sep 14 23:30:59 2020 building initial matrix
- Mon Sep 14 23:33:05 2020 memory use: 1602.5 MB
- Mon Sep 14 23:33:07 2020 read 4031381 cycles
- Mon Sep 14 23:33:07 2020 matrix is 4031204 x 4031381 (1926.6 MB) with weight 549730389 (136.36/col)
- Mon Sep 14 23:33:07 2020 sparse part has weight 460700929 (114.28/col)
- Mon Sep 14 23:33:50 2020 filtering completed in 2 passes
- Mon Sep 14 23:33:50 2020 matrix is 4031187 x 4031364 (1926.6 MB) with weight 549729845 (136.36/col)
- Mon Sep 14 23:33:50 2020 sparse part has weight 460700789 (114.28/col)
- Mon Sep 14 23:33:59 2020 matrix starts at (0, 0)
- Mon Sep 14 23:34:00 2020 matrix is 4031187 x 4031364 (1926.6 MB) with weight 549729845 (136.36/col)
- Mon Sep 14 23:34:00 2020 sparse part has weight 460700789 (114.28/col)
- Mon Sep 14 23:34:00 2020 saving the first 48 matrix rows for later
- Mon Sep 14 23:34:00 2020 matrix includes 64 packed rows
- Mon Sep 14 23:34:01 2020 matrix is 4031139 x 4031364 (1844.9 MB) with weight 474964836 (117.82/col)
- Mon Sep 14 23:34:01 2020 sparse part has weight 443313442 (109.97/col)
- Mon Sep 14 23:34:01 2020 using block size 8192 and superblock size 589824 for processor cache size 6144 kB
- Mon Sep 14 23:34:13 2020 commencing Lanczos iteration (4 threads)
- Mon Sep 14 23:34:13 2020 memory use: 1742.8 MB
- Mon Sep 14 23:34:28 2020 linear algebra at 0.0%, ETA 10h18m
- Mon Sep 14 23:34:33 2020 checkpointing every 390000 dimensions
- Tue Sep 15 10:04:10 2020 lanczos halted after 63749 iterations (dim = 4031139)
- Tue Sep 15 10:04:13 2020 recovered 35 nontrivial dependencies
- Tue Sep 15 10:04:13 2020 BLanczosTime: 38133
- Tue Sep 15 10:04:13 2020
- Tue Sep 15 10:04:13 2020 commencing square root phase
- Tue Sep 15 10:04:13 2020 handling dependencies 1 to 64
- Tue Sep 15 10:04:13 2020 reading relations for dependency 1
- Tue Sep 15 10:04:13 2020 read 2016051 cycles
- Tue Sep 15 10:04:16 2020 cycles contain 6427486 unique relations
- Tue Sep 15 10:04:56 2020 read 6427486 relations
- Tue Sep 15 10:05:16 2020 multiplying 6427486 relations
- Tue Sep 15 10:07:28 2020 multiply complete, coefficients have about 158.04 million bits
- Tue Sep 15 10:07:29 2020 initial square root is modulo 469717
- Tue Sep 15 10:10:07 2020 GCD is N, no factor found
- Tue Sep 15 10:10:07 2020 reading relations for dependency 2
- Tue Sep 15 10:10:07 2020 read 2017140 cycles
- Tue Sep 15 10:10:10 2020 cycles contain 6430382 unique relations
- Tue Sep 15 10:10:50 2020 read 6430382 relations
- Tue Sep 15 10:11:10 2020 multiplying 6430382 relations
- Tue Sep 15 10:13:22 2020 multiply complete, coefficients have about 158.11 million bits
- Tue Sep 15 10:13:22 2020 initial square root is modulo 472477
- Tue Sep 15 10:16:37 2020 sqrtTime: 744
- Tue Sep 15 10:16:37 2020 p93 factor: 529167283915512847198046816081347262641850412567202110871506328503616033931449404610000903937
- Tue Sep 15 10:16:37 2020 p131 factor: 15560601797899690717731972479176698867893685960372298042512101614959934651928002798638509534968718865299494813060933362378709515383
- Tue Sep 15 10:16:37 2020 elapsed time 11:34:11
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