Wed Dec 31 09:29:53 2025 Msieve v. 1.54 (SVN unknown) Wed Dec 31 09:29:53 2025 random seeds: ad94b3b8 0316481c Wed Dec 31 09:29:53 2025 factoring 437369438105068339136087718290750748516568715019897017216514963545479306096409333219489354870383730214266214162801021648059932972534372312408976259776900919683360221233817509372581287684803737284061061981687549227 (213 digits) Wed Dec 31 09:29:54 2025 no P-1/P+1/ECM available, skipping Wed Dec 31 09:29:54 2025 commencing number field sieve (213-digit input) Wed Dec 31 09:29:54 2025 R0: 178405961588244985132285746181186892047843328 Wed Dec 31 09:29:54 2025 R1: -1 Wed Dec 31 09:29:54 2025 A0: -2 Wed Dec 31 09:29:54 2025 A1: 0 Wed Dec 31 09:29:54 2025 A2: 0 Wed Dec 31 09:29:54 2025 A3: 0 Wed Dec 31 09:29:54 2025 A4: 0 Wed Dec 31 09:29:54 2025 A5: 0 Wed Dec 31 09:29:54 2025 A6: 5 Wed Dec 31 09:29:54 2025 skew 0.99, size 3.144e-13, alpha 2.819, combined = 4.903e-14 rroots = 2 Wed Dec 31 09:29:54 2025 Wed Dec 31 09:29:54 2025 commencing relation filtering Wed Dec 31 09:29:54 2025 setting target matrix density to 92.0 Wed Dec 31 09:29:54 2025 estimated available RAM is 128741.5 MB Wed Dec 31 09:29:54 2025 commencing duplicate removal, pass 1 Wed Dec 31 10:33:20 2025 error -11 reading relation 318546510 Wed Dec 31 10:38:02 2025 error -15 reading relation 342243903 Wed Dec 31 11:00:06 2025 error -1 reading relation 450517539 Wed Dec 31 11:01:32 2025 skipped 2039 relations with b > 2^32 Wed Dec 31 11:01:32 2025 skipped 1 relations with composite factors Wed Dec 31 11:01:32 2025 skipped 1 malformed relations Wed Dec 31 11:01:32 2025 found 22702003 hash collisions in 457247867 relations Wed Dec 31 11:01:50 2025 added 1218409 free relations Wed Dec 31 11:01:50 2025 commencing duplicate removal, pass 2 Wed Dec 31 11:07:29 2025 found 0 duplicates and 458466276 unique relations Wed Dec 31 11:07:29 2025 memory use: 1577.5 MB Wed Dec 31 11:07:29 2025 reading ideals above 720000 Wed Dec 31 11:07:30 2025 commencing singleton removal, initial pass Wed Dec 31 12:58:19 2025 memory use: 11024.0 MB Wed Dec 31 12:58:20 2025 reading all ideals from disk Wed Dec 31 13:00:32 2025 memory use: 22809.5 MB Wed Dec 31 13:02:28 2025 keeping 440700695 ideals with weight <= 200, target excess is 2379729 Wed Dec 31 13:04:45 2025 commencing in-memory singleton removal Wed Dec 31 13:07:35 2025 begin with 458466276 relations and 440700695 unique ideals Wed Dec 31 13:16:24 2025 reduce to 255162676 relations and 212771735 ideals in 14 passes Wed Dec 31 13:16:24 2025 max relations containing the same ideal: 144 Wed Dec 31 13:20:28 2025 removing 14436048 relations and 12436048 ideals in 2000000 cliques Wed Dec 31 13:20:38 2025 commencing in-memory singleton removal Wed Dec 31 13:21:58 2025 begin with 240726628 relations and 212771735 unique ideals Wed Dec 31 13:25:53 2025 reduce to 240120304 relations and 199722887 ideals in 9 passes Wed Dec 31 13:25:53 2025 max relations containing the same ideal: 141 Wed Dec 31 13:29:42 2025 removing 10873131 relations and 8873131 ideals in 2000000 cliques Wed Dec 31 13:29:55 2025 commencing in-memory singleton removal Wed Dec 31 13:31:08 2025 begin with 229247173 relations and 199722887 unique ideals Wed Dec 31 13:34:32 2025 reduce to 228859798 relations and 190458882 ideals in 8 passes Wed Dec 31 13:34:32 2025 max relations containing the same ideal: 137 Wed Dec 31 13:38:15 2025 removing 9753690 relations and 7753690 ideals in 2000000 cliques Wed Dec 31 13:38:24 2025 commencing in-memory singleton removal Wed Dec 31 13:39:35 2025 begin with 219106108 relations and 190458882 unique ideals Wed Dec 31 13:42:32 2025 reduce to 218769296 relations and 182365450 ideals in 8 passes Wed Dec 31 13:42:32 2025 max relations containing the same ideal: 132 Wed Dec 31 13:45:58 2025 removing 9150127 relations and 7150127 ideals in 2000000 cliques Wed Dec 31 13:46:06 2025 commencing in-memory singleton removal Wed Dec 31 13:47:13 2025 begin with 209619169 relations and 182365450 unique ideals Wed Dec 31 13:50:30 2025 reduce to 209310024 relations and 174903328 ideals in 9 passes Wed Dec 31 13:50:30 2025 max relations containing the same ideal: 129 Wed Dec 31 13:53:38 2025 removing 8743260 relations and 6743260 ideals in 2000000 cliques Wed Dec 31 13:53:47 2025 commencing in-memory singleton removal Wed Dec 31 13:54:52 2025 begin with 200566764 relations and 174903328 unique ideals Wed Dec 31 13:58:22 2025 reduce to 200270771 relations and 167861360 ideals in 10 passes Wed Dec 31 13:58:22 2025 max relations containing the same ideal: 125 Wed Dec 31 14:01:29 2025 removing 8466365 relations and 6466365 ideals in 2000000 cliques Wed Dec 31 14:01:37 2025 commencing in-memory singleton removal Wed Dec 31 14:02:37 2025 begin with 191804406 relations and 167861360 unique ideals Wed Dec 31 14:05:24 2025 reduce to 191513743 relations and 161101623 ideals in 8 passes Wed Dec 31 14:05:24 2025 max relations containing the same ideal: 123 Wed Dec 31 14:08:22 2025 removing 8263386 relations and 6263386 ideals in 2000000 cliques Wed Dec 31 14:08:30 2025 commencing in-memory singleton removal Wed Dec 31 14:09:28 2025 begin with 183250357 relations and 161101623 unique ideals Wed Dec 31 14:11:27 2025 reduce to 182960485 relations and 154545586 ideals in 6 passes Wed Dec 31 14:11:27 2025 max relations containing the same ideal: 117 Wed Dec 31 14:14:17 2025 removing 8109671 relations and 6109671 ideals in 2000000 cliques Wed Dec 31 14:14:24 2025 commencing in-memory singleton removal Wed Dec 31 14:15:17 2025 begin with 174850814 relations and 154545586 unique ideals Wed Dec 31 14:17:26 2025 reduce to 174559159 relations and 148141361 ideals in 7 passes Wed Dec 31 14:17:26 2025 max relations containing the same ideal: 114 Wed Dec 31 14:20:22 2025 removing 8002607 relations and 6002607 ideals in 2000000 cliques Wed Dec 31 14:20:32 2025 commencing in-memory singleton removal Wed Dec 31 14:21:23 2025 begin with 166556552 relations and 148141361 unique ideals Wed Dec 31 14:23:14 2025 reduce to 166261081 relations and 141840213 ideals in 7 passes Wed Dec 31 14:23:14 2025 max relations containing the same ideal: 110 Wed Dec 31 14:25:46 2025 removing 7918908 relations and 5918908 ideals in 2000000 cliques Wed Dec 31 14:25:52 2025 commencing in-memory singleton removal Wed Dec 31 14:26:39 2025 begin with 158342173 relations and 141840213 unique ideals Wed Dec 31 14:28:56 2025 reduce to 158039182 relations and 135614988 ideals in 9 passes Wed Dec 31 14:28:56 2025 max relations containing the same ideal: 107 Wed Dec 31 14:31:18 2025 removing 7865847 relations and 5865847 ideals in 2000000 cliques Wed Dec 31 14:31:24 2025 commencing in-memory singleton removal Wed Dec 31 14:32:09 2025 begin with 150173335 relations and 135614988 unique ideals Wed Dec 31 14:33:39 2025 reduce to 149860193 relations and 129432460 ideals in 7 passes Wed Dec 31 14:33:39 2025 max relations containing the same ideal: 101 Wed Dec 31 14:35:51 2025 removing 7829248 relations and 5829248 ideals in 2000000 cliques Wed Dec 31 14:35:57 2025 commencing in-memory singleton removal Wed Dec 31 14:36:39 2025 begin with 142030945 relations and 129432460 unique ideals Wed Dec 31 14:38:06 2025 reduce to 141704266 relations and 123272730 ideals in 7 passes Wed Dec 31 14:38:06 2025 max relations containing the same ideal: 97 Wed Dec 31 14:40:13 2025 removing 7816616 relations and 5816616 ideals in 2000000 cliques Wed Dec 31 14:40:19 2025 commencing in-memory singleton removal Wed Dec 31 14:40:59 2025 begin with 133887650 relations and 123272730 unique ideals Wed Dec 31 14:42:39 2025 reduce to 133544091 relations and 117108297 ideals in 8 passes Wed Dec 31 14:42:39 2025 max relations containing the same ideal: 94 Wed Dec 31 14:44:27 2025 removing 7814703 relations and 5814703 ideals in 2000000 cliques Wed Dec 31 14:44:33 2025 commencing in-memory singleton removal Wed Dec 31 14:45:11 2025 begin with 125729388 relations and 117108297 unique ideals Wed Dec 31 14:46:24 2025 reduce to 125366667 relations and 110926040 ideals in 7 passes Wed Dec 31 14:46:24 2025 max relations containing the same ideal: 91 Wed Dec 31 14:48:10 2025 removing 7828429 relations and 5828429 ideals in 2000000 cliques Wed Dec 31 14:48:16 2025 commencing in-memory singleton removal Wed Dec 31 14:48:49 2025 begin with 117538238 relations and 110926040 unique ideals Wed Dec 31 14:49:59 2025 reduce to 117152620 relations and 104706457 ideals in 8 passes Wed Dec 31 14:49:59 2025 max relations containing the same ideal: 87 Wed Dec 31 14:51:38 2025 removing 7865035 relations and 5865035 ideals in 2000000 cliques Wed Dec 31 14:51:44 2025 commencing in-memory singleton removal Wed Dec 31 14:52:15 2025 begin with 109287585 relations and 104706457 unique ideals Wed Dec 31 14:53:31 2025 reduce to 108871424 relations and 98419175 ideals in 8 passes Wed Dec 31 14:53:31 2025 max relations containing the same ideal: 84 Wed Dec 31 14:55:09 2025 removing 7914019 relations and 5914019 ideals in 2000000 cliques Wed Dec 31 14:55:14 2025 commencing in-memory singleton removal Wed Dec 31 14:55:43 2025 begin with 100957405 relations and 98419175 unique ideals Wed Dec 31 14:56:59 2025 reduce to 100503108 relations and 92043714 ideals in 8 passes Wed Dec 31 14:56:59 2025 max relations containing the same ideal: 79 Wed Dec 31 14:58:30 2025 removing 7985675 relations and 5985675 ideals in 2000000 cliques Wed Dec 31 14:58:34 2025 commencing in-memory singleton removal Wed Dec 31 14:59:00 2025 begin with 92517433 relations and 92043714 unique ideals Wed Dec 31 14:59:59 2025 reduce to 92014365 relations and 85546574 ideals in 7 passes Wed Dec 31 14:59:59 2025 max relations containing the same ideal: 75 Wed Dec 31 15:01:19 2025 removing 8077095 relations and 6077095 ideals in 2000000 cliques Wed Dec 31 15:01:27 2025 commencing in-memory singleton removal Wed Dec 31 15:01:51 2025 begin with 83937270 relations and 85546574 unique ideals Wed Dec 31 15:02:49 2025 reduce to 83376008 relations and 78897772 ideals in 8 passes Wed Dec 31 15:02:49 2025 max relations containing the same ideal: 71 Wed Dec 31 15:04:08 2025 removing 7248808 relations and 5531058 ideals in 1717750 cliques Wed Dec 31 15:04:12 2025 commencing in-memory singleton removal Wed Dec 31 15:04:32 2025 begin with 76127200 relations and 78897772 unique ideals Wed Dec 31 15:05:29 2025 reduce to 75629898 relations and 72860769 ideals in 8 passes Wed Dec 31 15:05:29 2025 max relations containing the same ideal: 66 Wed Dec 31 15:06:37 2025 removing 78973 relations and 70330 ideals in 8643 cliques Wed Dec 31 15:06:39 2025 commencing in-memory singleton removal Wed Dec 31 15:06:59 2025 begin with 75550925 relations and 72860769 unique ideals Wed Dec 31 15:07:19 2025 reduce to 75550903 relations and 72790417 ideals in 3 passes Wed Dec 31 15:07:19 2025 max relations containing the same ideal: 66 Wed Dec 31 15:07:39 2025 relations with 0 large ideals: 86726 Wed Dec 31 15:07:39 2025 relations with 1 large ideals: 82519 Wed Dec 31 15:07:39 2025 relations with 2 large ideals: 849492 Wed Dec 31 15:07:39 2025 relations with 3 large ideals: 4331374 Wed Dec 31 15:07:39 2025 relations with 4 large ideals: 11882391 Wed Dec 31 15:07:39 2025 relations with 5 large ideals: 19320178 Wed Dec 31 15:07:39 2025 relations with 6 large ideals: 19471116 Wed Dec 31 15:07:39 2025 relations with 7+ large ideals: 19527107 Wed Dec 31 15:07:39 2025 commencing 2-way merge Wed Dec 31 15:09:26 2025 reduce to 46711732 relation sets and 43951246 unique ideals Wed Dec 31 15:09:26 2025 commencing full merge Wed Dec 31 15:29:40 2025 memory use: 5406.6 MB Wed Dec 31 15:29:47 2025 found 23008074 cycles, need 22645446 Wed Dec 31 15:29:58 2025 weight of 22645446 cycles is about 2083432397 (92.00/cycle) Wed Dec 31 15:29:59 2025 distribution of cycle lengths: Wed Dec 31 15:29:59 2025 1 relations: 2240883 Wed Dec 31 15:29:59 2025 2 relations: 2101581 Wed Dec 31 15:29:59 2025 3 relations: 2113134 Wed Dec 31 15:29:59 2025 4 relations: 2017197 Wed Dec 31 15:29:59 2025 5 relations: 1972177 Wed Dec 31 15:29:59 2025 6 relations: 1870133 Wed Dec 31 15:29:59 2025 7 relations: 1746240 Wed Dec 31 15:29:59 2025 8 relations: 1582561 Wed Dec 31 15:29:59 2025 9 relations: 1415187 Wed Dec 31 15:29:59 2025 10+ relations: 5586353 Wed Dec 31 15:29:59 2025 heaviest cycle: 24 relations Wed Dec 31 15:30:08 2025 commencing cycle optimization Wed Dec 31 15:31:11 2025 start with 150559040 relations Wed Dec 31 15:37:12 2025 pruned 4615265 relations Wed Dec 31 15:37:14 2025 memory use: 4615.6 MB Wed Dec 31 15:37:14 2025 distribution of cycle lengths: Wed Dec 31 15:37:14 2025 1 relations: 2240883 Wed Dec 31 15:37:14 2025 2 relations: 2146424 Wed Dec 31 15:37:14 2025 3 relations: 2187140 Wed Dec 31 15:37:14 2025 4 relations: 2080514 Wed Dec 31 15:37:14 2025 5 relations: 2043052 Wed Dec 31 15:37:14 2025 6 relations: 1928472 Wed Dec 31 15:37:14 2025 7 relations: 1801998 Wed Dec 31 15:37:14 2025 8 relations: 1620297 Wed Dec 31 15:37:14 2025 9 relations: 1439193 Wed Dec 31 15:37:14 2025 10+ relations: 5157473 Wed Dec 31 15:37:14 2025 heaviest cycle: 23 relations Wed Dec 31 15:38:20 2025 RelProcTime: 22106 Wed Dec 31 15:38:20 2025 elapsed time 06:08:27 Wed Dec 31 16:05:08 2025 Wed Dec 31 16:05:08 2025 Wed Dec 31 16:05:08 2025 Msieve v. 1.54 (SVN unknown) Wed Dec 31 16:05:08 2025 random seeds: 62ae0f3d efaf87e2 Wed Dec 31 16:05:08 2025 factoring 437369438105068339136087718290750748516568715019897017216514963545479306096409333219489354870383730214266214162801021648059932972534372312408976259776900919683360221233817509372581287684803737284061061981687549227 (213 digits) Wed Dec 31 16:05:10 2025 no P-1/P+1/ECM available, skipping Wed Dec 31 16:05:10 2025 commencing number field sieve (213-digit input) Wed Dec 31 16:05:10 2025 R0: 178405961588244985132285746181186892047843328 Wed Dec 31 16:05:10 2025 R1: -1 Wed Dec 31 16:05:10 2025 A0: -2 Wed Dec 31 16:05:10 2025 A1: 0 Wed Dec 31 16:05:10 2025 A2: 0 Wed Dec 31 16:05:10 2025 A3: 0 Wed Dec 31 16:05:10 2025 A4: 0 Wed Dec 31 16:05:10 2025 A5: 0 Wed Dec 31 16:05:10 2025 A6: 5 Wed Dec 31 16:05:10 2025 skew 0.99, size 3.144e-13, alpha 2.819, combined = 4.903e-14 rroots = 2 Wed Dec 31 16:05:10 2025 Wed Dec 31 16:05:10 2025 commencing linear algebra Wed Dec 31 16:05:10 2025 using VBITS=128 Wed Dec 31 16:05:14 2025 read 22645446 cycles Wed Dec 31 16:06:16 2025 cycles contain 73816664 unique relations Wed Dec 31 16:19:01 2025 read 73816664 relations Wed Dec 31 16:22:05 2025 using 20 quadratic characters above 4294917295 Wed Dec 31 16:29:27 2025 building initial matrix Wed Dec 31 16:51:24 2025 memory use: 9477.6 MB Wed Dec 31 16:51:49 2025 read 22645446 cycles Wed Dec 31 16:51:53 2025 matrix is 22645265 x 22645446 (8460.1 MB) with weight 2430185660 (107.31/col) Wed Dec 31 16:51:53 2025 sparse part has weight 1991315745 (87.93/col) Wed Dec 31 16:59:15 2025 filtering completed in 2 passes Wed Dec 31 16:59:20 2025 matrix is 22637949 x 22638129 (8459.5 MB) with weight 2429942692 (107.34/col) Wed Dec 31 16:59:20 2025 sparse part has weight 1991213274 (87.96/col) Wed Dec 31 17:01:38 2025 matrix starts at (0, 0) Wed Dec 31 17:01:41 2025 matrix is 22637949 x 22638129 (8459.5 MB) with weight 2429942692 (107.34/col) Wed Dec 31 17:01:41 2025 sparse part has weight 1991213274 (87.96/col) Wed Dec 31 17:01:41 2025 saving the first 112 matrix rows for later Wed Dec 31 17:01:46 2025 matrix includes 128 packed rows Wed Dec 31 17:01:52 2025 matrix is 22637837 x 22638129 (8019.5 MB) with weight 1915936081 (84.63/col) Wed Dec 31 17:01:52 2025 sparse part has weight 1830599009 (80.86/col) Wed Dec 31 17:01:53 2025 using GPU 0 (Tesla P100-PCIE-16GB) Wed Dec 31 17:01:53 2025 selected card has CUDA arch 6.0 Wed Dec 31 17:29:37 2025 commencing Lanczos iteration Wed Dec 31 17:29:40 2025 memory use: 17075.2 MB Wed Dec 31 17:39:42 2025 linear algebra at 0.1%, ETA 122h41m Wed Dec 31 17:42:11 2025 checking every 10000 dimensions, checkpointing every 190000 dimensions Mon Jan 5 21:08:37 2026 lanczos halted after 177926 iterations (dim = 22637836) Mon Jan 5 21:15:34 2026 recovered 38 nontrivial dependencies Mon Jan 5 21:15:57 2026 BLanczosTime: 450647 Mon Jan 5 21:15:57 2026 Mon Jan 5 21:15:57 2026 commencing square root phase Mon Jan 5 21:15:57 2026 handling dependencies 1 to 64 Mon Jan 5 21:15:57 2026 reading relations for dependency 1 Mon Jan 5 22:27:02 2026 read 11319252 cycles Mon Jan 5 22:27:49 2026 cycles contain 36910144 unique relations Mon Jan 5 22:35:45 2026 read 36910144 relations Mon Jan 5 22:41:39 2026 multiplying 36910144 relations Mon Jan 5 23:35:53 2026 multiply complete, coefficients have about 1045.56 million bits Mon Jan 5 23:35:59 2026 initial square root is modulo 2399831221 Tue Jan 6 00:17:57 2026 GCD is 1, no factor found Tue Jan 6 00:17:57 2026 reading relations for dependency 2 Tue Jan 6 00:18:09 2026 read 11320528 cycles Tue Jan 6 00:18:53 2026 cycles contain 36905758 unique relations Tue Jan 6 00:26:05 2026 read 36905758 relations Tue Jan 6 00:32:40 2026 multiplying 36905758 relations Tue Jan 6 01:26:54 2026 multiply complete, coefficients have about 1045.43 million bits Tue Jan 6 01:27:00 2026 initial square root is modulo 2393570167 Tue Jan 6 02:09:21 2026 sqrtTime: 17604 Tue Jan 6 02:09:21 2026 p67 factor: 8323427721936039756459525309989210303714280209151457411915617935093 Tue Jan 6 02:09:21 2026 p146 factor: 52546793546653836714676855276126406750737685984945567087592611853725322392357968997795800401358850656033783883606256341272471920334959216760334239 Tue Jan 6 02:09:21 2026 elapsed time 130:04:13