Fri Sep 11 11:06:17 2026 Fri Sep 11 11:06:17 2026 Fri Sep 11 11:06:17 2026 Msieve v. 1.54 (SVN unknown) Fri Sep 11 11:06:17 2026 random seeds: 7bca380a b4eb5adb Fri Sep 11 11:06:17 2026 Using 8 OpenMP threads Fri Sep 11 11:06:17 2026 factoring 5432975631044391390437593926487362688783819994439506471369376226901246768626485986157473605898185923509925992604279462091144977894077886847956305713416711953658228072259889 (172 digits) Fri Sep 11 11:06:17 2026 no P-1/P+1/ECM available, skipping Fri Sep 11 11:06:17 2026 commencing number field sieve (172-digit input) Fri Sep 11 11:06:17 2026 R0: 49401993336845850288045768393087296917 Fri Sep 11 11:06:17 2026 R1: -1 Fri Sep 11 11:06:17 2026 A0: 1 Fri Sep 11 11:06:17 2026 A1: 1 Fri Sep 11 11:06:17 2026 A2: 1 Fri Sep 11 11:06:17 2026 A3: 1 Fri Sep 11 11:06:17 2026 A4: 1 Fri Sep 11 11:06:17 2026 A5: 1 Fri Sep 11 11:06:17 2026 A6: 1 Fri Sep 11 11:06:17 2026 skew 1.35, size 3.306e-11, alpha 2.428, combined = 1.526e-12 rroots = 0 Fri Sep 11 11:06:17 2026 Fri Sep 11 11:06:17 2026 commencing relation filtering Fri Sep 11 11:06:17 2026 setting 3 target densities:Fri Sep 11 11:06:17 2026 90Fri Sep 11 11:06:17 2026 110Fri Sep 11 11:06:17 2026 130Fri Sep 11 11:06:17 2026 Fri Sep 11 11:06:17 2026 estimated available RAM is 78540.1 MB Fri Sep 11 11:06:17 2026 commencing duplicate removal, pass 1 Fri Sep 11 11:07:36 2026 error -1 reading relation 73924255 Fri Sep 11 11:07:40 2026 error -1 reading relation 78610705 Fri Sep 11 11:07:40 2026 error -1 reading relation 78694649 Fri Sep 11 11:07:44 2026 error -1 reading relation 82947423 Fri Sep 11 11:08:32 2026 skipped 15 relations with b > 2^32 Fri Sep 11 11:08:32 2026 skipped 58 malformed relations Fri Sep 11 11:08:32 2026 found 17718693 hash collisions in 128700298 relations Fri Sep 11 11:08:35 2026 added 2438534 free relations Fri Sep 11 11:08:35 2026 commencing duplicate removal, pass 2 Fri Sep 11 11:09:14 2026 found 13832689 duplicates and 117306143 unique relations Fri Sep 11 11:09:14 2026 memory use: 660.8 MB Fri Sep 11 11:09:14 2026 reading ideals above 720000 Fri Sep 11 11:09:14 2026 commencing singleton removal, initial pass Fri Sep 11 11:13:22 2026 memory use: 3012.0 MB Fri Sep 11 11:13:22 2026 reading all ideals from disk Fri Sep 11 11:13:24 2026 memory use: 5305.5 MB Fri Sep 11 11:13:30 2026 keeping 115693002 ideals with weight <= 200, target excess is 585053 Fri Sep 11 11:13:36 2026 commencing in-memory singleton removal Fri Sep 11 11:13:37 2026 begin with 117306143 relations and 115693002 unique ideals Fri Sep 11 11:13:46 2026 reduce to 61005467 relations and 52009956 ideals in 16 passes Fri Sep 11 11:13:46 2026 max relations containing the same ideal: 137 Fri Sep 11 11:13:59 2026 removing 6264075 relations and 5264075 ideals in 1000000 cliques Fri Sep 11 11:14:00 2026 commencing in-memory singleton removal Fri Sep 11 11:14:01 2026 begin with 54741392 relations and 52009956 unique ideals Fri Sep 11 11:14:04 2026 reduce to 54145760 relations and 46137058 ideals in 10 passes Fri Sep 11 11:14:04 2026 max relations containing the same ideal: 127 Fri Sep 11 11:14:18 2026 removing 4878274 relations and 3878274 ideals in 1000000 cliques Fri Sep 11 11:14:19 2026 commencing in-memory singleton removal Fri Sep 11 11:14:19 2026 begin with 49267486 relations and 46137058 unique ideals Fri Sep 11 11:14:22 2026 reduce to 48884816 relations and 41868744 ideals in 9 passes Fri Sep 11 11:14:22 2026 max relations containing the same ideal: 121 Fri Sep 11 11:14:34 2026 removing 4448597 relations and 3448597 ideals in 1000000 cliques Fri Sep 11 11:14:35 2026 commencing in-memory singleton removal Fri Sep 11 11:14:35 2026 begin with 44436219 relations and 41868744 unique ideals Fri Sep 11 11:14:38 2026 reduce to 44099669 relations and 38077109 ideals in 9 passes Fri Sep 11 11:14:38 2026 max relations containing the same ideal: 106 Fri Sep 11 11:14:49 2026 removing 4215266 relations and 3215266 ideals in 1000000 cliques Fri Sep 11 11:14:50 2026 commencing in-memory singleton removal Fri Sep 11 11:14:51 2026 begin with 39884403 relations and 38077109 unique ideals Fri Sep 11 11:14:53 2026 reduce to 39558549 relations and 34528939 ideals in 8 passes Fri Sep 11 11:14:53 2026 max relations containing the same ideal: 104 Fri Sep 11 11:15:03 2026 removing 4071614 relations and 3071614 ideals in 1000000 cliques Fri Sep 11 11:15:04 2026 commencing in-memory singleton removal Fri Sep 11 11:15:04 2026 begin with 35486935 relations and 34528939 unique ideals Fri Sep 11 11:15:06 2026 reduce to 35154553 relations and 31117225 ideals in 8 passes Fri Sep 11 11:15:06 2026 max relations containing the same ideal: 96 Fri Sep 11 11:15:14 2026 removing 3981896 relations and 2981896 ideals in 1000000 cliques Fri Sep 11 11:15:15 2026 commencing in-memory singleton removal Fri Sep 11 11:15:15 2026 begin with 31172657 relations and 31117225 unique ideals Fri Sep 11 11:15:17 2026 reduce to 30819388 relations and 27772998 ideals in 8 passes Fri Sep 11 11:15:17 2026 max relations containing the same ideal: 85 Fri Sep 11 11:15:25 2026 removing 3927873 relations and 2927873 ideals in 1000000 cliques Fri Sep 11 11:15:26 2026 commencing in-memory singleton removal Fri Sep 11 11:15:26 2026 begin with 26891515 relations and 27772998 unique ideals Fri Sep 11 11:15:28 2026 reduce to 26507301 relations and 24449828 ideals in 10 passes Fri Sep 11 11:15:28 2026 max relations containing the same ideal: 75 Fri Sep 11 11:15:34 2026 removing 3887774 relations and 2887774 ideals in 1000000 cliques Fri Sep 11 11:15:35 2026 commencing in-memory singleton removal Fri Sep 11 11:15:35 2026 begin with 22619527 relations and 24449828 unique ideals Fri Sep 11 11:15:36 2026 reduce to 22187732 relations and 21115704 ideals in 9 passes Fri Sep 11 11:15:36 2026 max relations containing the same ideal: 67 Fri Sep 11 11:15:42 2026 removing 1857304 relations and 1463938 ideals in 393366 cliques Fri Sep 11 11:15:42 2026 commencing in-memory singleton removal Fri Sep 11 11:15:42 2026 begin with 20330428 relations and 21115704 unique ideals Fri Sep 11 11:15:43 2026 reduce to 20221642 relations and 19541313 ideals in 8 passes Fri Sep 11 11:15:43 2026 max relations containing the same ideal: 64 Fri Sep 11 11:15:49 2026 trying target density 90 Fri Sep 11 11:15:50 2026 relations with 0 large ideals: 41233 Fri Sep 11 11:15:50 2026 relations with 1 large ideals: 10710 Fri Sep 11 11:15:50 2026 relations with 2 large ideals: 131027 Fri Sep 11 11:15:50 2026 relations with 3 large ideals: 786016 Fri Sep 11 11:15:50 2026 relations with 4 large ideals: 2508638 Fri Sep 11 11:15:50 2026 relations with 5 large ideals: 4700973 Fri Sep 11 11:15:50 2026 relations with 6 large ideals: 5384843 Fri Sep 11 11:15:50 2026 relations with 7+ large ideals: 6658202 Fri Sep 11 11:15:50 2026 commencing 2-way merge Fri Sep 11 11:15:58 2026 reduce to 12697962 relation sets and 12017633 unique ideals Fri Sep 11 11:15:58 2026 commencing full merge Fri Sep 11 11:18:51 2026 memory use: 1706.4 MB Fri Sep 11 11:18:52 2026 found 6272689 cycles, need 6193833 Fri Sep 11 11:18:54 2026 weight of 6193833 cycles is about 558006204 (90.09/cycle) Fri Sep 11 11:18:54 2026 distribution of cycle lengths: Fri Sep 11 11:18:54 2026 1 relations: 511339 Fri Sep 11 11:18:54 2026 2 relations: 561263 Fri Sep 11 11:18:54 2026 3 relations: 555197 Fri Sep 11 11:18:54 2026 4 relations: 533497 Fri Sep 11 11:18:54 2026 5 relations: 506273 Fri Sep 11 11:18:54 2026 6 relations: 476153 Fri Sep 11 11:18:54 2026 7 relations: 442681 Fri Sep 11 11:18:54 2026 8 relations: 411109 Fri Sep 11 11:18:54 2026 9 relations: 373890 Fri Sep 11 11:18:54 2026 10+ relations: 1822431 Fri Sep 11 11:18:54 2026 heaviest cycle: 27 relations Fri Sep 11 11:18:55 2026 commencing cycle optimization Fri Sep 11 11:19:02 2026 start with 45024522 relations Fri Sep 11 11:19:57 2026 pruned 1525693 relations Fri Sep 11 11:19:57 2026 memory use: 1293.9 MB Fri Sep 11 11:19:57 2026 distribution of cycle lengths: Fri Sep 11 11:19:57 2026 1 relations: 511339 Fri Sep 11 11:19:57 2026 2 relations: 571132 Fri Sep 11 11:19:57 2026 3 relations: 573996 Fri Sep 11 11:19:57 2026 4 relations: 550037 Fri Sep 11 11:19:57 2026 5 relations: 525863 Fri Sep 11 11:19:57 2026 6 relations: 491548 Fri Sep 11 11:19:57 2026 7 relations: 458846 Fri Sep 11 11:19:57 2026 8 relations: 422665 Fri Sep 11 11:19:57 2026 9 relations: 383524 Fri Sep 11 11:19:57 2026 10+ relations: 1704883 Fri Sep 11 11:19:57 2026 heaviest cycle: 26 relations Fri Sep 11 11:20:04 2026 trying target density 110 Fri Sep 11 11:20:06 2026 relations with 0 large ideals: 41233 Fri Sep 11 11:20:06 2026 relations with 1 large ideals: 10710 Fri Sep 11 11:20:06 2026 relations with 2 large ideals: 131027 Fri Sep 11 11:20:06 2026 relations with 3 large ideals: 786016 Fri Sep 11 11:20:06 2026 relations with 4 large ideals: 2508638 Fri Sep 11 11:20:06 2026 relations with 5 large ideals: 4700973 Fri Sep 11 11:20:06 2026 relations with 6 large ideals: 5384843 Fri Sep 11 11:20:06 2026 relations with 7+ large ideals: 6658202 Fri Sep 11 11:20:06 2026 commencing 2-way merge Fri Sep 11 11:20:13 2026 reduce to 12697962 relation sets and 12017633 unique ideals Fri Sep 11 11:20:13 2026 commencing full merge Fri Sep 11 11:23:53 2026 memory use: 1757.1 MB Fri Sep 11 11:23:54 2026 found 5858662 cycles, need 5831833 Fri Sep 11 11:23:56 2026 weight of 5831833 cycles is about 641779571 (110.05/cycle) Fri Sep 11 11:23:56 2026 distribution of cycle lengths: Fri Sep 11 11:23:56 2026 1 relations: 338891 Fri Sep 11 11:23:56 2026 2 relations: 412363 Fri Sep 11 11:23:56 2026 3 relations: 434016 Fri Sep 11 11:23:56 2026 4 relations: 425672 Fri Sep 11 11:23:56 2026 5 relations: 414821 Fri Sep 11 11:23:56 2026 6 relations: 398001 Fri Sep 11 11:23:56 2026 7 relations: 378761 Fri Sep 11 11:23:56 2026 8 relations: 357998 Fri Sep 11 11:23:56 2026 9 relations: 338157 Fri Sep 11 11:23:56 2026 10+ relations: 2333153 Fri Sep 11 11:23:56 2026 heaviest cycle: 28 relations Fri Sep 11 11:23:57 2026 commencing cycle optimization Fri Sep 11 11:24:05 2026 start with 51720678 relations Fri Sep 11 11:25:25 2026 pruned 2202151 relations Fri Sep 11 11:25:25 2026 memory use: 1363.3 MB Fri Sep 11 11:25:25 2026 distribution of cycle lengths: Fri Sep 11 11:25:25 2026 1 relations: 338891 Fri Sep 11 11:25:25 2026 2 relations: 420695 Fri Sep 11 11:25:25 2026 3 relations: 450113 Fri Sep 11 11:25:25 2026 4 relations: 441009 Fri Sep 11 11:25:25 2026 5 relations: 433496 Fri Sep 11 11:25:25 2026 6 relations: 414214 Fri Sep 11 11:25:25 2026 7 relations: 395420 Fri Sep 11 11:25:25 2026 8 relations: 372685 Fri Sep 11 11:25:25 2026 9 relations: 352186 Fri Sep 11 11:25:25 2026 10+ relations: 2213124 Fri Sep 11 11:25:25 2026 heaviest cycle: 28 relations Fri Sep 11 11:25:32 2026 trying target density 130 Fri Sep 11 11:25:33 2026 relations with 0 large ideals: 41233 Fri Sep 11 11:25:33 2026 relations with 1 large ideals: 10710 Fri Sep 11 11:25:33 2026 relations with 2 large ideals: 131027 Fri Sep 11 11:25:33 2026 relations with 3 large ideals: 786016 Fri Sep 11 11:25:33 2026 relations with 4 large ideals: 2508638 Fri Sep 11 11:25:33 2026 relations with 5 large ideals: 4700973 Fri Sep 11 11:25:33 2026 relations with 6 large ideals: 5384843 Fri Sep 11 11:25:33 2026 relations with 7+ large ideals: 6658202 Fri Sep 11 11:25:33 2026 commencing 2-way merge Fri Sep 11 11:25:41 2026 reduce to 12697962 relation sets and 12017633 unique ideals Fri Sep 11 11:25:41 2026 commencing full merge Fri Sep 11 11:33:21 2026 memory use: 560.8 MB Fri Sep 11 11:33:21 2026 found 52362 cycles, need 2820253 Fri Sep 11 11:33:21 2026 too few cycles, matrix probably cannot build Fri Sep 11 11:33:21 2026 RelProcTime: 1624 Fri Sep 11 11:33:21 2026 Fri Sep 11 11:33:21 2026 commencing linear algebra Fri Sep 11 11:33:21 2026 using VBITS=256 Fri Sep 11 11:33:21 2026 building matrices for all densities Fri Sep 11 11:33:21 2026 found 2 density files Fri Sep 11 11:33:21 2026 building matrix for density 90 Fri Sep 11 11:33:21 2026 read 6193833 cycles Fri Sep 11 11:33:27 2026 cycles contain 19797506 unique relations Fri Sep 11 11:33:38 2026 read 19797506 relations Fri Sep 11 11:33:41 2026 using 20 quadratic characters above 4294917295 Fri Sep 11 11:33:48 2026 building initial matrix Fri Sep 11 11:35:57 2026 memory use: 2424.3 MB Fri Sep 11 11:35:59 2026 read 6193833 cycles Fri Sep 11 11:36:00 2026 matrix is 6193655 x 6193833 (2286.7 MB) with weight 654669816 (105.70/col) Fri Sep 11 11:36:00 2026 sparse part has weight 531303013 (85.78/col) Fri Sep 11 11:36:28 2026 filtering completed in 2 passes Fri Sep 11 11:36:29 2026 matrix is 6192711 x 6192876 (2286.6 MB) with weight 654636779 (105.71/col) Fri Sep 11 11:36:29 2026 sparse part has weight 531289378 (85.79/col) Fri Sep 11 11:36:37 2026 building matrix for density 110 Fri Sep 11 11:36:37 2026 read 5831833 cycles Fri Sep 11 11:36:43 2026 cycles contain 19799813 unique relations Fri Sep 11 11:36:53 2026 read 19799813 relations Fri Sep 11 11:36:57 2026 using 20 quadratic characters above 4294917295 Fri Sep 11 11:37:04 2026 building initial matrix Fri Sep 11 11:39:16 2026 memory use: 2436.5 MB Fri Sep 11 11:39:17 2026 read 5831833 cycles Fri Sep 11 11:39:18 2026 matrix is 5831656 x 5831833 (2543.5 MB) with weight 724845404 (124.29/col) Fri Sep 11 11:39:18 2026 sparse part has weight 602607171 (103.33/col) Fri Sep 11 11:39:49 2026 filtering completed in 2 passes Fri Sep 11 11:39:50 2026 matrix is 5831478 x 5831642 (2543.5 MB) with weight 724838476 (124.29/col) Fri Sep 11 11:39:50 2026 sparse part has weight 602604345 (103.33/col) Fri Sep 11 11:39:56 2026 BLanczosTime: 395 Fri Sep 11 11:39:56 2026 elapsed time 00:33:39 Fri Sep 11 16:11:09 2026 Fri Sep 11 16:11:09 2026 Fri Sep 11 16:11:09 2026 Msieve v. 1.54 (SVN unknown) Fri Sep 11 16:11:09 2026 random seeds: ac89c8d5 b4b99a9c Fri Sep 11 16:11:09 2026 factoring 5432975631044391390437593926487362688783819994439506471369376226901246768626485986157473605898185923509925992604279462091144977894077886847956305713416711953658228072259889 (172 digits) Fri Sep 11 16:11:10 2026 no P-1/P+1/ECM available, skipping Fri Sep 11 16:11:10 2026 commencing number field sieve (172-digit input) Fri Sep 11 16:11:10 2026 R0: 49401993336845850288045768393087296917 Fri Sep 11 16:11:10 2026 R1: -1 Fri Sep 11 16:11:10 2026 A0: 1 Fri Sep 11 16:11:10 2026 A1: 1 Fri Sep 11 16:11:10 2026 A2: 1 Fri Sep 11 16:11:10 2026 A3: 1 Fri Sep 11 16:11:10 2026 A4: 1 Fri Sep 11 16:11:10 2026 A5: 1 Fri Sep 11 16:11:10 2026 A6: 1 Fri Sep 11 16:11:10 2026 skew 1.35, size 3.306e-11, alpha 2.428, combined = 1.526e-12 rroots = 0 Fri Sep 11 16:11:10 2026 Fri Sep 11 16:11:10 2026 commencing linear algebra Fri Sep 11 16:11:10 2026 using VBITS=256 Fri Sep 11 16:11:10 2026 skipping matrix build Fri Sep 11 16:11:14 2026 matrix starts at (0, 0) Fri Sep 11 16:11:15 2026 matrix is 5831478 x 5831642 (2543.5 MB) with weight 724838476 (124.29/col) Fri Sep 11 16:11:15 2026 sparse part has weight 602604345 (103.33/col) Fri Sep 11 16:11:15 2026 saving the first 240 matrix rows for later Fri Sep 11 16:11:18 2026 matrix includes 256 packed rows Fri Sep 11 16:11:21 2026 matrix is 5831238 x 5831642 (2335.6 MB) with weight 548295212 (94.02/col) Fri Sep 11 16:11:21 2026 sparse part has weight 518954924 (88.99/col) Fri Sep 11 16:11:21 2026 using GPU 0 (NVIDIA GeForce RTX 5090) Fri Sep 11 16:11:21 2026 selected card has CUDA arch 12.0 Fri Sep 11 16:11:22 2026 computed block_nnz 139968385 (L2 cache 100663296 bytes, average column weight 89.0) Fri Sep 11 16:11:22 2026 nonzeros per matrix block: 256000000 Fri Sep 11 16:12:17 2026 commencing Lanczos iteration Fri Sep 11 16:12:17 2026 memory use: 5516.5 MB Fri Sep 11 16:12:21 2026 linear algebra at 0.5%, ETA 0h12m Fri Sep 11 16:12:26 2026 checking every 510000 dimensions, checkpointing every 31110000 dimensions Fri Sep 11 16:23:27 2026 lanczos halted after 22848 iterations (dim = 5831234) Fri Sep 11 16:24:03 2026 recovered 36 nontrivial dependencies Fri Sep 11 16:24:03 2026 BLanczosTime: 773 Fri Sep 11 16:24:03 2026 elapsed time 00:12:54 Fri Sep 11 12:25:51 2026 Fri Sep 11 12:25:51 2026 Fri Sep 11 12:25:51 2026 Msieve v. 1.54 (SVN unknown) Fri Sep 11 12:25:51 2026 random seeds: 292d2b73 8d7ebcac Fri Sep 11 12:25:51 2026 Using 8 OpenMP threads Fri Sep 11 12:25:51 2026 factoring 5432975631044391390437593926487362688783819994439506471369376226901246768626485986157473605898185923509925992604279462091144977894077886847956305713416711953658228072259889 (172 digits) Fri Sep 11 12:25:51 2026 no P-1/P+1/ECM available, skipping Fri Sep 11 12:25:51 2026 commencing number field sieve (172-digit input) Fri Sep 11 12:25:51 2026 R0: 49401993336845850288045768393087296917 Fri Sep 11 12:25:51 2026 R1: -1 Fri Sep 11 12:25:51 2026 A0: 1 Fri Sep 11 12:25:51 2026 A1: 1 Fri Sep 11 12:25:51 2026 A2: 1 Fri Sep 11 12:25:51 2026 A3: 1 Fri Sep 11 12:25:51 2026 A4: 1 Fri Sep 11 12:25:51 2026 A5: 1 Fri Sep 11 12:25:51 2026 A6: 1 Fri Sep 11 12:25:51 2026 skew 1.35, size 3.306e-11, alpha 2.428, combined = 1.526e-12 rroots = 0 Fri Sep 11 12:25:51 2026 Fri Sep 11 12:25:51 2026 commencing square root phase Fri Sep 11 12:25:51 2026 reading relations for dependency 1 Fri Sep 11 12:25:53 2026 read 2915000 cycles Fri Sep 11 12:25:57 2026 cycles contain 9893496 unique relations Fri Sep 11 12:27:23 2026 read 9893496 relations Fri Sep 11 12:27:47 2026 multiplying 9893496 relations Fri Sep 11 12:28:20 2026 multiply complete, coefficients have about 243.53 million bits Fri Sep 11 12:28:20 2026 initial square root is modulo 549029521 Fri Sep 11 12:29:20 2026 GCD is 1, no factor found Fri Sep 11 12:29:20 2026 reading relations for dependency 2 Fri Sep 11 12:29:20 2026 read 2915495 cycles Fri Sep 11 12:29:24 2026 cycles contain 9902602 unique relations Fri Sep 11 12:29:37 2026 read 9902602 relations Fri Sep 11 12:30:00 2026 multiplying 9902602 relations Fri Sep 11 12:30:31 2026 multiply complete, coefficients have about 243.76 million bits Fri Sep 11 12:30:32 2026 initial square root is modulo 559555099 Fri Sep 11 12:31:30 2026 sqrtTime: 339 Fri Sep 11 12:31:30 2026 p80 factor: 23927282593604275877628655391901243956493925389608087181675428946013198024870421 Fri Sep 11 12:31:30 2026 p93 factor: 227061957821178449714443115806800071916174512601466246216591062777497573985672539572885704109 Fri Sep 11 12:31:30 2026 elapsed time 00:05:39