-- Apr 30, 2015 (Kurt Beschorner) -- n=1279: c1201(1830129884......) = 530204158403866252456650409410396227 * c1165(3451745625......) # ECM B1=11e6, sigma=2331580022 -- Apr 27, 2015 (Maksym Voznyy) -- n=15332: p7647(3599323721......) is definitely prime. # Certification is available at: http://stdkmd.com/nrr/cert/Phi/index.htm#CERT_PHI_15332_10 # See also http://stdkmd.com/nrr/repunit/prpfactors.htm -- Apr 26, 2015 (Kurt Beschorner) -- n=1279: c1241(4140878907......) = 22626147700033558648177735039851291979603 * c1201(1830129884......) # ECM B1=11e6, sigma=2181490157 -- Apr 24, 2015 (Alfred Eichhorn) -- # via Kurt Beschorner n=45433: c45433(1111111111......) = 437428188279565499431 * c45412(2540099474......) # ECM B1= 2e3, sigma=991780849 # 75935 of 100000 Phi_n(10) factorizations were cracked. # 7468 of 9592 R_prime factorizations were cracked. -- Apr 13, 2015 (Maksym Voznyy) -- n=59340M: p7393(2555229610......) is definitely prime. # Certification is available at: http://stdkmd.com/nrr/cert/Phi/index.htm#CERT_PHI_59340M_10 # See also http://stdkmd.com/nrr/repunit/prpfactors.htm -- Apr 12, 2015 (Bo Chen, Maksym Voznyy, Marcus Osso and Kurt Beschorner) -- n=417: c161(2801979440......) = 4236651046107678488081335638323958061433054078591556082042947538117 * p94(6613665864......) # NFS # ----------------8<----------------8<----------------8<---------------- # Thu Apr 09 05:30:00 2015 Msieve v. 1.52 (SVN 883 pre-release) # Thu Apr 09 05:30:00 2015 random seeds: dcda265c 0e594179 # Thu Apr 09 05:30:00 2015 factoring 28019794405013793623642890609109486956784606668213180770106821133915494856938323150986313922023884356213539292902781538969655446565698130104102912687833422470093 (161 digits) # Thu Apr 09 05:30:01 2015 searching for 15-digit factors # Thu Apr 09 05:30:01 2015 commencing number field sieve (161-digit input) # Thu Apr 09 05:30:01 2015 R0: -31962234505809194168773726275065 # Thu Apr 09 05:30:01 2015 R1: 1475112950817047 # Thu Apr 09 05:30:01 2015 A0: -581766484092816356996701398489819690630816 # Thu Apr 09 05:30:01 2015 A1: -47873314491471353279373482371425568 # Thu Apr 09 05:30:01 2015 A2: 1513466361882649055514108474 # Thu Apr 09 05:30:01 2015 A3: 83081102633142963173 # Thu Apr 09 05:30:01 2015 A4: -404464321538 # Thu Apr 09 05:30:01 2015 A5: 840 # Thu Apr 09 05:30:01 2015 skew 62898719.57, size 1.084e-015, alpha -8.077, combined = 1.165e-012 rroots = 3 # Thu Apr 09 05:30:01 2015 commencing relation filtering # Thu Apr 09 05:30:01 2015 estimated available RAM is 16301.6 MB # Thu Apr 09 05:30:01 2015 commencing duplicate removal, pass 1 # Thu Apr 09 05:50:40 2015 found 15725189 hash collisions in 146641486 relations # Thu Apr 09 05:51:48 2015 added 55386 free relations # Thu Apr 09 05:51:48 2015 commencing duplicate removal, pass 2 # Thu Apr 09 05:55:04 2015 found 13007232 duplicates and 133689639 unique relations # Thu Apr 09 05:55:04 2015 memory use: 554.4 MB # Thu Apr 09 05:55:04 2015 reading ideals above 50266112 # Thu Apr 09 05:55:04 2015 commencing singleton removal, initial pass # Thu Apr 09 06:14:47 2015 memory use: 3012.0 MB # Thu Apr 09 06:14:47 2015 reading all ideals from disk # Thu Apr 09 06:15:07 2015 memory use: 2486.6 MB # Thu Apr 09 06:15:16 2015 commencing in-memory singleton removal # Thu Apr 09 06:15:26 2015 begin with 133689639 relations and 141398184 unique ideals # Thu Apr 09 06:17:10 2015 reduce to 46594216 relations and 38191107 ideals in 22 passes # Thu Apr 09 06:17:10 2015 max relations containing the same ideal: 75 # Thu Apr 09 06:17:17 2015 reading ideals above 720000 # Thu Apr 09 06:17:17 2015 commencing singleton removal, initial pass # Thu Apr 09 06:27:34 2015 memory use: 1378.0 MB # Thu Apr 09 06:27:34 2015 reading all ideals from disk # Thu Apr 09 06:27:47 2015 memory use: 1747.4 MB # Thu Apr 09 06:27:54 2015 keeping 43973770 ideals with weight <= 200, target excess is 250535 # Thu Apr 09 06:28:02 2015 commencing in-memory singleton removal # Thu Apr 09 06:28:08 2015 begin with 46594219 relations and 43973770 unique ideals # Thu Apr 09 06:29:55 2015 reduce to 46585892 relations and 43965433 ideals in 13 passes # Thu Apr 09 06:29:55 2015 max relations containing the same ideal: 200 # Thu Apr 09 06:30:30 2015 removing 4698408 relations and 4298408 ideals in 400000 cliques # Thu Apr 09 06:30:32 2015 commencing in-memory singleton removal # Thu Apr 09 06:30:38 2015 begin with 41887484 relations and 43965433 unique ideals # Thu Apr 09 06:32:05 2015 reduce to 41487319 relations and 39261759 ideals in 12 passes # Thu Apr 09 06:32:05 2015 max relations containing the same ideal: 193 # Thu Apr 09 06:32:37 2015 removing 3397408 relations and 2997408 ideals in 400000 cliques # Thu Apr 09 06:32:38 2015 commencing in-memory singleton removal # Thu Apr 09 06:32:44 2015 begin with 38089911 relations and 39261759 unique ideals # Thu Apr 09 06:33:50 2015 reduce to 37851392 relations and 36023340 ideals in 10 passes # Thu Apr 09 06:33:50 2015 max relations containing the same ideal: 183 # Thu Apr 09 06:34:18 2015 removing 2995378 relations and 2595378 ideals in 400000 cliques # Thu Apr 09 06:34:20 2015 commencing in-memory singleton removal # Thu Apr 09 06:34:24 2015 begin with 34856014 relations and 36023340 unique ideals # Thu Apr 09 06:35:30 2015 reduce to 34651256 relations and 33221022 ideals in 11 passes # Thu Apr 09 06:35:30 2015 max relations containing the same ideal: 175 # Thu Apr 09 06:35:56 2015 removing 2777951 relations and 2377951 ideals in 400000 cliques # Thu Apr 09 06:35:58 2015 commencing in-memory singleton removal # Thu Apr 09 06:36:02 2015 begin with 31873305 relations and 33221022 unique ideals # Thu Apr 09 06:36:56 2015 reduce to 31677886 relations and 30645464 ideals in 10 passes # Thu Apr 09 06:36:56 2015 max relations containing the same ideal: 164 # Thu Apr 09 06:37:20 2015 removing 2646751 relations and 2246751 ideals in 400000 cliques # Thu Apr 09 06:37:21 2015 commencing in-memory singleton removal # Thu Apr 09 06:37:25 2015 begin with 29031135 relations and 30645464 unique ideals # Thu Apr 09 06:38:14 2015 reduce to 28836535 relations and 28201805 ideals in 10 passes # Thu Apr 09 06:38:14 2015 max relations containing the same ideal: 154 # Thu Apr 09 06:38:36 2015 removing 2270668 relations and 1926559 ideals in 344109 cliques # Thu Apr 09 06:38:37 2015 commencing in-memory singleton removal # Thu Apr 09 06:38:40 2015 begin with 26565867 relations and 28201805 unique ideals # Thu Apr 09 06:39:20 2015 reduce to 26410245 relations and 26117912 ideals in 9 passes # Thu Apr 09 06:39:20 2015 max relations containing the same ideal: 144 # Thu Apr 09 06:39:45 2015 relations with 0 large ideals: 756 # Thu Apr 09 06:39:45 2015 relations with 1 large ideals: 1028 # Thu Apr 09 06:39:45 2015 relations with 2 large ideals: 16030 # Thu Apr 09 06:39:45 2015 relations with 3 large ideals: 169295 # Thu Apr 09 06:39:45 2015 relations with 4 large ideals: 942701 # Thu Apr 09 06:39:45 2015 relations with 5 large ideals: 3072138 # Thu Apr 09 06:39:45 2015 relations with 6 large ideals: 6113340 # Thu Apr 09 06:39:45 2015 relations with 7+ large ideals: 16094957 # Thu Apr 09 06:39:45 2015 commencing 2-way merge # Thu Apr 09 06:40:14 2015 reduce to 14728177 relation sets and 14435844 unique ideals # Thu Apr 09 06:40:14 2015 commencing full merge # Thu Apr 09 06:45:20 2015 memory use: 1659.2 MB # Thu Apr 09 06:45:23 2015 found 7965765 cycles, need 7926044 # Thu Apr 09 06:45:23 2015 weight of 7926044 cycles is about 555025926 (70.03/cycle) # Thu Apr 09 06:45:23 2015 distribution of cycle lengths: # Thu Apr 09 06:45:23 2015 1 relations: 1096176 # Thu Apr 09 06:45:23 2015 2 relations: 1066442 # Thu Apr 09 06:45:23 2015 3 relations: 1044464 # Thu Apr 09 06:45:23 2015 4 relations: 879987 # Thu Apr 09 06:45:23 2015 5 relations: 798041 # Thu Apr 09 06:45:23 2015 6 relations: 660079 # Thu Apr 09 06:45:23 2015 7 relations: 546175 # Thu Apr 09 06:45:23 2015 8 relations: 450828 # Thu Apr 09 06:45:23 2015 9 relations: 370965 # Thu Apr 09 06:45:23 2015 10+ relations: 1012887 # Thu Apr 09 06:45:23 2015 heaviest cycle: 20 relations # Thu Apr 09 06:45:25 2015 commencing cycle optimization # Thu Apr 09 06:45:40 2015 start with 40778488 relations # Thu Apr 09 06:46:52 2015 pruned 559790 relations # Thu Apr 09 06:46:52 2015 memory use: 1491.8 MB # Thu Apr 09 06:46:52 2015 distribution of cycle lengths: # Thu Apr 09 06:46:52 2015 1 relations: 1096176 # Thu Apr 09 06:46:52 2015 2 relations: 1083895 # Thu Apr 09 06:46:52 2015 3 relations: 1068937 # Thu Apr 09 06:46:52 2015 4 relations: 890362 # Thu Apr 09 06:46:52 2015 5 relations: 804836 # Thu Apr 09 06:46:52 2015 6 relations: 660526 # Thu Apr 09 06:46:52 2015 7 relations: 544483 # Thu Apr 09 06:46:52 2015 8 relations: 446513 # Thu Apr 09 06:46:52 2015 9 relations: 365905 # Thu Apr 09 06:46:52 2015 10+ relations: 964411 # Thu Apr 09 06:46:52 2015 heaviest cycle: 20 relations # Thu Apr 09 06:47:04 2015 RelProcTime: 4623 # Thu Apr 09 06:47:04 2015 commencing linear algebra # Thu Apr 09 06:47:06 2015 read 7926044 cycles # Thu Apr 09 06:47:24 2015 cycles contain 26045842 unique relations # Thu Apr 09 06:51:27 2015 read 26045842 relations # Thu Apr 09 06:52:01 2015 using 20 quadratic characters above 2147483498 # Thu Apr 09 06:53:57 2015 building initial matrix # Thu Apr 09 06:59:03 2015 memory use: 3534.8 MB # Thu Apr 09 06:59:22 2015 read 7926044 cycles # Thu Apr 09 06:59:26 2015 matrix is 7925865 x 7926044 (2434.0 MB) with weight 767809776 (96.87/col) # Thu Apr 09 06:59:26 2015 sparse part has weight 542939132 (68.50/col) # Thu Apr 09 07:00:54 2015 filtering completed in 2 passes # Thu Apr 09 07:00:58 2015 matrix is 7914426 x 7914604 (2433.2 MB) with weight 767422253 (96.96/col) # Thu Apr 09 07:00:58 2015 sparse part has weight 542864953 (68.59/col) # Thu Apr 09 07:01:15 2015 matrix starts at (0, 0) # Thu Apr 09 07:01:19 2015 matrix is 7914426 x 7914604 (2433.2 MB) with weight 767422253 (96.96/col) # Thu Apr 09 07:01:19 2015 sparse part has weight 542864953 (68.59/col) # Thu Apr 09 07:01:19 2015 saving the first 48 matrix rows for later # Thu Apr 09 07:01:21 2015 matrix includes 64 packed rows # Thu Apr 09 07:01:23 2015 matrix is 7914378 x 7914604 (2359.8 MB) with weight 615209252 (77.73/col) # Thu Apr 09 07:01:23 2015 sparse part has weight 539449825 (68.16/col) # Thu Apr 09 07:01:23 2015 using block size 65536 for processor cache size 12288 kB # Thu Apr 09 07:02:00 2015 commencing Lanczos iteration (12 threads) # Thu Apr 09 07:02:00 2015 memory use: 2557.5 MB # Thu Apr 09 07:02:44 2015 linear algebra at 0.0%, ETA 60h58m # Thu Apr 09 07:02:58 2015 checkpointing every 130000 dimensions # Sat Apr 11 21:20:33 2015 lanczos halted after 125159 iterations (dim = 7914375) # Sat Apr 11 21:20:46 2015 recovered 30 nontrivial dependencies # Sat Apr 11 21:20:49 2015 BLanczosTime: 225225 # Sat Apr 11 21:20:49 2015 commencing square root phase # Sat Apr 11 21:20:49 2015 reading relations for dependency 1 # Sat Apr 11 21:20:51 2015 read 3953715 cycles # Sat Apr 11 21:20:58 2015 cycles contain 13017464 unique relations # Sat Apr 11 21:24:11 2015 read 13017464 relations # Sat Apr 11 21:25:41 2015 multiplying 13017464 relations # Sat Apr 11 21:50:37 2015 multiply complete, coefficients have about 647.56 million bits # Sat Apr 11 21:50:45 2015 initial square root is modulo 645329 # Sat Apr 11 22:21:02 2015 GCD is 1, no factor found # Sat Apr 11 22:21:02 2015 reading relations for dependency 2 # Sat Apr 11 22:21:06 2015 read 3956903 cycles # Sat Apr 11 22:21:13 2015 cycles contain 13023988 unique relations # Sat Apr 11 22:24:12 2015 read 13023988 relations # Sat Apr 11 22:25:45 2015 multiplying 13023988 relations # Sat Apr 11 22:50:44 2015 multiply complete, coefficients have about 647.88 million bits # Sat Apr 11 22:50:52 2015 initial square root is modulo 649483 # Sat Apr 11 23:21:44 2015 GCD is 1, no factor found # Sat Apr 11 23:21:44 2015 reading relations for dependency 3 # Sat Apr 11 23:21:46 2015 read 3957766 cycles # Sat Apr 11 23:21:54 2015 cycles contain 13026612 unique relations # Sat Apr 11 23:25:01 2015 read 13026612 relations # Sat Apr 11 23:26:30 2015 multiplying 13026612 relations # Sat Apr 11 23:51:50 2015 multiply complete, coefficients have about 648.02 million bits # Sat Apr 11 23:51:59 2015 initial square root is modulo 651347 # Sun Apr 12 00:22:52 2015 GCD is 1, no factor found # Sun Apr 12 00:22:52 2015 reading relations for dependency 4 # Sun Apr 12 00:22:55 2015 read 3955676 cycles # Sun Apr 12 00:23:02 2015 cycles contain 13012810 unique relations # Sun Apr 12 00:26:13 2015 read 13012810 relations # Sun Apr 12 00:27:44 2015 multiplying 13012810 relations # Sun Apr 12 00:52:57 2015 multiply complete, coefficients have about 647.33 million bits # Sun Apr 12 00:53:06 2015 initial square root is modulo 642011 # Sun Apr 12 01:23:46 2015 sqrtTime: 14577 # Sun Apr 12 01:23:46 2015 prp67 factor: 4236651046107678488081335638323958061433054078591556082042947538117 # Sun Apr 12 01:23:46 2015 prp94 factor: 6613665864871336888159281741249451029123017235753420336761415494939294742484891072205191009129 # Sun Apr 12 01:23:46 2015 elapsed time 67:53:46 # ----------------8<----------------8<----------------8<---------------- # n=417 (c161) was the smallest composite. # n=417 had the 5th biggest factored part. # 1088 of 100000 Phi_n(10) factorizations were finished. -- Apr 7, 2015 (Kurt Beschorner) -- n=5665: c4058(3156890474......) = 4656638729550687011642171383281121 * c4024(6779333030......) # ECM B1=1e6, sigma=684626219 -- Apr 1, 2015 (Kurt Beschorner) -- n=1243: c1097(6080025363......) = 223888145433163128588378773539598664530236060382826677 * c1044(2715653100......) # ECM B1=11e6, sigma=2683099087