-- 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