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April 30, 2015 2015 年 4 月 30 日 (Kurt Beschorner)

n=1279: c1201(1830129884......) = 530204158403866252456650409410396227 * c1165(3451745625......)

# ECM B1=11e6, sigma=2331580022

April 27, 2015 2015 年 4 月 27 日 (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

April 26, 2015 2015 年 4 月 26 日 (Kurt Beschorner)

n=1279: c1241(4140878907......) = 22626147700033558648177735039851291979603 * c1201(1830129884......)

# ECM B1=11e6, sigma=2181490157

April 24, 2015 2015 年 4 月 24 日 (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.

April 13, 2015 2015 年 4 月 13 日 (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

April 12, 2015 2015 年 4 月 12 日 (Bo Chen, Maksym Voznyy, Marcus Osso and Kurt Beschorner)

n=417: c161(2801979440......) = 4236651046107678488081335638323958061433054078591556082042947538117 * p94(6613665864......)

# NFS

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

# n=417 (c161) was the smallest composite.

# n=417 had the 5th biggest factored part.

# 1088 of 100000 Phi_n(10) factorizations were finished.

April 7, 2015 2015 年 4 月 7 日 (Kurt Beschorner)

n=5665: c4058(3156890474......) = 4656638729550687011642171383281121 * c4024(6779333030......)

# ECM B1=1e6, sigma=684626219

April 1, 2015 2015 年 4 月 1 日 (Kurt Beschorner)

n=1243: c1097(6080025363......) = 223888145433163128588378773539598664530236060382826677 * c1044(2715653100......)

# ECM B1=11e6, sigma=2683099087

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