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February 26, 2015 2015 年 2 月 26 日 (Bo Chen and Kurt Beschorner)

n=495: c164(8841509271......) = 5898361538755660499929123185996968161779290911542722951712487387346014412041 * p89(1498977167......)

# NFS

Mon Feb 23 08:28:16 2015  Msieve v. 1.52 (SVN 883 pre-release)
Mon Feb 23 08:28:16 2015  factoring 88415092713367678139008031849456036531214635443710603842417450647749425991456343388066542975721610469026836129783834813518385505575072089337317444944320083700084281 (164 digits)
Mon Feb 23 08:28:18 2015  commencing number field sieve (164-digit input)
Mon Feb 23 08:28:18 2015  R0: -151936021790866734760949074966731
Mon Feb 23 08:28:18 2015  R1: 11197298509350953
Mon Feb 23 08:28:18 2015  A0: 7188474167420357145710728869952852625116160
Mon Feb 23 08:28:18 2015  A1: 164074274020152035109954866065637672
Mon Feb 23 08:28:18 2015  A2: -4287367632410376403738394678
Mon Feb 23 08:28:18 2015  A3: -40793478113902744349
Mon Feb 23 08:28:18 2015  A4: 472724187378
Mon Feb 23 08:28:18 2015  A5: 1092
Mon Feb 23 08:28:18 2015  skew 107047465.92, size 6.381e-016, alpha -8.042, combined = 8.720e-013 rroots = 5
Mon Feb 23 08:28:18 2015  commencing relation filtering
Mon Feb 23 08:39:18 2015  found 10036986 hash collisions in 85117830 relations
Mon Feb 23 08:40:26 2015  added 122031 free relations
Mon Feb 23 08:42:04 2015  found 8211102 duplicates and 77028758 unique relations
...
Mon Feb 23 09:05:58 2015  begin with 24881626 relations and 25494102 unique ideals
Mon Feb 23 09:06:28 2015  reduce to 24854930 relations and 24640312 ideals in 7 passes
...
Mon Feb 23 09:07:20 2015  reduce to 14565437 relation sets and 14350819 unique ideals
Mon Feb 23 09:13:01 2015  found 7845497 cycles, need 7817019
Mon Feb 23 09:13:01 2015  weight of 7817019 cycles is about 547375786 (70.02/cycle)
Mon Feb 23 09:13:17 2015  start with 40138921 relations
Mon Feb 23 09:14:36 2015  pruned 686862 relations
...   
Mon Feb 23 09:17:02 2015  commencing linear algebra
Mon Feb 23 09:17:04 2015  read 7817019 cycles
Mon Feb 23 09:17:22 2015  cycles contain 24632855 unique relations
Mon Feb 23 09:20:36 2015  read 24632855 relations
Mon Feb 23 09:29:44 2015  read 7817019 cycles
Mon Feb 23 09:31:44 2015  matrix is 7812129 x 7812354 (2327.4 MB) with weight 605967995 (77.57/col)
...
Wed Feb 25 23:53:46 2015  commencing square root phase
Wed Feb 25 23:53:48 2015  read 3905863 cycles
Wed Feb 25 23:53:56 2015  cycles contain 12316224 unique relations
Thu Feb 26 00:52:39 2015  read 12313154 relations
Thu Feb 26 00:54:10 2015  multiplying 12313154 relations
Thu Feb 26 01:18:04 2015  multiply complete, coefficients have about 621.60 million bits
Thu Feb 26 01:18:12 2015  initial square root is modulo 377387
Thu Feb 26 01:47:26 2015  prp76 factor: 5898361538755660499929123185996968161779290911542722951712487387346014412041
Thu Feb 26 01:47:26 2015  prp89 factor: 14989771673443409019874558921389684608157138239906931183380750230163484811077013632926641

# c164 was the smallest composite.

# 1086 of 100000 Phi_n(10) factorizations were finished.

February 23, 2015 2015 年 2 月 23 日 (Kurt Beschorner)

n=5327: c4534(1202637078......) = 177954362685648225352955701649963 * c4501(6758120790......)

# ECM B1=1e6, sigma=2095876934

n=5425: c3561(2120255507......) = 1900120195137189771656214528928201 * c3528(1115853361......)

# ECM B1=1e6, sigma=1777095829

February 13, 2015 2015 年 2 月 13 日 (Kurt Beschorner)

n=5391: c3588(9990000009......) = 18222939721437243497267118121 * c3560(5482101221......)

# ECM B1=1e6, sigma=3290266606

n=5485: c4375(2266224143......) = 337252720410513968986951403021321 * c4342(6719661567......)

# ECM B1=1e6, sigma=3477306955

# 75929 of 100000 Phi_n(10) factorizations were cracked.

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