Factorizations, using the post-processing program Msieve, usually take an average of 2 attempted sqrt calculations to split composite numbers into two factors. Sometimes we are unlucky and it takes three, four or more times. If there are more factors, more sqrts are required.

In this case it took 33. Yes, that’s right 33. The mathematical probability is 1/2 for each step to split the number into two factors. Here, things went wrong when almost every step said “Newton iteration failed to converge”, so it seems there are hidden bugs there somewhere.

The sqrt phase started on Saturday morning (Oct 29, 2011) and continued until Monday morning (Oct 31).

The Lanczos matrix step said that it had found 40 nontrivial dependencies, so if all 40 had failed, we would normally either reduce the number of relations from the 73,520,074 found or continue the sieving to find more. Either way would involve another possible 21+ hours of matrix inversion followed by the sqrt steps.

What a relief.

By the way, the number being factored was the 220-digit composite from 131^{48} + 48^{131} = 7 • C220.

Results were posted as message 2433 on XYYXF (in Yahoo Groups) Mon, 31 Oct 2011:

(See http://tech.groups.yahoo.com/group/xyyxf/message/2433 )

Factor Results for C220_131_48: (by SNFS) — Dep 33 with many errors

prp46 factor:

1359529908141779271184277189171489400662\

097997

prp62 factor:

1911874395935236064025593241578389628028\

2870589357747809888407

prp113 factor:

9608507490790427829994761954763147371788\

3403021818589315152706842120055325258281\

894963227008240264378713088470181

–Bob.

This number came out at Dependency 33 after many mysterious “failed to converge” errors:

…

Fri Oct 28 13:19:41 2011 commencing linear algebra

Fri Oct 28 13:19:43 2011 read 3845291 cycles

Fri Oct 28 13:19:48 2011 cycles contain 10133440 unique relations

Fri Oct 28 13:21:11 2011 read 10133440 relations

Fri Oct 28 13:21:25 2011 using 20 quadratic characters above 536870684

Fri Oct 28 13:22:11 2011 building initial matrix

Fri Oct 28 13:24:02 2011 memory use: 1329.5 MB

Fri Oct 28 13:24:03 2011 read 3845291 cycles

Fri Oct 28 13:24:05 2011 matrix is 3845114 x 3845291 (1134.9 MB) with weight 334702241 (87.04/col)

Fri Oct 28 13:24:05 2011 sparse part has weight 259050938 (67.37/col)

Fri Oct 28 13:24:41 2011 filtering completed in 2 passes

Fri Oct 28 13:24:41 2011 matrix is 3844718 x 3844895 (1134.9 MB) with weight 334691813 (87.05/col)

Fri Oct 28 13:24:41 2011 sparse part has weight 259047871 (67.37/col)

Fri Oct 28 13:24:56 2011 read 3844895 cycles

Fri Oct 28 13:24:57 2011 matrix is 3844718 x 3844895 (1134.9 MB) with weight 334691813 (87.05/col)

Fri Oct 28 13:24:57 2011 sparse part has weight 259047871 (67.37/col)

Fri Oct 28 13:24:57 2011 saving the first 48 matrix rows for later

Fri Oct 28 13:24:59 2011 matrix is 3844670 x 3844895 (1092.3 MB) with weight 265839582 (69.14/col)

Fri Oct 28 13:24:59 2011 sparse part has weight 247878277 (64.47/col)

Fri Oct 28 13:24:59 2011 matrix includes 64 packed rows

Fri Oct 28 13:24:59 2011 using block size 65536 for processor cache size 8192 kB

Fri Oct 28 13:25:12 2011 commencing Lanczos iteration (8 threads)

Fri Oct 28 13:25:12 2011 memory use: 1301.2 MB

Fri Oct 28 13:25:28 2011 linear algebra at 0.0%, ETA 21h11m

Sat Oct 29 10:02:43 2011 lanczos halted after 60804 iterations (dim = 3844670)

Sat Oct 29 10:02:51 2011 recovered 40 nontrivial dependencies

Sat Oct 29 10:02:51 2011 BLanczosTime: 74590

Sat Oct 29 10:02:51 2011

Sat Oct 29 10:02:51 2011 commencing square root phase

Sat Oct 29 10:02:51 2011 reading relations for dependency 1

Sat Oct 29 10:02:52 2011 read 1922895 cycles

Sat Oct 29 10:02:54 2011 cycles contain 5065912 unique relations

Sat Oct 29 10:03:58 2011 read 5065912 relations

Sat Oct 29 10:04:24 2011 multiplying 5065912 relations

Sat Oct 29 10:17:44 2011 multiply complete, coefficients have about 133.03 million bits

Sat Oct 29 10:17:45 2011 warning: no irreducible prime found, switching to small primes

Sat Oct 29 10:17:45 2011 initial square root is modulo 53

Sat Oct 29 10:53:50 2011 Newton iteration failed to converge

Sat Oct 29 10:53:50 2011 algebraic square root failed

Sat Oct 29 10:53:50 2011 reading relations for dependency 2

Sat Oct 29 10:53:51 2011 read 1921916 cycles

Sat Oct 29 10:53:54 2011 cycles contain 5066996 unique relations

Sat Oct 29 10:54:57 2011 read 5066996 relations

Sat Oct 29 10:55:23 2011 multiplying 5066996 relations

Sat Oct 29 11:13:17 2011 multiply complete, coefficients have about 133.06 million bits

Sat Oct 29 11:13:17 2011 warning: no irreducible prime found, switching to small primes

Sat Oct 29 11:13:18 2011 initial square root is modulo 53

Sat Oct 29 12:09:36 2011 Newton iteration failed to converge

Sat Oct 29 12:09:36 2011 algebraic square root failed

Sat Oct 29 12:09:36 2011 reading relations for dependency 3

Sat Oct 29 12:09:36 2011 read 1922386 cycles

Sat Oct 29 12:09:40 2011 cycles contain 5067592 unique relations

Sat Oct 29 12:10:55 2011 read 5067592 relations

Sat Oct 29 12:11:34 2011 multiplying 5067592 relations

Sat Oct 29 12:32:27 2011 multiply complete, coefficients have about 133.08 million bits

Sat Oct 29 12:32:28 2011 warning: no irreducible prime found, switching to small primes

Sat Oct 29 12:32:28 2011 initial square root is modulo 53

Sat Oct 29 13:28:48 2011 Newton iteration failed to converge

Sat Oct 29 13:28:48 2011 algebraic square root failed

Sat Oct 29 13:28:48 2011 reading relations for dependency 4

Sat Oct 29 13:28:49 2011 read 1920514 cycles

Sat Oct 29 13:28:53 2011 cycles contain 5062796 unique relations

Sat Oct 29 13:30:07 2011 read 5062796 relations

Sat Oct 29 13:30:46 2011 multiplying 5062796 relations

Sat Oct 29 13:51:37 2011 multiply complete, coefficients have about 132.95 million bits

Sat Oct 29 13:51:38 2011 warning: no irreducible prime found, switching to small primes

Sat Oct 29 13:51:38 2011 initial square root is modulo 53

Sat Oct 29 14:47:58 2011 Newton iteration failed to converge

Sat Oct 29 14:47:58 2011 algebraic square root failed

Sat Oct 29 14:47:58 2011 reading relations for dependency 5

Sat Oct 29 14:47:59 2011 read 1921542 cycles

Sat Oct 29 14:48:03 2011 cycles contain 5063820 unique relations

Sat Oct 29 14:49:18 2011 read 5063820 relations

Sat Oct 29 14:49:57 2011 multiplying 5063820 relations

Sat Oct 29 15:10:49 2011 multiply complete, coefficients have about 132.98 million bits

Sat Oct 29 15:10:50 2011 warning: no irreducible prime found, switching to small primes

Sat Oct 29 15:10:50 2011 initial square root is modulo 53

Sat Oct 29 16:07:08 2011 reading relations for dependency 6

Sat Oct 29 16:07:09 2011 read 1921070 cycles

Sat Oct 29 16:07:13 2011 cycles contain 5062324 unique relations

Sat Oct 29 16:08:27 2011 read 5062324 relations

Sat Oct 29 16:09:06 2011 multiplying 5062324 relations

Sat Oct 29 16:29:56 2011 multiply complete, coefficients have about 132.94 million bits

Sat Oct 29 16:29:57 2011 warning: no irreducible prime found, switching to small primes

Sat Oct 29 16:29:57 2011 initial square root is modulo 53

Sat Oct 29 17:26:15 2011 reading relations for dependency 7

Sat Oct 29 17:26:16 2011 read 1922582 cycles

Sat Oct 29 17:26:20 2011 cycles contain 5066668 unique relations

Sat Oct 29 17:27:35 2011 read 5066668 relations

Sat Oct 29 17:28:14 2011 multiplying 5066668 relations

Sat Oct 29 17:49:07 2011 multiply complete, coefficients have about 133.05 million bits

Sat Oct 29 17:49:07 2011 warning: no irreducible prime found, switching to small primes

Sat Oct 29 17:49:08 2011 initial square root is modulo 53

Sat Oct 29 18:45:29 2011 Newton iteration failed to converge

Sat Oct 29 18:45:29 2011 algebraic square root failed

Sat Oct 29 18:45:29 2011 reading relations for dependency 8

Sat Oct 29 18:45:29 2011 read 1921431 cycles

Sat Oct 29 18:45:33 2011 cycles contain 5063694 unique relations

Sat Oct 29 18:46:48 2011 read 5063694 relations

Sat Oct 29 18:47:28 2011 multiplying 5063694 relations

Sat Oct 29 19:08:20 2011 multiply complete, coefficients have about 132.97 million bits

Sat Oct 29 19:08:21 2011 warning: no irreducible prime found, switching to small primes

Sat Oct 29 19:08:21 2011 initial square root is modulo 53

Sat Oct 29 20:04:44 2011 Newton iteration failed to converge

Sat Oct 29 20:04:44 2011 algebraic square root failed

Sat Oct 29 20:04:44 2011 reading relations for dependency 9

Sat Oct 29 20:04:45 2011 read 1922781 cycles

Sat Oct 29 20:04:49 2011 cycles contain 5069110 unique relations

Sat Oct 29 20:06:04 2011 read 5069110 relations

Sat Oct 29 20:06:43 2011 multiplying 5069110 relations

Sat Oct 29 20:27:36 2011 multiply complete, coefficients have about 133.12 million bits

Sat Oct 29 20:27:37 2011 warning: no irreducible prime found, switching to small primes

Sat Oct 29 20:27:37 2011 initial square root is modulo 53

Sat Oct 29 21:23:57 2011 Newton iteration failed to converge

Sat Oct 29 21:23:57 2011 algebraic square root failed

Sat Oct 29 21:23:57 2011 reading relations for dependency 10

Sat Oct 29 21:23:58 2011 read 1920899 cycles

Sat Oct 29 21:24:02 2011 cycles contain 5064278 unique relations

Sat Oct 29 21:25:16 2011 read 5064278 relations

Sat Oct 29 21:25:56 2011 multiplying 5064278 relations

Sat Oct 29 21:46:48 2011 multiply complete, coefficients have about 132.99 million bits

Sat Oct 29 21:46:48 2011 warning: no irreducible prime found, switching to small primes

Sat Oct 29 21:46:49 2011 initial square root is modulo 53

Sat Oct 29 22:43:09 2011 Newton iteration failed to converge

Sat Oct 29 22:43:09 2011 algebraic square root failed

Sat Oct 29 22:43:09 2011 reading relations for dependency 11

Sat Oct 29 22:43:10 2011 read 1922664 cycles

Sat Oct 29 22:43:14 2011 cycles contain 5068604 unique relations

Sat Oct 29 22:44:27 2011 read 5068604 relations

Sat Oct 29 22:45:06 2011 multiplying 5068604 relations

Sat Oct 29 23:05:57 2011 multiply complete, coefficients have about 133.11 million bits

Sat Oct 29 23:05:58 2011 warning: no irreducible prime found, switching to small primes

Sat Oct 29 23:05:58 2011 initial square root is modulo 53

Sun Oct 30 00:02:22 2011 Newton iteration failed to converge

Sun Oct 30 00:02:22 2011 algebraic square root failed

Sun Oct 30 00:02:22 2011 reading relations for dependency 12

Sun Oct 30 00:02:22 2011 read 1922119 cycles

Sun Oct 30 00:02:26 2011 cycles contain 5064340 unique relations

Sun Oct 30 00:03:41 2011 read 5064340 relations

Sun Oct 30 00:04:21 2011 multiplying 5064340 relations

Sun Oct 30 00:25:12 2011 multiply complete, coefficients have about 132.99 million bits

Sun Oct 30 00:25:13 2011 warning: no irreducible prime found, switching to small primes

Sun Oct 30 00:25:13 2011 initial square root is modulo 53

Sun Oct 30 01:21:33 2011 Newton iteration failed to converge

Sun Oct 30 01:21:33 2011 algebraic square root failed

Sun Oct 30 01:21:33 2011 reading relations for dependency 13

Sun Oct 30 01:21:34 2011 read 1923598 cycles

Sun Oct 30 01:21:38 2011 cycles contain 5068416 unique relations

Sun Oct 30 01:22:51 2011 read 5068416 relations

Sun Oct 30 01:23:30 2011 multiplying 5068416 relations

Sun Oct 30 01:44:22 2011 multiply complete, coefficients have about 133.10 million bits

Sun Oct 30 01:44:23 2011 warning: no irreducible prime found, switching to small primes

Sun Oct 30 01:44:23 2011 initial square root is modulo 53

Sun Oct 30 02:40:43 2011 Newton iteration failed to converge

Sun Oct 30 02:40:43 2011 algebraic square root failed

Sun Oct 30 02:40:43 2011 reading relations for dependency 14

Sun Oct 30 02:40:44 2011 read 1922990 cycles

Sun Oct 30 02:40:48 2011 cycles contain 5066768 unique relations

Sun Oct 30 02:42:02 2011 read 5066768 relations

Sun Oct 30 02:42:41 2011 multiplying 5066768 relations

Sun Oct 30 03:03:33 2011 multiply complete, coefficients have about 133.06 million bits

Sun Oct 30 03:03:33 2011 warning: no irreducible prime found, switching to small primes

Sun Oct 30 03:03:34 2011 initial square root is modulo 53

Sun Oct 30 03:59:54 2011 reading relations for dependency 15

Sun Oct 30 03:59:55 2011 read 1923933 cycles

Sun Oct 30 03:59:59 2011 cycles contain 5068060 unique relations

Sun Oct 30 04:01:18 2011 read 5068060 relations

Sun Oct 30 04:01:57 2011 multiplying 5068060 relations

Sun Oct 30 04:22:51 2011 multiply complete, coefficients have about 133.09 million bits

Sun Oct 30 04:22:52 2011 warning: no irreducible prime found, switching to small primes

Sun Oct 30 04:22:52 2011 initial square root is modulo 53

Sun Oct 30 05:19:10 2011 Newton iteration failed to converge

Sun Oct 30 05:19:10 2011 algebraic square root failed

Sun Oct 30 05:19:10 2011 reading relations for dependency 16

Sun Oct 30 05:19:11 2011 read 1923668 cycles

Sun Oct 30 05:19:15 2011 cycles contain 5068872 unique relations

Sun Oct 30 05:20:28 2011 read 5068872 relations

Sun Oct 30 05:21:07 2011 multiplying 5068872 relations

Sun Oct 30 05:41:58 2011 multiply complete, coefficients have about 133.11 million bits

Sun Oct 30 05:41:59 2011 warning: no irreducible prime found, switching to small primes

Sun Oct 30 05:41:59 2011 initial square root is modulo 53

Sun Oct 30 06:38:18 2011 Newton iteration failed to converge

Sun Oct 30 06:38:18 2011 algebraic square root failed

Sun Oct 30 06:38:18 2011 reading relations for dependency 17

Sun Oct 30 06:38:19 2011 read 1921938 cycles

Sun Oct 30 06:38:23 2011 cycles contain 5065234 unique relations

Sun Oct 30 06:39:37 2011 read 5065234 relations

Sun Oct 30 06:40:16 2011 multiplying 5065234 relations

Sun Oct 30 07:01:06 2011 multiply complete, coefficients have about 133.01 million bits

Sun Oct 30 07:01:07 2011 warning: no irreducible prime found, switching to small primes

Sun Oct 30 07:01:07 2011 initial square root is modulo 53

Sun Oct 30 07:57:23 2011 Newton iteration failed to converge

Sun Oct 30 07:57:23 2011 algebraic square root failed

Sun Oct 30 07:57:23 2011 reading relations for dependency 18

Sun Oct 30 07:57:24 2011 read 1920749 cycles

Sun Oct 30 07:57:28 2011 cycles contain 5065534 unique relations

Sun Oct 30 07:58:42 2011 read 5065534 relations

Sun Oct 30 07:59:21 2011 multiplying 5065534 relations

Sun Oct 30 08:20:12 2011 multiply complete, coefficients have about 133.02 million bits

Sun Oct 30 08:20:13 2011 warning: no irreducible prime found, switching to small primes

Sun Oct 30 08:20:13 2011 initial square root is modulo 53

Sun Oct 30 09:16:32 2011 Newton iteration failed to converge

Sun Oct 30 09:16:32 2011 algebraic square root failed

Sun Oct 30 09:16:32 2011 reading relations for dependency 19

Sun Oct 30 09:16:33 2011 read 1921228 cycles

Sun Oct 30 09:16:38 2011 cycles contain 5063624 unique relations

Sun Oct 30 09:17:51 2011 read 5063624 relations

Sun Oct 30 09:18:31 2011 multiplying 5063624 relations

Sun Oct 30 09:39:22 2011 multiply complete, coefficients have about 132.97 million bits

Sun Oct 30 09:39:23 2011 warning: no irreducible prime found, switching to small primes

Sun Oct 30 09:39:23 2011 initial square root is modulo 53

Sun Oct 30 10:35:42 2011 Newton iteration failed to converge

Sun Oct 30 10:35:42 2011 algebraic square root failed

Sun Oct 30 10:35:42 2011 reading relations for dependency 20

Sun Oct 30 10:35:43 2011 read 1922751 cycles

Sun Oct 30 10:35:47 2011 cycles contain 5064916 unique relations

Sun Oct 30 10:37:02 2011 read 5064916 relations

Sun Oct 30 10:37:42 2011 multiplying 5064916 relations

Sun Oct 30 10:58:33 2011 multiply complete, coefficients have about 133.01 million bits

Sun Oct 30 10:58:34 2011 warning: no irreducible prime found, switching to small primes

Sun Oct 30 10:58:35 2011 initial square root is modulo 53

Sun Oct 30 11:54:54 2011 Newton iteration failed to converge

Sun Oct 30 11:54:54 2011 algebraic square root failed

Sun Oct 30 11:54:54 2011 reading relations for dependency 21

Sun Oct 30 11:54:55 2011 read 1922658 cycles

Sun Oct 30 11:54:59 2011 cycles contain 5067126 unique relations

Sun Oct 30 11:56:13 2011 read 5067126 relations

Sun Oct 30 11:56:52 2011 multiplying 5067126 relations

Sun Oct 30 12:17:44 2011 multiply complete, coefficients have about 133.06 million bits

Sun Oct 30 12:17:45 2011 warning: no irreducible prime found, switching to small primes

Sun Oct 30 12:17:45 2011 initial square root is modulo 53

Sun Oct 30 13:14:04 2011 Newton iteration failed to converge

Sun Oct 30 13:14:04 2011 algebraic square root failed

Sun Oct 30 13:14:04 2011 reading relations for dependency 22

Sun Oct 30 13:14:06 2011 read 1922046 cycles

Sun Oct 30 13:14:10 2011 cycles contain 5065688 unique relations

Sun Oct 30 13:15:25 2011 read 5065688 relations

Sun Oct 30 13:16:04 2011 multiplying 5065688 relations

Sun Oct 30 13:36:56 2011 multiply complete, coefficients have about 133.02 million bits

Sun Oct 30 13:36:57 2011 warning: no irreducible prime found, switching to small primes

Sun Oct 30 13:36:57 2011 initial square root is modulo 53

Sun Oct 30 14:33:17 2011 Newton iteration failed to converge

Sun Oct 30 14:33:17 2011 algebraic square root failed

Sun Oct 30 14:33:17 2011 reading relations for dependency 23

Sun Oct 30 14:33:18 2011 read 1921561 cycles

Sun Oct 30 14:33:22 2011 cycles contain 5065824 unique relations

Sun Oct 30 14:34:36 2011 read 5065824 relations

Sun Oct 30 14:35:16 2011 multiplying 5065824 relations

Sun Oct 30 14:56:07 2011 multiply complete, coefficients have about 133.03 million bits

Sun Oct 30 14:56:08 2011 warning: no irreducible prime found, switching to small primes

Sun Oct 30 14:56:08 2011 initial square root is modulo 53

Sun Oct 30 15:52:24 2011 Newton iteration failed to converge

Sun Oct 30 15:52:24 2011 algebraic square root failed

Sun Oct 30 15:52:24 2011 reading relations for dependency 24

Sun Oct 30 15:52:26 2011 read 1922653 cycles

Sun Oct 30 15:52:30 2011 cycles contain 5068270 unique relations

Sun Oct 30 15:53:43 2011 read 5068270 relations

Sun Oct 30 15:54:23 2011 multiplying 5068270 relations

Sun Oct 30 16:15:14 2011 multiply complete, coefficients have about 133.10 million bits

Sun Oct 30 16:15:14 2011 warning: no irreducible prime found, switching to small primes

Sun Oct 30 16:15:15 2011 initial square root is modulo 53

Sun Oct 30 17:11:31 2011 Newton iteration failed to converge

Sun Oct 30 17:11:31 2011 algebraic square root failed

Sun Oct 30 17:11:31 2011 reading relations for dependency 25

Sun Oct 30 17:11:32 2011 read 1923008 cycles

Sun Oct 30 17:11:36 2011 cycles contain 5067092 unique relations

Sun Oct 30 17:12:50 2011 read 5067092 relations

Sun Oct 30 17:13:30 2011 multiplying 5067092 relations

Sun Oct 30 17:34:20 2011 multiply complete, coefficients have about 133.06 million bits

Sun Oct 30 17:34:21 2011 warning: no irreducible prime found, switching to small primes

Sun Oct 30 17:34:21 2011 initial square root is modulo 53

Sun Oct 30 18:30:37 2011 Newton iteration failed to converge

Sun Oct 30 18:30:37 2011 algebraic square root failed

Sun Oct 30 18:30:37 2011 reading relations for dependency 26

Sun Oct 30 18:30:38 2011 read 1921717 cycles

Sun Oct 30 18:30:42 2011 cycles contain 5064030 unique relations

Sun Oct 30 18:31:56 2011 read 5064030 relations

Sun Oct 30 18:32:36 2011 multiplying 5064030 relations

Sun Oct 30 18:53:26 2011 multiply complete, coefficients have about 132.98 million bits

Sun Oct 30 18:53:26 2011 warning: no irreducible prime found, switching to small primes

Sun Oct 30 18:53:27 2011 initial square root is modulo 53

Sun Oct 30 19:49:44 2011 Newton iteration failed to converge

Sun Oct 30 19:49:44 2011 algebraic square root failed

Sun Oct 30 19:49:44 2011 reading relations for dependency 27

Sun Oct 30 19:49:45 2011 read 1920575 cycles

Sun Oct 30 19:49:50 2011 cycles contain 5062388 unique relations

Sun Oct 30 19:51:05 2011 read 5062388 relations

Sun Oct 30 19:51:44 2011 multiplying 5062388 relations

Sun Oct 30 20:12:34 2011 multiply complete, coefficients have about 132.94 million bits

Sun Oct 30 20:12:35 2011 warning: no irreducible prime found, switching to small primes

Sun Oct 30 20:12:35 2011 initial square root is modulo 53

Sun Oct 30 21:08:53 2011 reading relations for dependency 28

Sun Oct 30 21:08:54 2011 read 1922721 cycles

Sun Oct 30 21:08:58 2011 cycles contain 5067978 unique relations

Sun Oct 30 21:10:11 2011 read 5067978 relations

Sun Oct 30 21:10:51 2011 multiplying 5067978 relations

Sun Oct 30 21:31:43 2011 multiply complete, coefficients have about 133.09 million bits

Sun Oct 30 21:31:44 2011 warning: no irreducible prime found, switching to small primes

Sun Oct 30 21:31:44 2011 initial square root is modulo 53

Sun Oct 30 22:28:07 2011 Newton iteration failed to converge

Sun Oct 30 22:28:07 2011 algebraic square root failed

Sun Oct 30 22:28:07 2011 reading relations for dependency 29

Sun Oct 30 22:28:08 2011 read 1924199 cycles

Sun Oct 30 22:28:12 2011 cycles contain 5069314 unique relations

Sun Oct 30 22:29:27 2011 read 5069314 relations

Sun Oct 30 22:30:07 2011 multiplying 5069314 relations

Sun Oct 30 22:50:59 2011 multiply complete, coefficients have about 133.12 million bits

Sun Oct 30 22:51:00 2011 warning: no irreducible prime found, switching to small primes

Sun Oct 30 22:51:00 2011 initial square root is modulo 53

Sun Oct 30 23:47:21 2011 Newton iteration failed to converge

Sun Oct 30 23:47:21 2011 algebraic square root failed

Sun Oct 30 23:47:21 2011 reading relations for dependency 30

Sun Oct 30 23:47:22 2011 read 1923086 cycles

Sun Oct 30 23:47:26 2011 cycles contain 5068548 unique relations

Sun Oct 30 23:48:41 2011 read 5068548 relations

Sun Oct 30 23:49:21 2011 multiplying 5068548 relations

Mon Oct 31 00:10:14 2011 multiply complete, coefficients have about 133.10 million bits

Mon Oct 31 00:10:15 2011 warning: no irreducible prime found, switching to small primes

Mon Oct 31 00:10:15 2011 initial square root is modulo 53

Mon Oct 31 01:06:36 2011 Newton iteration failed to converge

Mon Oct 31 01:06:36 2011 algebraic square root failed

Mon Oct 31 01:06:36 2011 reading relations for dependency 31

Mon Oct 31 01:06:38 2011 read 1921195 cycles

Mon Oct 31 01:06:42 2011 cycles contain 5064628 unique relations

Mon Oct 31 01:07:57 2011 read 5064628 relations

Mon Oct 31 01:08:36 2011 multiplying 5064628 relations

Mon Oct 31 01:29:28 2011 multiply complete, coefficients have about 133.00 million bits

Mon Oct 31 01:29:29 2011 warning: no irreducible prime found, switching to small primes

Mon Oct 31 01:29:29 2011 initial square root is modulo 53

Mon Oct 31 02:25:50 2011 Newton iteration failed to converge

Mon Oct 31 02:25:50 2011 algebraic square root failed

Mon Oct 31 02:25:50 2011 reading relations for dependency 32

Mon Oct 31 02:25:52 2011 read 1921864 cycles

Mon Oct 31 02:25:56 2011 cycles contain 5066216 unique relations

Mon Oct 31 02:27:10 2011 read 5066216 relations

Mon Oct 31 02:27:50 2011 multiplying 5066216 relations

Mon Oct 31 02:48:42 2011 multiply complete, coefficients have about 133.04 million bits

Mon Oct 31 02:48:43 2011 warning: no irreducible prime found, switching to small primes

Mon Oct 31 02:48:43 2011 initial square root is modulo 53

Mon Oct 31 03:45:02 2011 Newton iteration failed to converge

Mon Oct 31 03:45:02 2011 algebraic square root failed

Mon Oct 31 03:45:02 2011 reading relations for dependency 33

Mon Oct 31 03:45:03 2011 read 1921618 cycles

Mon Oct 31 03:45:07 2011 cycles contain 5065538 unique relations

Mon Oct 31 03:46:21 2011 read 5065538 relations

Mon Oct 31 03:47:01 2011 multiplying 5065538 relations

Mon Oct 31 04:07:53 2011 multiply complete, coefficients have about 133.02 million bits

Mon Oct 31 04:07:54 2011 warning: no irreducible prime found, switching to small primes

Mon Oct 31 04:07:54 2011 initial square root is modulo 53

Mon Oct 31 05:04:17 2011 sqrtTime: 154886

Mon Oct 31 05:04:17 2011 prp46 factor: 1359529908141779271184277189171489400662097997

Mon Oct 31 05:04:17 2011 prp62 factor: 19118743959352360640255932415783896280282870589357747809888407

Mon Oct 31 05:04:17 2011 prp113 factor: 96085074907904278299947619547631473717883403021818589315152706842120055325258281894963227008240264378713088470181

Mon Oct 31 05:04:17 2011 elapsed time 64:20:38

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parabens pelo blog, belissimo trabalho