ryanp



Jun 2012 Boulder, CO

B5 16 Posts

RSA-210 factored



RSA-210 has been factored by GNFS. The 210-digit composite



Code: N = 245246644900278211976517663573088018467026787678332759743414451715061600830038587216952208399332071549103626827191679864079776723243005600592035631246561218465817904100131859299619933817012149335034875870551067



Code: Thu Sep 26 07:17:57 2013 prp105 factor: 435958568325940791799951965387214406385470910265220196318705482144524085345275999740244625255428455944579 Thu Sep 26 07:17:57 2013 prp105 factor: 562545761726884103756277007304447481743876944007510545104946851094548396577479473472146228550799322939273



Code: Mon Sep 23 11:09:41 2013 commencing Lanczos iteration (32 threads) Mon Sep 23 11:09:41 2013 memory use: 26956.9 MB Mon Sep 23 11:10:27 2013 restarting at iteration 1026631 (dim = 64920012) Mon Sep 23 11:13:33 2013 linear algebra at 99.3%, ETA 15h43m Mon Sep 23 11:14:32 2013 checkpointing every 30000 dimensions Tue Sep 24 02:21:56 2013 lanczos halted after 1033963 iterations (dim = 65383602) Tue Sep 24 02:24:01 2013 recovered 22 nontrivial dependencies Tue Sep 24 02:24:17 2013 BLanczosTime: 55712 Tue Sep 24 02:24:17 2013 elapsed time 15:28:33 Tue Sep 24 03:21:13 2013 Tue Sep 24 03:21:13 2013 Tue Sep 24 03:21:13 2013 Msieve v. 1.52 (SVN 936M) Tue Sep 24 03:21:13 2013 random seeds: 6af9ef2b 972abb4d Tue Sep 24 03:21:13 2013 factoring 245246644900278211976517663573088018467026787678332759743414451715061600830038587216952208399332071549103626827191679864079776723243005600592035631246561218465817904100131859299619933817012149335034875870551067 (210 digits) Tue Sep 24 03:21:14 2013 no P-1/P+1/ECM available, skipping Tue Sep 24 03:21:14 2013 commencing number field sieve (210-digit input) Tue Sep 24 03:21:14 2013 R0: -8311128239923121259046301811046853 Tue Sep 24 03:21:14 2013 R1: 63190692009226810471 Tue Sep 24 03:21:14 2013 A0: -46373978032319633360321876974395396247530766893600 Tue Sep 24 03:21:14 2013 A1: 4926444336634688706035599320492329943566740 Tue Sep 24 03:21:14 2013 A2: 415031002380786834672968277117654072 Tue Sep 24 03:21:14 2013 A3: -35317070927593920606305065701 Tue Sep 24 03:21:14 2013 A4: -1333072472407237353592 Tue Sep 24 03:21:14 2013 A5: 44263602924186 Tue Sep 24 03:21:14 2013 A6: 744120 Tue Sep 24 03:21:14 2013 skew 21829368.04, size 3.501e-15, alpha -11.183, combined = 1.204e-15 rroots = 6 Tue Sep 24 03:21:14 2013 Tue Sep 24 03:21:14 2013 commencing square root phase Tue Sep 24 03:21:14 2013 reading relations for dependency 1 Tue Sep 24 03:21:25 2013 read 32695123 cycles Tue Sep 24 03:22:39 2013 cycles contain 106934058 unique relations Tue Sep 24 05:32:17 2013 read 106934058 relations Tue Sep 24 05:44:28 2013 multiplying 106934058 relations Tue Sep 24 11:02:59 2013 multiply complete, coefficients have about 6529.43 million bits Tue Sep 24 11:03:59 2013 initial square root is modulo 21002549 Tue Sep 24 16:02:07 2013 GCD is 1, no factor found Tue Sep 24 16:02:07 2013 reading relations for dependency 2 Tue Sep 24 16:03:51 2013 read 32693851 cycles Tue Sep 24 16:05:11 2013 cycles contain 106953756 unique relations Tue Sep 24 18:27:03 2013 read 106953756 relations Tue Sep 24 18:40:10 2013 multiplying 106953756 relations Wed Sep 25 00:19:45 2013 multiply complete, coefficients have about 6530.65 million bits Wed Sep 25 00:20:52 2013 initial square root is modulo 21068617 Wed Sep 25 05:22:23 2013 GCD is N, no factor found Wed Sep 25 05:22:23 2013 reading relations for dependency 3 Wed Sep 25 05:22:52 2013 read 32688271 cycles Wed Sep 25 05:24:16 2013 cycles contain 106919358 unique relations Wed Sep 25 07:44:54 2013 read 106919358 relations Wed Sep 25 07:58:11 2013 multiplying 106919358 relations Wed Sep 25 13:29:11 2013 multiply complete, coefficients have about 6528.53 million bits Wed Sep 25 13:30:14 2013 initial square root is modulo 20953879 Wed Sep 25 18:25:01 2013 GCD is N, no factor found Wed Sep 25 18:25:01 2013 reading relations for dependency 4 Wed Sep 25 18:26:40 2013 read 32684333 cycles Wed Sep 25 18:27:56 2013 cycles contain 106923636 unique relations Wed Sep 25 20:42:16 2013 read 106923636 relations Wed Sep 25 20:53:54 2013 multiplying 106923636 relations Thu Sep 26 02:18:38 2013 multiply complete, coefficients have about 6528.80 million bits Thu Sep 26 02:19:46 2013 initial square root is modulo 20968403 Thu Sep 26 07:17:57 2013 sqrtTime: 187003 Thu Sep 26 07:17:57 2013 prp105 factor: 435958568325940791799951965387214406385470910265220196318705482144524085345275999740244625255428455944579 Thu Sep 26 07:17:57 2013 prp105 factor: 562545761726884103756277007304447481743876944007510545104946851094548396577479473472146228550799322939273 Thu Sep 26 07:17:57 2013 elapsed time 51:56:44 Hello all,RSA-210 has been factored by GNFS. The 210-digit compositeis the product of two 105-primes:I'll write a more thorough report when I get some free time, but for now here's a portion of the msieve log showing at least the poly used, as well as some stats about the linear algebra and square root phases.Thanks to the authors of msieve and GGNFS for helping make this factorization possible!