20130926, 14:48  #1 
Jun 2012
Boulder, CO
263 Posts 
RSA210 factored
Hello all,
RSA210 has been factored by GNFS. The 210digit 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 P1/P+1/ECM available, skipping Tue Sep 24 03:21:14 2013 commencing number field sieve (210digit 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 3.501e15, alpha 11.183, combined = 1.204e15 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 
20130926, 14:58  #2 
I moo ablest echo power!
May 2013
1,741 Posts 
Congrats! What hardware did you use to accomplish this?

20130926, 16:07  #3 
Bemusing Prompter
"Danny"
Dec 2002
California
2^{2}·3·197 Posts 
Congratulations. It looks like you have broken the record for the largest nontrivial factorization done by an individual.
I wouldn't be surprised if you manage to find a new Mersenne prime next. :D 
20130926, 17:43  #5 
Tribal Bullet
Oct 2004
6716_{8} Posts 
Congrats on another huge job done.
You should update wikipedia too, and submit your report to eprint.iacr.org 
20131006, 23:14  #6 
May 2011
23 Posts 
Congratulations on the factorization!

20131126, 09:33  #7 
Nov 2013
Västerås Sweden
3_{16} Posts 
adresse?
Hello!
I am wondering if I solve one of the RSA challenges where can I send my result? can anyone help me with adresse or how can I apply?informations necessary for that? Thanks very much! 
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