20180124, 00:01  #1 
Oct 2017
++41
5^{3} Posts 
How are such big factors found? (M1193)
https://www.mersenne.org/report_expo...ll=1&ecmhist=1
That's 104 digits. Is there another option besides massive computing power and massive luck? 
20180124, 00:35  #2 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3·29·83 Posts 
M1193, and other Mersennes of generally similar size (5001200 bits) can be fully factored, with difficulty, by the Special Number Field Sieve.
NFS@Home has done many of them, but also a special variant of SNFS was demonstrated by factoring several such Mersennes all at once: http://eprint.iacr.org/2014/653.pdf Last fiddled with by Dubslow on 20180124 at 00:37 
20180124, 03:17  #3  
"Curtis"
Feb 2005
Riverside, CA
13×359 Posts 
Quote:
Doing such a computation is, mostly, highly parallelizable; but the final step of solving a substantial matrix must be done on a single machine or tightlylinked cluster. That cluster access is the limiting constraint on mere mortals trying similar factorizations; for the most part, only the CADO group and NFS@home have even tried. Something like $1000 on an Amazon rentaserver might take care of such a matrix; I would be interested in pricing such an endeavor, but it's not easy to estimate the amount of computation it will take to solve such a matrix. Edit: "similar" meant 1000+ bits. SNFS tasks up to 900 bits can be done by a solo enthusiast with a couple machines and some patience (or more of one and less of the other). 9001000 can be done by a team or a [few] dozen machines and a few months for the matrix step on a single machine. Last fiddled with by VBCurtis on 20180124 at 03:26 

20180124, 09:53  #4 
Oct 2017
++41
5^{3} Posts 
Thanks for the information regarding SNFS.
So I guess the Information "Type: FECM" on mersenne.org isn't entirely correct. 
20180124, 15:18  #5 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
16065_{8} Posts 

20180124, 15:43  #6  
Aug 2006
2^{2}×1,493 Posts 
Quote:


20180124, 16:45  #7  
Sep 2003
2583_{10} Posts 
Quote:


20180124, 16:54  #8  
Aug 2006
2^{2}·1,493 Posts 
Quote:


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