20170210, 02:40  #45  
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3·29·83 Posts 
Quote:
For a project of such monumental magnitude, I imagine a detailed bayesian analysis of the ECM odds of success would be required to get anywhere useful, but I'd bet it'd be notably below a t80. Either way, to answer the OP's question by elaborating on another of VBCurtis' points, note that there is no current way for us measly homecomputing contributors to contribute any meaningful effort towards the factorization of M1277. VBCurtis is quite correct about the conditions required for NFS@Home to begin to tackle it, and at such time us homecomputing folk could contribute to NFS@Home. One other possible means of tackling this number might be some variant of the multipletargetsharedsieving variant of the number field sieve that was successfully trialed some years ago which factored several similar Mersenne numbers of slightly smaller size. 

20170210, 06:28  #46  
"Curtis"
Feb 2005
Riverside, CA
138A_{16} Posts 
Quote:
This is a nice reminder that I should catalogue my results files from my ECM work on M1277; I did something like 500 curves at B1=4.3e9, B2 = 210e12. I suppose I'll dig those up next week at work and learn to use the manual submission page. 

20170210, 10:28  #47  
Nov 2008
501_{10} Posts 
Quote:
On M4007, a single curve at 2.9E612E14 returns over 4000 Ghz days... Last fiddled with by Gordon on 20170210 at 10:37 Reason: Correct B2 value 

20170210, 17:21  #48  
Sep 2008
Masontown, PA
2×19 Posts 
Very excellent!
Quote:
Congratulations, too, on having so many cores at your disposal and THANK YOU for contributing to the effort! If I may ask, do you have a "preferred range" of exponents for which you are trying to solve, or are you just working on the ones with the least amount of work done on them so far? Just curious, thank you! 

20170213, 04:42  #49 
Sep 2003
5·11·47 Posts 

20170213, 16:42  #50 
Sep 2008
Masontown, PA
2·19 Posts 
Just wanted to express my thanks and appreciation to Dubslow, VBCurtis, Gordon, and GP2 for keeping this thread alive and helping me learn!
If I may ask another question, why is the level of ECM effort we are on called "t65"? For what does the "t' stand, please? Just "digits", as in, our level of ECM effort could return a ~ 65digit factor for M1277? Thank you ALL again! 
20170213, 17:34  #51  
"Geoffrey Yeung"
Feb 2017
London
2·3^{2} Posts 
Quote:


20170213, 20:30  #52 
"Curtis"
Feb 2005
Riverside, CA
2·41·61 Posts 
if you have access via your school/other:
https://www.jstor.org/stable/2152967...n_tab_contents That's the Silverman paper about ECM parameter choice. 
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