mersenneforum.org  

Go Back   mersenneforum.org > Factoring Projects > Factoring

Reply
 
Thread Tools
Old 2017-02-10, 02:40   #45
Dubslow
Basketry That Evening!
 
Dubslow's Avatar
 
"Bunslow the Bold"
Jun 2011
40<A<43 -89<O<-88

3·2,399 Posts
Default

Quote:
Originally Posted by VBCurtis View Post
This "rule of thumb" is used for smaller projects widely (0.21 or 0.22), but is *not* accurate for any size of project;
Although these statements are quite true, I would also say it's true that the rule of thumb is *more* accurate for the more usual size suspects (GNFS100 - ~160 equivalent, my SNFS sense of scale doesn't exist), and for something like SNFS >300 digits, that rule of thumb is... wrong. Quite wrong.

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 home-computing 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 home-computing folk could contribute to NFS@Home.

One other possible means of tackling this number might be some variant of the multiple-target-shared-sieving variant of the number field sieve that was successfully trialed some years ago which factored several similar Mersenne numbers of slightly smaller size.
Dubslow is offline   Reply With Quote
Old 2017-02-10, 06:28   #46
VBCurtis
 
VBCurtis's Avatar
 
"Curtis"
Feb 2005
Riverside, CA

118416 Posts
Default

Quote:
Originally Posted by Dubslow View Post
Although these statements are quite true, I would also say it's true that the rule of thumb is *more* accurate for the more usual size suspects (GNFS100 - ~160 equivalent, my SNFS sense of scale doesn't exist), and for something like SNFS >300 digits, that rule of thumb is... wrong. Quite wrong.
Sorry, I meant to say that the 0.21-0.22 rule of thumb for SNFS is not accurate for *all* sizes of project, rather than "any" that I used. I think 0.22 * difficulty is best for 13e range projects, 0.21* difficulty is best for 14e range SNFS (say, 200-240 difficulty), and I'm not sure if 0.21 * difficulty is a bit too much ECM for 15e projects. I fully agree that by the time we're over 300 digits, a Bayesian plan is far preferred over 0.21 * difficulty.

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.
VBCurtis is offline   Reply With Quote
Old 2017-02-10, 10:28   #47
Gordon
 
Gordon's Avatar
 
Nov 2008

7658 Posts
Default

Quote:
Originally Posted by VBCurtis View Post
Sorry, I meant to say that the 0.21-0.22 rule of thumb for SNFS is not accurate for *all* sizes of project, rather than "any" that I used. I think 0.22 * difficulty is best for 13e range projects, 0.21* difficulty is best for 14e range SNFS (say, 200-240 difficulty), and I'm not sure if 0.21 * difficulty is a bit too much ECM for 15e projects. I fully agree that by the time we're over 300 digits, a Bayesian plan is far preferred over 0.21 * difficulty.

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.
Wow, as per the other thread about getting credit, that'll likely shoot you to the top of the lifetime pile, or very near it anyway.

On M4007, a single curve at 2.9E6-12E14 returns over 4000 Ghz days...

Last fiddled with by Gordon on 2017-02-10 at 10:37 Reason: Correct B2 value
Gordon is offline   Reply With Quote
Old 2017-02-10, 17:21   #48
UberNumberGeek
 
UberNumberGeek's Avatar
 
Sep 2008
Masontown, PA

3810 Posts
Thumbs up Very excellent!

Quote:
Originally Posted by GP2 View Post
It varies. I have about 8 cores with high memory doing P−1 stage 2. I would use more, but the need for lots of memory is a constraint. I used a bunch of cores with low memory to do P−1 stage 1 earlier and still have a few doing that.

I also have about 20 cores doing ECM, which doesn't need much memory at all and is probably a more promising approach than P−1, in hindsight.

Found one more first factor, M56843
Congratulations on another great find!

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!
UberNumberGeek is offline   Reply With Quote
Old 2017-02-13, 04:42   #49
GP2
 
GP2's Avatar
 
Sep 2003

50258 Posts
Default

Quote:
Originally Posted by UberNumberGeek View Post
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?
I'm staying below 500k, with particular emphasis on under 100k.
GP2 is offline   Reply With Quote
Old 2017-02-13, 16:42   #50
UberNumberGeek
 
UberNumberGeek's Avatar
 
Sep 2008
Masontown, PA

2×19 Posts
Default

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 ~ 65-digit factor for M1277?

Thank you ALL again!
UberNumberGeek is offline   Reply With Quote
Old 2017-02-13, 17:34   #51
GeoffreyY
 
"Geoffrey Yeung"
Feb 2017
London

2·32 Posts
Default

Quote:
"t30", has had enough ecm curves run on it so that the probability
that a factor of size 30 has been missed is exp(-1) (about 37%)
You can also read more in the docfile.txt of yafu.
GeoffreyY is offline   Reply With Quote
Old 2017-02-13, 20:30   #52
VBCurtis
 
VBCurtis's Avatar
 
"Curtis"
Feb 2005
Riverside, CA

22·19·59 Posts
Default

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.
VBCurtis is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Modular restrictions on factors of Mersenne numbers siegert81 Math 23 2014-03-18 11:50
Mersenne prime factors of very large numbers devarajkandadai Miscellaneous Math 15 2012-05-29 13:18
Factors of Mersenne Numbers asdf Math 17 2004-07-24 14:00
Factoring Smallest Fermat Numbers Erasmus Factoring 32 2004-02-27 11:41
Factors of Mersenne numbers ? Fusion_power Math 13 2003-10-28 20:52

All times are UTC. The time now is 07:10.

Sat Nov 28 07:10:22 UTC 2020 up 79 days, 4:21, 3 users, load averages: 1.40, 1.25, 1.20

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.