20111117, 07:36  #1 
6809 > 6502
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Aug 2003
101×103 Posts
2^{3}×3^{2}×149 Posts 
GPU attack on double Mersennes?
MM61 and MM127 have been vexing us for a while. Anyone think that an attack on these numbers using GPU's to TF is worth the effort? (This excludes RDS, as I already know his opinion.) The current versions of mfaktx can't do numbers that large (am I right?)

20111117, 07:52  #2 
Romulan Interpreter
"name field"
Jun 2011
Thailand
2×7^{2}×103 Posts 
Someone checked already and there are no known factors below 100 bits or so. I think the value is 10^33 times something. I think it is not easy to go above that value, even with a GPU.

20111117, 09:46  #3  
"Lucan"
Dec 2006
England
2×3×13×83 Posts 
Quote:
David 

20111117, 09:53  #4  
"Brian"
Jul 2007
The Netherlands
2·3·5·109 Posts 
Quote:
It would be a lucky strike to discover a factor in the several extra bit levels that a concerted effort with GPU's might achieve. The most likely result of the effort would still be "no factor found". But that doesn't say it that it isn't worth the effort. 

20111117, 10:00  #5 
Romulan Interpreter
"name field"
Jun 2011
Thailand
2×7^{2}×103 Posts 
And why not MM127? (which I believe is prime, I am a big fan of Catalan conjecture, and hope that all numbers in the sequence are prime :D). Now joking apart, I assume we would have more chances to find a (small) factor of MM89 and MM107 (as for MM61 and MM127 there is a lot of work done, and the lower bounds for factors are already incredible high). Assuming we have the (software) tools to play with them.

20111117, 10:19  #6 
"Lucan"
Dec 2006
England
2×3×13×83 Posts 

20111118, 01:30  #7 
Dec 2010
Monticello
5·359 Posts 
mfaktc would be the starting point for the software for such a GPU attack...but I don't think it handles FCs above about 90 bits.
So someone would need to take that up, and I'm not volunteering at the moment. 
20111118, 02:23  #8 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3·29·83 Posts 
https://sites.google.com/site/anthon...s/mm61prog.htm
Current progress as of half a month ago. It also seems our very own Ernest Mayer found a factor of MM31 some years ago. 
20111118, 02:38  #9 
6809 > 6502
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Aug 2003
101×103 Posts
2^{3}·3^{2}·149 Posts 
That is exactly why I did not mention it in my original post.
Last fiddled with by Uncwilly on 20111118 at 02:38 
20111118, 02:39  #10  
"Lucan"
Dec 2006
England
2×3×13×83 Posts 
The Importance of not being Ernest
Quote:
composite even earlier. David Last fiddled with by davieddy on 20111118 at 02:47 

20130907, 14:41  #11 
Sep 2013
China
4_{8} Posts 
A factor of MM61 and MM127 can be found, I guess, above 10^100 or even 10^1000. Well, probably.

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