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?)

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.

[QUOTE=Uncwilly;278878]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?)[/QUOTE]
If MM61 counts as a double mersenne, why not MM89 and MM107 ?

David

[QUOTE=LaurV;278879]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.[/QUOTE]
[URL="http://www.mersenneforum.org/showthread.php?t=10732"]This thread[/URL] discusses some of the progress if you take care to avoid the crank postings in it. In the case of MM127 it is apparently more like no factor to about 176 bits thanks to Ernst Mayer.

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.

[QUOTE=davieddy;278891]If MM61 counts as a double mersenne, why not MM89 and MM107 ?

David[/QUOTE]

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.

[QUOTE=LaurV;278894]And why not MM127?[/QUOTE]
No reason at all, except that Uncwilly had already mentioned it,
and 127 is 2^7 - 1 whereas 61 is 2^6 - 3.

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.

[url]https://sites.google.com/site/anthonydforbes/mm61prog.htm[/url]

Current progress as of half a month ago. It also seems our very own Ernest Mayer found a factor of MM31 some years ago.

[QUOTE=Dubslow;279006]It also seems our very own Ernest Mayer found a factor of MM31 some years ago.[/QUOTE]That is exactly why I did not mention it in my original post.:cmd:

The Importance of not being Ernest
 

[QUOTE=Dubslow;279006][URL]https://sites.google.com/site/anthonydforbes/mm61prog.htm[/URL]

Current progress as of half a month ago. It also seems our very own Ernest Mayer found a factor of MM31 some years ago.[/QUOTE]

Note also that Alex Kruppa proved F[sub]31[/sub]
composite even earlier.

David

A factor of MM61 and MM127 can be found, I guess, above 10^100 or even 10^1000. Well, probably.