Congratulation, Gary, and happy holidays!

Strong, Gary strong. Congratulations. Haven't heard anything from Luigi. And merry Christmas to all.

Another Factor from Gary!
 

I'm back, sorry for the delayed updates.

January 28th, 2017
New Fermat factor from FermatSearch!
3370842847 . 2[sup]3058[/sup]+1 is a Factor of F[sub]3056[/sub]!!!
Gary Gostin found this new Fermat factor using his GMP-based pmfs program running on an HPE Superdome X system
with 240 Ivy Bridge cores (E7-8890 v2 @ 2.80 GHz).
Congratulations to Gary from FermatSearch, for his first factor of the year!

Luigi

A new Fermat factor from FermatSearch
 

I would like to report the following new Fermat factor:
[INDENT][FONT=Calibri]15,071,297 * 2^18347 + 1 divides F18345[/FONT]

[/INDENT][FONT=Calibri][FONT=Calibri]This was discovered on Sept 7 by pmfs running on an HPE Superdome X system with 240 Ivy Bridge cores (E7-8890 v2 @ 2.8GHz). [/FONT][/FONT]

[FONT=Calibri][FONT=Calibri]Gary[/FONT][/FONT]

You're definitely on a roll. I wouldn't be surprised if you find soon a new Mersenne prime too!

Another new Fermat factor from FermatSearch
 

[FONT=Calibri][SIZE=3]I am happy to report another new Fermat factor:[/SIZE][/FONT]

[FONT=Calibri][SIZE=3]15,175,951* 2^18936 + 1 divides F18933[/SIZE][/FONT]

[FONT=Calibri][SIZE=3]This was discovered on Sept 13 running pmfs on the same system that found the F18345 factor a few days ago. It’s interesting that these two factors are very close together on a log N/log K graph, having almost identical Ks and fairly similar values in N. Probably nothing mathematically significant, but I have always been fascinated how Fermat factors form clumps and filaments on the log/log graph, not unlike galaxies in the universe.[/SIZE][/FONT]

[FONT=Calibri][SIZE=3]Danny, thanks for the encouragement. I spent some time searching for Mersenne primes long ago, before GIMPS got started. Walt Colquitt and I both had FFT based programs, and we discovered that both programs had [/SIZE][SIZE=3]bugs in FFT multiplication by comparing residues. Once fixed, I spent several months searching, but decided the likely time to find a new Mersenne prime was too long, and went back to searching for Fermat factors. Today, with the 1.5 million CPUs that are part of the GIMPS project, my chances of finding a new Mersenne prime are even more remote. So for now I will continue to search for Fermat factors.[/SIZE][/FONT]

Congratulations Gary, and thank you for your heavy work on Fermat Search project :smile: :bow:

Congrats, [b]Gary[/b]. What's most impressive to me (though I'm no expert) is the size of the odd multipliers, especially with your recent finds for F1680 and F2123 (not to mention [b]Roman[/b]'s recent find for F287).

Good luck finding more!

26277*2^135854+1 is a Factor of GF(135852,8)!!!
31707*2^123642+1 is a Factor of xGF(123641,7,3)!!!!
39583*2^122002+1 is a Factor of xGF(122001,8,5)!!!!

[QUOTE=rogue;468275]26277*2^135854+1 is a Factor of GF(135852,8)!!!
31707*2^123642+1 is a Factor of xGF(123641,7,3)!!!!
39583*2^122002+1 is a Factor of xGF(122001,8,5)!!!![/QUOTE]

Did you email the results to Prof. Keller?

No. You can do so if you wish.