20110322, 21:27  #1 
"Phil"
Sep 2002
Tracktown, U.S.A.
2×13×43 Posts 
New Fermat factors
I see on Wilfrid Keller's site: http://www.prothsearch.net/fermat.html that two new factors of Fermat numbers have been discovered recently including a 49digit factor of F17 by David Bessel that appears to have been discovered using ECM with prime95/mprime. The other factor, the second known of F42 is credited to Roman Maznichenko, and Keller credits Durman for the software, but Luigi says over at http://www.fermatsearch.org/news.html that it was discovered using Mark Rodenkirch's program GMPFactor. Congratulations to everyone involved!

20110322, 21:30  #2 
"Phil"
Sep 2002
Tracktown, U.S.A.
10001011110_{2} Posts 
I see David's factor was already discussed in this thread:
http://www.mersenneforum.org/showthread.php?t=15358 I don't know how I overlooked it, congrats again! Moderators: feel free to append this to the other thread. 
20110322, 21:59  #3  
"Mark"
Apr 2003
Between here and the
2^{2}·7·223 Posts 
Quote:
BTW Luigi, it is GMPFermat, not GMPFactor. Would you mind fixing it? 

20110323, 01:18  #4 
P90 years forever!
Aug 2002
Yeehaw, FL
1110010111000_{2} Posts 
In reviewing Keller's page, is there any reason why F25 and F26 (and maybe F27) cannot be moved to the "Factorizations known to be incomplete" section?
Who wants to volunteer to do the PRP tests? 
20110323, 01:56  #5 
Bemusing Prompter
"Danny"
Dec 2002
California
2^{2}×3×197 Posts 
ATH tested those cofactors a while back and found them to be composite. However, I think that Wilfrid wants them to be independently verified first.
Last fiddled with by ixfd64 on 20110323 at 01:56 
20110323, 02:17  #6  
Einyen
Dec 2003
Denmark
3,037 Posts 
Quote:


20110323, 13:09  #7 
Banned
"Luigi"
Aug 2002
Team Italia
2^{6}·3·5^{2} Posts 

20110323, 19:29  #8  
"Phil"
Sep 2002
Tracktown, U.S.A.
10001011110_{2} Posts 
Quote:


20110324, 01:36  #9 
Einyen
Dec 2003
Denmark
3,037 Posts 
I tried using the GMP function mpz_powm to calculate 3^{2[sup]2^(n1)}[/sup] mod F_{n}=2^{2[sup]n}[/sup]+1 and timed it:
n=14: 1.945s n=15: 12.143s n=16: 73.373s n=17: 415.121s this suggest the time is roughly 2.6*10^{11} * 5.98^{n} with R^{2} = 0.9999225. This means n=25 would take roughly 7*10^{8} sec ~ 22 years. Last fiddled with by ATH on 20110324 at 01:37 
20110324, 01:47  #10 
Tribal Bullet
Oct 2004
3534_{10} Posts 
GMP has had a subquadratic GCD for several years now, and even F31size GCDs take only a few hours and < 5GB of memory.

20110324, 02:32  #11  
"Robert Gerbicz"
Oct 2005
Hungary
5A2_{16} Posts 
Quote:


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