20120918, 19:01  #1 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{2}·2,281 Posts 
New Generalized Fermat factors
Embarassingly easily, I have found a factor for F_20(6)
http://www1.unihamburg.de/RRZ/W.Keller/GFN06.html P1 found a factor in stage #2, B1=100000, B2=10000000, E=12. 6^1048576+1 has a factor: 522767209448794182647809 k = 124637415277670427, N=22 (No previously known factors.) It is possible that the new Prime95 binary preloads the group order with a necessary amount of "2"s, maybe? 
20120919, 04:20  #2 
Jun 2003
13·19^{2} Posts 

20120919, 04:42  #3 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{2}×2,281 Posts 
It looks easier to find than other (e.g. G.Reynolds') factors.
The cofactor is surely composite but I am running a 5PRP test just in case on a slow computer. I've tested my luck on m=3,5,6,8,10,12; 17<=N<=24 and found nothing else so far. I was actually building a chimera of mmff and mfaktcrepunit (c) Danilo MrRepunit; ran P1 on Gfn_20(6) just out of boredom. Imagine my surprize. ;) W.Keller didn't respond yet. 
20120919, 06:34  #4  
Jun 2003
4693_{10} Posts 
Quote:
If you're serious about running big P1 job on GFNs, then porting P1 algorithm using Genefer FFT routines might be the way to go (will be useful for the Prime Grid searches as well). [Easier said than done ] 

20120919, 07:02  #5 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{2}×2,281 Posts 
Yep, "we can rebuild him! We have the technology!"
I had built it with modifications before. I am more interested to make the mmffGFN work first though. (Not much hassle, just some preinits to be rewritten and the classes redefined. And of course N>=m+1, not 2) 
20120919, 08:08  #6  
Banned
"Luigi"
Aug 2002
Team Italia
2·2,383 Posts 
Quote:
Do you plan to integrate xGF also? Luigi Last fiddled with by ET_ on 20120919 at 08:09 

20120919, 09:25  #7 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{2}·2,281 Posts 
Axn, you are right, it is still not preloaded in 27.7 neither:
ecm.c:line ~4560 Code:
/* For Mersenne numbers, 2^n1, make sure we include 2n in the calculated */ /* exponent (since factors are of the form 2kn+1). For (Generalized) Fermat numbers, */ /* 
20120919, 09:30  #8 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{2}·2,281 Posts 
P.S. For Fermat (b=2), g should be rather 4n, and for GNF (b>2), 2n.
But even n would do the trick already. I do remember this bit of code having already been discussed on the forum years ago. 
20120919, 09:45  #9  
Jun 2003
13×19^{2} Posts 
Quote:
My preferred solution is to _always_ throw in n (or 4n) in there, regardless of the form of the number. Last fiddled with by axn on 20120919 at 09:45 Reason: once > one 

20120919, 10:36  #10 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{2}·2,281 Posts 
I found a livedin old (26.6) code that I had used for tests on linux64. That's less hassle than try to get VStudio and curl and everything and start anew on my new Win64 machine (old one is gone).
The vanilla mprime didn't find some easy factors for GFN(6), m=18,19... The patched one found the easy ones (as could have been expected) in Step 1. Now, I'll load some reruns for m=3,5,6,8,10,12 and go to sleep. Harvest in the morning. The F_20(6) factor is genuine, though. The cofactor is composite. 
20120919, 19:37  #11 
P90 years forever!
Aug 2002
Yeehaw, FL
7·1,021 Posts 

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Generalized Fermat numbers (in our case primes)  pepi37  Conjectures 'R Us  4  20151009 14:49 
Pseudoprimality Hypothesis for Specific Class of Generalized Fermat Numbers  primus  Miscellaneous Math  1  20150325 22:18 
Generalized Fermat factors  why?  siegert81  Factoring  1  20110905 23:00 
Generalized Fermat Numbers  ET_  Programming  4  20080623 07:59 
Generalized Fermat Prime Search?  pacionet  Lounge  3  20060125 15:40 