20130519, 00:37  #89 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
9261_{10} Posts 
15·2^{4246384}+1 divides GF(4246381,6)

20130607, 10:36  #90 
Apr 2012
993438: i1090
2·73 Posts 
42777*2^73616+1 is a Factor of GF(73614,6)

20130830, 05:18  #91 
"Tapio Rajala"
Feb 2010
Finland
100111011_{2} Posts 
That didn't take too long:
12093892381215*2^66+1 is a Factor of GF(64,3) 
20130830, 05:35  #92 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
9261_{10} Posts 
Hey! The horse is not dead. I keep telling y'all.
Anyone else? Dudes, don't be shy! There's plenty more where this came from. Tapio, now you'd need a 6 and a 10? ;) Easy! Good luck! 
20130830, 05:58  #93 
"Tapio Rajala"
Feb 2010
Finland
3^{2}·5·7 Posts 
Yeah, I'll continue with a range on 6 next once I'm done with the current 3. I don't want to abandon the range even if I already found what I was looking for. :)
I'm not crunching 24/7; I turned off the computing on the 580 while I'm at work. So, even the current range will take a couple of days. 
20130905, 05:21  #94 
"Tapio Rajala"
Feb 2010
Finland
3^{2}×5×7 Posts 
Two down, one to go:
51651074664519*2^49+1 is a Factor of GF(46,10) Next is gfn6 which was most tested base so far. I'm expecting it to take a bit longer than the gfn3 and gfn10. 
20130905, 08:11  #95 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
3^{3}·7^{3} Posts 

20130905, 16:32  #96 
Just call me Henry
"David"
Sep 2007
Cambridge (GMT/BST)
13242_{8} Posts 
Has any work ever been done on factoring with b > 2?
The factors seem to be of the form and is divisible by . There seems to be something further than that going on though. 
20130905, 17:12  #97 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
3^{3}×7^{3} Posts 
GFNs are interesting because some of them are prime.
Factoring them is a roadside attraction (like TF for the GIMPS project), and at that, an attraction with long history. Now, if m>2, then all b^{m[SUP]n}[/SUP]+1 are composite; they are no more interesting than any other Cunninghamlike composites. Last fiddled with by Batalov on 20130908 at 21:53 Reason: ...except m=2^s, of course (comment w/o edit) 
20131205, 08:47  #98 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
3^{3}×7^{3} Posts 
107·2^{2081775}+1 divides GF(2081774,6)

20140103, 19:17  #99 
Apr 2010
Over the rainbow
2×1,259 Posts 
Hi.
While looking for fermat factor, I stumbled upon 85110047*2^6151+1 is a Factor of xGF(6150,4,3)!!!! I looked on this exponent from 300e3 up to 100e6 and found no other xGF or GF. In this range 23273 prime were found, 1 only was a fermat factor. 
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