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 2013-05-19, 00:37 #89 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 926110 Posts 15·24246384+1 divides GF(4246381,6)
 2013-06-07, 10:36 #90 Jatheski     Apr 2012 993438: i1090 2·73 Posts 42777*2^73616+1 is a Factor of GF(73614,6)
 2013-08-30, 05:18 #91 rajula     "Tapio Rajala" Feb 2010 Finland 1001110112 Posts That didn't take too long: 12093892381215*2^66+1 is a Factor of GF(64,3)
 2013-08-30, 05:35 #92 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 926110 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!
2013-08-30, 05:58   #93
rajula

"Tapio Rajala"
Feb 2010
Finland

32·5·7 Posts

Quote:
 Originally Posted by Batalov Tapio, now you'd need a 6 and a 10? ;-) Easy! Good luck!
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.

 2013-09-05, 05:21 #94 rajula     "Tapio Rajala" Feb 2010 Finland 32×5×7 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.
 2013-09-05, 08:11 #95 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 33·73 Posts Allll-righty then. ;-) Folks, I told you that it was that easy? And you didn't believe me!
 2013-09-05, 16:32 #96 henryzz Just call me Henry     "David" Sep 2007 Cambridge (GMT/BST) 132428 Posts Has any work ever been done on factoring $a^{b^n}+1$ with b > 2? The factors seem to be of the form $k*b^n+1$ and $a^{b^n}+1$ is divisible by $(a^{b^{n-1}}+1)$. There seems to be something further than that going on though.
 2013-09-05, 17:12 #97 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 33×73 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 bm[SUP]n[/SUP]+1 are composite; they are no more interesting than any other Cunningham-like composites. Last fiddled with by Batalov on 2013-09-08 at 21:53 Reason: ...except m=2^s, of course (comment w/o edit)
 2013-12-05, 08:47 #98 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 33×73 Posts 107·22081775+1 divides GF(2081774,6)
 2014-01-03, 19:17 #99 firejuggler     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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