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Old 2013-05-19, 00:37   #89
Batalov
 
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Phi(4,2^7658614+1)/2

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15·24246384+1 divides GF(4246381,6)
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Old 2013-06-07, 10:36   #90
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42777*2^73616+1 is a Factor of GF(73614,6)
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Old 2013-08-30, 05:18   #91
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That didn't take too long:

12093892381215*2^66+1 is a Factor of GF(64,3)
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Old 2013-08-30, 05:35   #92
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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!
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Old 2013-08-30, 05:58   #93
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Quote:
Originally Posted by Batalov View Post
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.
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Old 2013-09-05, 05:21   #94
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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.
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Old 2013-09-05, 08:11   #95
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Allll-righty then. ;-)

Folks, I told you that it was that easy? And you didn't believe me!
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Old 2013-09-05, 16:32   #96
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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.
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Old 2013-09-05, 17:12   #97
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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)
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Old 2013-12-05, 08:47   #98
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107·22081775+1 divides GF(2081774,6)
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Old 2014-01-03, 19:17   #99
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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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