New Generalized Fermat factors - Page 9

Batalov · 2013-05-19, 00:37

15·2^4246384+1 divides GF(4246381,6)

Jatheski · 2013-06-07, 10:36

42777*2^73616+1 is a Factor of GF(73614,6)

rajula · 2013-08-30, 05:18

That didn't take too long:

12093892381215*2^66+1 is a Factor of GF(64,3)

Batalov · 2013-08-30, 05:35

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!

rajula · 2013-08-30, 05:58

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.

rajula · 2013-09-05, 05:21

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.

Batalov · 2013-09-05, 08:11

Allll-righty then. ;-)

Folks, I told you that it was that easy? And you didn't believe me!

henryzz · 2013-09-05, 16:32

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.

Batalov · 2013-09-05, 17:12

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 Cunningham-like composites.

Batalov · 2013-12-05, 08:47

107·2^2081775+1 divides GF(2081774,6)

firejuggler · 2014-01-03, 19:17

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.

2013-09-05, 17:12	#97
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 3⁶×13 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 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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2013-05-19, 00:37	#89
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 3⁶×13 Posts	15·2^4246384+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 315₁₀ 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 10010100000101₂ 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!

2013-09-05, 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 3⁶×13 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) 2³·3·5·7² 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.

2013-12-05, 08:47	#98
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 3⁶·13 Posts	107·2^2081775+1 divides GF(2081774,6)

2014-01-03, 19:17	#99
firejuggler Apr 2010 Over the rainbow 2³·5²·13 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.