gfn results

ET_ · 2017-01-30, 14:13

119252085*2^6162+1 is a Factor of GF(6160,10)!!!!
168888633*2^6189+1 is a Factor of xGF(6188,11,2)!!!!
(from Frederik Hermanns - N=6150-6200 - K: 100,000,000 - 200,000,000

ET_ · 2017-02-20, 12:02

N from 14,000 to 14,500 and k from 20,000,000 to 30,000,000 completed with pfgw and the switch -gx

Here are the extended factors:

20085603*2^14098+1 is a Factor of xGF(14097,9,5)!!!!
21704897*2^14499+1 is a Factor of xGF(14498,9,5)!!!!
28371113*2^14393+1 is a Factor of xGF(14392,7,2)!!!!

houding · 2017-02-21, 09:04

86229*2^82319+1 is a Factor of xGF(82318,10,3)!!!!

17105181*2^14973+1 is a Factor of xGF(14969,11,5)!!!!

Adolf

Batalov · 2018-01-02, 18:39

120769*2^72390+1 is a Factor of GF(72389,3)
(plus some xGFs)

The bigger boat gets more fish, but still no tuna this year...

rogue · 2018-06-03, 02:23

Finished n=10000-10999 for k=269e6-300e6:

289602611*2^10879+1 is a Factor of GF(10876,10)!!!!

ET_ · 2019-04-19, 08:48

A new Generalized Fermat has been found
2788032⁵²⁴²⁸⁸ + 1
While not the largest Generalized Fermat it is the largest prime for 2019 with 3'379,193 digits.

Congratulations to user "Sheep"

ET_ · 2019-06-01, 09:02

I completed the following GFN-xGF range :

5600 <= N <= 5699 - 1,200,000,000 < K < 2,500,000,000

and found the following factors:

2491340445*2^5654+1 is a Factor of xGF(5652,11,10)!!!!
1755293137*2^5672+1 is a Factor of xGF(5671,8,3)!!!!
2004304135*2^5672+1 is a Factor of xGF(5671,7,2)!!!!
1982981535*2^5675+1 is a Factor of xGF(5674,8,7)!!!!

Dr Sardonicus · 2019-06-02, 01:49

Quote:

Originally Posted by ET_

A new Generalized Fermat has been found
2788032⁵²⁴²⁸⁸ + 1
While not the largest Generalized Fermat it is the largest prime for 2019 with 3'379,193 digits.

Congratulations to user "Sheep"

That would be 2788032⁵²⁴²⁸⁸ + 1 or 2788032^524288 + 1, as reported here, with the official announcement here.

Thank you for the correction, the factor should look right now

Luigi

Dr Sardonicus · 2019-06-02, 12:09

Quote:

Originally Posted by Dr Sardonicus

That would be 2788032⁵²⁴²⁸⁸ + 1 or 2788032^524288 + 1, as reported here, with the official announcement here.

Thank you for the correction, the factor should look right now

Luigi

Looks OK in the quotation in my post. As of now, the typo is still there in your post, though

I make so many typos, I have a Black Belt of transfinite degree

Gary · 2021-02-10, 13:46

Here are a couple of GFN divisibilities for a new large Proth prime reported on PrimesPages. Reporting here because I don't have the ability to post user comments on PrimesPages, likely because I have not yet submitted a new prime.

27 * 2^12184319 + 1 divides GF(12184313,8)
27 * 2^12184319 + 1 divides xGF(12184318,10,9)

Batalov · 2021-02-10, 18:03

Quote:

Originally Posted by Gary

Here are a couple of GFN divisibilities for a new large Proth prime reported on PrimesPages. Reporting here because I don't have the ability to post user comments on PrimesPages, likely because I have not yet submitted a new prime.

27 * 2^12184319 + 1 divides GF(12184313,8)
27 * 2^12184319 + 1 divides xGF(12184318,10,9)

I can post these (and attribute to you... I think. No it appears that I can't, and cannot with Anonymous either)
Generally it is with &comment=1 added to the URL, by hand.
You can email to C.C.

2017-01-30, 14:13	#1
ET_ Banned "Luigi" Aug 2002 Team Italia 2·11·13·17 Posts	gfn results 1192520852^6162+1 is a Factor of GF(6160,10)!!!! 1688886332^6189+1 is a Factor of xGF(6188,11,2)!!!! (from Frederik Hermanns - N=6150-6200 - K: 100,000,000 - 200,000,000 Last fiddled with by ET_ on 2017-01-30 at 14:54

2017-02-20, 12:02	#2
ET_ Banned "Luigi" Aug 2002 Team Italia 2×11×13×17 Posts	gfn range completed N from 14,000 to 14,500 and k from 20,000,000 to 30,000,000 completed with pfgw and the switch -gx Here are the extended factors: 200856032^14098+1 is a Factor of xGF(14097,9,5)!!!! 217048972^14499+1 is a Factor of xGF(14498,9,5)!!!! 28371113*2^14393+1 is a Factor of xGF(14392,7,2)!!!!

2019-04-19, 08:48	#6
ET_ Banned "Luigi" Aug 2002 Team Italia 2·11·13·17 Posts	A new Generalized Fermat has been found 2788032⁵²⁴²⁸⁸ + 1 While not the largest Generalized Fermat it is the largest prime for 2019 with 3'379,193 digits. Congratulations to user "Sheep" Last fiddled with by ET_ on 2019-06-02 at 18:08

2021-02-10, 13:46	#10
Gary "Gary Gostin" Aug 2015 Texas, USA 7·11 Posts	Proth prime GFN divisibilities Here are a couple of GFN divisibilities for a new large Proth prime reported on PrimesPages. Reporting here because I don't have the ability to post user comments on PrimesPages, likely because I have not yet submitted a new prime. 27 * 2^12184319 + 1 divides GF(12184313,8) 27 * 2^12184319 + 1 divides xGF(12184318,10,9)

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2017-02-21, 09:04	#3
houding "Adolf" Nov 2013 South Africa 2×3×11 Posts	862292^82319+1 is a Factor of xGF(82318,10,3)!!!! 171051812^14973+1 is a Factor of xGF(14969,11,5)!!!! Adolf

2018-01-02, 18:39	#4
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2³·3·5²·17 Posts	120769*2^72390+1 is a Factor of GF(72389,3) (plus some xGFs) The bigger boat gets more fish, but still no tuna this year...

2018-06-03, 02:23	#5
rogue "Mark" Apr 2003 Between here and the 3×19×127 Posts	Finished n=10000-10999 for k=269e6-300e6: 289602611*2^10879+1 is a Factor of GF(10876,10)!!!!

2019-06-01, 09:02	#7
ET_ Banned "Luigi" Aug 2002 Team Italia 2×11×13×17 Posts	I completed the following GFN-xGF range : 5600 <= N <= 5699 - 1,200,000,000 < K < 2,500,000,000 and found the following factors: 24913404452^5654+1 is a Factor of xGF(5652,11,10)!!!! 17552931372^5672+1 is a Factor of xGF(5671,8,3)!!!! 20043041352^5672+1 is a Factor of xGF(5671,7,2)!!!! 19829815352^5675+1 is a Factor of xGF(5674,8,7)!!!!