[QUOTE=JohnFullspeed;265912]
The only factor find is 319546020820551643220672513 John[/QUOTE] This is a factor of F13, not F14. 
25*2^2141884+1 Divides F2141872, by PrimeGrid

[QUOTE=rogue;271545]25*2^2141884+1 Divides F2141872, by PrimeGrid[/QUOTE]
The comment is not proper. It is not archived under "Divides Fermat" category. Would come at number 5 there. EDIT: Also, Divides GF comments are missing. 
[QUOTE=axn;271554]The comment is not proper. It is not archived under "Divides Fermat" category. Would come at number 5 there.
EDIT: Also, Divides GF comments are missing.[/QUOTE] I'm not clear about your objection here. The Prime pages gives the complete Primegrid report as [code] 25*2^2141884+1 Divides F2141872 25*2^2141884+1 Divides GF(2141871,5) 25*2^2141884+1 Divides xGF(2141872,5,2) 25*2^2141884+1 Divides xGF(2141867,5,4) 25*2^2141884+1 Divides xGF(2141872,8,5) 25*2^2141884+1 Divides GF(2141872,10) [/code] So that, while this newly found prime divides several GF's and xGF's, the first line asserts that this prime also divides the given Fermat number. Further, while this is listed as a "user comment", we also have [code] Official Comment: Divides F2141872!!!!, generalized Fermat [/code] The front page on Primegrid also notes [code] ... [this is] PrimeGrid's 8th Prime Fermat Divisor in the Proth Prime Search project: 25*2^2141884+1 Divides F(2141872). This is the 292nd known divisor and the 9th found in 2011. [/code] I don't see a "number 5" there. :question: Bruce* 
The archival tags section ([url]http://primes.utm.edu/primes/page.php?id=101943#tags[/url]) only shows Generalized Fermat.
It should also be filed under "Divides Fermat", "Divides GF(*,5)", and "Divides GF(*,10)" ([url]http://primes.utm.edu/top20/sizes.php[/url]). i.e. these entries should be properly mentioned in the "official comments" section, not just the "unofficial comments" section. Perhaps someone can email Prof Caldwell? 
[QUOTE=axn;271588]The archival tags section ([url]http://primes.utm.edu/primes/page.php?id=101943#tags[/url]) only shows Generalized Fermat.
It should also be filed under "Divides Fermat", "Divides GF(*,5)", and "Divides GF(*,10)" ([url]http://primes.utm.edu/top20/sizes.php[/url]). i.e. these entries should be properly mentioned in the "official comments" section, not just the "unofficial comments" section. Perhaps someone can email Prof Caldwell?[/QUOTE] Ah, you're objecting to the Prime Pages report; not disputing that this is a new Fermat divisor. Thanks. I crunched a bunch of these n = 2M+ primality tests myself, before that range completed; but haven't gotten above n = 1.738M yet. Just finding the prime is such an unlikely occurance, being a Fermat divisor with k = 25 a great bonus (cf. 1/k chance). The divisor itself is relatively unusual; many of the recent Primegrid finds have primes with exponent n+3 or n+4 dividing F_n, while this one has n+12. bdodson* 
329*2^1246017+1 Divides F(1246013), discovered by PrimeGrid

[QUOTE=rogue;285145]329*2^1246017+1 Divides F(1246013), discovered by PrimeGrid[/QUOTE]
Completed "Proth Prime searches"  1,871,042 with 313 positive llr tests, for my first Fermat factor. Found on one of the old 32bit xeons; it's amazing that I didn't get DC credit instead. And note the k = 329, with only 1/329 chance of a Proth giving a Fermat divisor. Currently the 6th largest. bdodson* 
PrimeGrid observation
[QUOTE=bdodson;285366]Completed "Proth Prime searches"  1,871,042 with 313 positive
llr tests, for my first Fermat factor. ... And note the k = 329, with only 1/329 chance of a Proth giving a Fermat divisor. Currently the 6th largest. bdodson*[/QUOTE] John Blazek, of PrimeGrid, points to a link at the Prime Pages to the effect that [QUOTE] your prime ranks first among "weighted" Fermat primes [url]http://primes.utm.edu/top20/page.php?id=8#weighted[/url] [/QUOTE] where Caldwell remarks about the ranking [code] For purposes of amusement only, we decided to try to rank [Fermat] divisors based on the facts that (1) large primes are harder to find than small ones; and (2) the probability that N = k*2^n+1 divides a Fermat numbers appears to be O(1/k). [/code] As a factoring person, I won't argue with Caldwell on this prime! 
I wonder if PrimeGrid will ever find a factor to F(8675309). They probably can if they found a megabit prime factor for F(1246013). It wouldn't take very long if they have enough people connected. It would be one of the 20 largest known primes. :smile:

PrimeGrid finds another one:
131*2^1494099+1 Divides F(1494096) 
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