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-   -   New Fermat factors (https://www.mersenneforum.org/showthread.php?t=15449)

 philmoore 2011-07-09 18:32

[QUOTE=JohnFullspeed;265912]
The only factor find is 319546020820551643220672513
John[/QUOTE]

This is a factor of F13, not F14.

 rogue 2011-09-12 16:15

25*2^2141884+1 Divides F2141872, by PrimeGrid

 axn 2011-09-12 18:00

[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.

 bdodson 2011-09-13 02:45

[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]
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*

 axn 2011-09-13 03:23

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?

 bdodson 2011-09-13 13:39

[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*

 rogue 2012-01-06 23:10

329*2^1246017+1 Divides F(1246013), discovered by PrimeGrid

 bdodson 2012-01-08 07:46

[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 32-bit
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*

 bdodson 2012-01-09 23:51

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!

 Stargate38 2012-01-13 00:22

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:

 rogue 2012-02-07 16:46

PrimeGrid finds another one:

131*2^1494099+1 Divides F(1494096)

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