F22 factored!

[unconnected]

Originally Posted by Batalov

...cofactor status?

F22/64658705994591851009055774868504577 is not prime. RES64: BEAE94F64C12B741. Wd1: 98BEB11D,00000000

[alpertron]

A great discovery. We are waiting for prime factors of F20 and F24.

Now we could write F22 = a² + b² where the numbers a and b are not trivial as I did for F14 , but in this case the numbers are extremely long to be posted here.

[rogue]

Originally Posted by rogue

What software was used to find the factor?

I have yet to get an answer on this rather basic question.

[ixfd64]

Don't forget to tell Wilfrid Keller about this!

http://www.prothsearch.net/fermat.html

edit: Oh, and congrats. :D

[devarajkandadai]

Originally Posted by unconnected

Yesterday Buckle have found first factor of F22: 64658705994591851009055774868504577 !

Congratulations!

Cd u pl explain the procedure?

Devaraj

[bdodson]

Originally Posted by rogue

I have yet to get an answer on this rather basic question.

I replied to this (and a subsequent post/inquiry) on the F19 thread. Buckle
used GIMPS ecm for Fermat numbers. Err, that's prime95, yes? Like this
_is_ the mersenneforum? -Bruce

[Mini-Geek]

Originally Posted by rogue

I have yet to get an answer on this rather basic question.

Prime95, I suppose.

[henryzz]

Originally Posted by Mini-Geek

Interesting idea. I don't know how useful it'd be in application, (especially for Mersenne numbers, where I know that you only do a small amount of TF after P-1, and individual candidates are quickly checked) but I see no reason why it wouldn't be correct.

To put it another way:
When P-1 factoring has proven that any potential k in k*2^n+1 or 2kp+1 must be smoother than certain bounds, you can skip checking k's that are smoother than those bounds.

From a GIMPS perspective I think it would encourage an earlier and possibly deeper P-1.

[philmoore]

Originally Posted by ewmayer

Very nice ... note that it would have needed a p-1 with stage 1 bound just over 10^9 (specifically, >= 1045429261) and stage 2 bound >= 52795084261 to find this factor.

64658705994591851009055774868504577 = 2²⁴ * 31 * 2252461 * 1045429261 * 52795084261 + 1

I remember a discussion on this with Ernst in the Math thread in the early days of this forum, where his insistence on the value of P-1 on Fermat numbers led me to estimate that perhaps 6% or so of the total P-1/ECM effort on these numbers should be spent on P-1. Had that been done in this case, this factor might have been found by P-1.

Congratulations to all involved!

[Buckle]

[Fri Mar 26 07:10:39 2010]
ECM found a factor in curve #1, stage #2
Sigma=8776953345765668, B1=1000000, B2=100000000.
UID: Buckle/NetworkMan, F22 has a factor: 64658705994591851009055774868504577, AID: C8CD1E588F7C58B514C621A586054979

David Bessell
(No relation to Uncle Friedrich)

[Merfighters]

Originally Posted by Andi47

Congrats!

This year seems to be a very good one for Fermat factors!!

The year that the most Fermat factors were found was 2001 (22 factors), and 1956 (14 factors).
At this year, we found 5 factors in 3 months! We will find about 20 factors on this year!