Stupid Question Re: Fermat Factor search

[c10ck3r]

Okay, so all factors of a Fermat number are of the form k*2^n+1, right? So, theoretically, P-1 would find factors as long as the k is b-smooth? Is the limitation of this the ~1e15 k value, the size of 2^2^n, or something else that I'm missing? Thanks, Johann.

[MattcAnderson]

Hi,

Fermat numbers have the form 2^(2^m) + 1.
Factors of Fermat numbers have the form k*2^n + 1, where n >= m+2.

My reference is http://www.fermatsearch.org/

Using a trial division software downloaded from the above website, I have been searching n=36 and k>1.4e16

Luigi Morelli has a new software that runs about 50 times faster than this, and can find factors of Fermat and Double Mersenne numbers, but it requires a Graphics Processing Unit, and can be downloaded from -

http://www.doublemersennes.org/

Regards,
Matt

[Dubslow]

Originally Posted by MattcAnderson

Hi,

Fermat numbers have the form 2^(2^m) + 1.
Factors of Fermat numbers have the form k*2^n + 1, where n >= m+2.

My reference is http://www.fermatsearch.org/

Using a trial division software downloaded from the above website, I have been searching n=36 and k>1.4e16

Luigi Morelli has a new software that runs about 50 times faster than this, and can find factors of Fermat and Double Mersenne numbers, but it requires a Graphics Processing Unit, and can be downloaded from -

http://www.doublemersennes.org/

Regards,
Matt

Thank you Captain Obvious. (To quote Batalov.)

[Batalov]

Captain Obvious adds that if "Luigi has a new software", then in that sense everyone has it. The author who had it (as a baby) was one Woltman.

But anyway, that had nothing to do with the OP's question.

Originally Posted by c10ck3r

Okay, so all factors of a Fermat number are of the form k*2^n+1, right? So, theoretically, P-1 would find factors as long as the k is b-smooth? Is the limitation of this the ~1e15 k value, the size of 2^2^n, or something else that I'm missing? Thanks, Johann.

To that, the answer is "yes".

In fact, P-1 had been run with high limits already, so one would not expect to succeed where others* failed. Sometimes, though, - as the Russian proverb goes, even a stick shoots.

_______________
*to quote from "Almost Famous": " I'm about to boldly go where... ummm... many men have gone before"