On Sat, 26 Jun 1999 13:59:15 -0400, you wrote:
>I found another factor for Fermat 16. What do I do now? How can I factor
>this number that I found? Are there programs out there that will let me do
>that?
>
>FYI, the factor is:
>
>M16384 has a factor:
>3178457030898592746194675570663374420833971377365687459461386297851584459031
>8073180374859604847822828243686877928403667633015295
>
>G-Man
G-Man,
I'm afraid I have some bad news. M16384 is not a Fermat number. It is
2^(2^14)-1 whereas a Fermat number is of the form 2^(2^n)+1. [Note the
signs]. If you want to factor Fermat numbers, try P16384.
However, all may not be lost. We can factorise M16384 algebraically as
(2^8192+1)(2^4096+1)(2^2048+1)...(2^4+1)(2^2+1)(2^1+1) [ie
F13*F12*F11...*F2*F1*F0] That means that if we remove all the known
factors of these Fermat numbers from your factor, we may be left with
a residue greater than 1. That must be a previously unknown factor
either of F12 or F13 (all the others having only known factors).
Unfortunately, as I'm not a mathematician, I don't have a factoring
program that can deal with numbers of that size - but I'm sure some of
the real mathematicians on the list can oblige. If you want a factorer
that can handle somewhat smaller numbers, try factor.exe. You can
download this from Chris Caldwell's prime pages
(http://www.utm.edu/research/primes/index.html) which also contain a
lot of other interesting prime-related information.
Best of luck
Steve
29 Mersenne factors found and counting
Well, if you do find a factor of a Fermat number,
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