Quote:
Originally Posted by MattcAnderson
A Fermat number is F(m) = 2^(2^m) + 1.
It has been shown that any factor of a Fermat number
has the form
k*2^n + 1.
with n greater than or equal to m+2
This information is at fermatsearch.org.
if k is not odd then we have an equivalent representation
since
2*k*2^c + 1 = k*2^(c+1) + 1
I assume that mmff and other Fermat search programs
only search for odd k because the even cases will
be searched in increased exponent
Also, in the log of known Fermat factors,
http://www.prothsearch.com/fermat.html
All the k values are odd.
Regards,
Matt |
AFAIK, they eliminate even k. I know that gfndsieve does so I assume the others do as well.