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Old 2020-12-25, 15:21   #1
MattcAnderson
 
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"Matthew Anderson"
Dec 2010
Oregon, USA

13108 Posts
Default possible overlapping Fermat factor ranges

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
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