Lucas Wiman wrote:

> P-1 factoring is based upon Fermat's little theorem which states that
>
> [...]
> What if we use 2 as a base?  Well, for mersenne numbers, this might be to

The problem is that 2 is not a primitive root (mod Mp). From a computers
point of view, the mod Mp operation is a rotate and add, so if you
start with a single bit set (2d = 10b), that bit will rotate around the
p possible positions like mad but youŽll only ever get values of 2^n,
2^E == 2^n (mod Mp). So you could only find factors of the form
2^n-1.

Ciao,
  Alex.

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