The only number that can divide a Mersenne is a base 2 pseudoprime or a prime.

Now all composite Mersennes are, in fact, base 2 pseudoprimes.

This means that at the simplest level, you only need know what the

differences are between a pseudoprime and a prime.

What I was getting at was that I have a method that differentiates a prime

from a pseudoprime. Only that this method doesn't work (well) for Mersennes.

But in order to understand why the method works you also need to understand

what it is about a base 2 pseudoprime that lets it divide a Mersenne.

Hence my earlier post.

Regards,

Kevin.

At 12:22 PM 30/06/2004, David Broadhurst wrote:> > A prime number divides at most one prime-exponent Mersenne.

>

>A moment of reflection should tell you that this implies

>that _every_ number > 1 divides at most prime exponent Mersenne.

>[I omit the half-line proof.]

>

>So why single out this irrelevant special case:

>

> > A base 2 pseudo prime number divides at most one prime-exponent

> > Mersenne.

>

>when it is a trivial consequnce of the statement

>about prime divisors?