Re: A base 2 pseudo prime divides at most one prime-exponent Mersenne
- Hi David,
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.
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?