> Chris Nash writes:
>
> The smallest factor of 2^p-1, p a prime, is at least as big as
> 2p+1. All factors of a Mersenne number of prime exponent are of the
> form 2kp+1 - similarly for all 'new' factors of a composite
> exponent (ie that haven't appeared in any Mersenne number with an
> exponent that is a factor of the original one).
>
> Everything here is correct except that many "primitive" factors of
> composite exponent Mersennes are _not_ congruent to 1 mod twice the
> exponent. There are numerous counter-examples, starting with 5, which
> is a factor of M(4) = 15 but not a factor of any smaller Mersenne.
But since 4 is not prime, I doubt that would (pardon the pun) be a factor
when looking for divisors of 2^p-1 (where p is prime).
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