--- In

primenumbers@yahoogroups.com, "Nathan Russell"

<windrunner@g...> wrote:

> As someone (Brian Beesley?) once remarked, we want to be careful about

> how we define such things. The largest Mersenne composite with prime

> exponent is an interesting record. Likewise, the largest

> double-checked LL test result (which is most likely smaller).

> However, the "largest Mersenne composite" is not. For example, since

> Graham's number is composite, 2^(Graham's number)-1 is likewise

> composite.

>

> Nathan

>

I don't know if there is an "official" definition for Mersenne numbers...

As Paulo Ribenboim and many others, I use to call so 2^p-1 numbers

with p prime. In spite of his errors, I think that Marin Mersenne

never searched for primes amongst 2^n-1 numbers with composite exponents !

Jean