Quote:
Originally Posted by axn
"... where Mp is a Mersenne prime" would be more accurate.

No. The definition should say nothing about primality. Mersenne numbers Mp are defined for all p, not only for primes. Later on, there is usually a discussion about when a mersenne number can be prime and when it can not, but primality of p should not be required in the definition. A double mersenne number is just a mersenne number whose exponent is also a mersenne number.