メルセンヌ数
A double Mersenne number that is prime is called a double Mersenne prime. Since a Mersenne number "M""p" can be prime only if "p" is prime, (see Mersenne prime for a proof), a double Mersenne number formula_6 can be prime only if "M""p" is itself a Mersenne prime. For the first values of "p" for which "M""p" is prime, formula_7 is known to be prime for "p" = 2, 3, 5, 7 while explicit factors of formula_7 have been found for "p" = 13, 17, 19, and 31.