Double Mersenne number

Double Mersenne primes

No. of known terms	4
Conjectured no. of terms	4
First terms	7, 127, 2147483647
Largest known term	170141183460469231731687303715884105727
OEIS index	A077586

In mathematics, a double Mersenne number is a Mersenne number of the form

where p is a prime exponent.

The first four terms of the sequence of double Mersenne numbers are (sequence in the OEIS):

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 ${\displaystyle M_{M_{p}}}$ can be prime only if M_p is itself a Mersenne prime. For the first values of p for which M_p is prime, ${\displaystyle M_{M_{p}}}$ is known to be prime for p = 2, 3, 5, 7 while explicit factors of ${\displaystyle M_{M_{p}}}$ have been found for p = 13, 17, 19, and 31.

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