MersennePrimeExponentQ

MersennePrimeExponentQ[n] returns True if n is a Mersenne prime exponent, and False otherwise.

Examples

Test known exponents:

MersennePrimeExponentQ[7]
(* True, since 2^7 - 1 = 127 is prime *)

Non-exponent:

MersennePrimeExponentQ[8]
(* False *)

First several exponents:

Select[Range[100], MersennePrimeExponentQ]
(* {2, 3, 5, 7, 13, 17, 19, 31, 61, 89} *)

Please visit the official Wolfram Language Reference for more details.