# MersennePrimeExponent

gives the n Mersenne prime exponent.

# Details • A Mersenne prime exponent is a prime number p for which the Mersenne number is prime.
• In , n must be a positive integer.
• As of this version of the Wolfram Language, only 47 Mersenne prime exponents have definite ranking. Four more Mersenne prime exponents are known, but their ranking is still unknown. will attempt to find Mersenne prime exponents for n larger than 47, but cannot be expected to return results in a reasonable time.

# Examples

open allclose all

## Basic Examples(1)

Return the first ten Mersenne prime exponents:

Construct the corresponding Mersenne primes:

Check that they are all primes:

## Properties & Relations(5)

Mersenne prime exponents generate even perfect numbers:

Triangular numbers of Mersenne primes generate even perfect numbers:

Hexagonal numbers related to Mersenne prime exponents generate even perfect numbers:

Mersenne prime exponents generate superperfect numbers:

A trinomial whose order is a Mersenne prime exponent is primitive modulo 2 if and only if it is irreducible:

## Possible Issues(1)

As of this version of the Wolfram Language, only 47 Mersenne prime exponents have definite ranking:

Four more Mersenne prime exponents are known, but their ranking is still unknown: