Test whether a number is a Mersenne prime exponent:

The number is not a Mersenne prime exponent:

MersennePrimeExponentQ works over integers:

Negative integers are not Mersenne prime exponents:

Noninteger numbers are not Mersenne prime exponents:

Mersenne prime exponents are prime numbers:

Composite numbers cannot be MersennePrimeExponents:

The only even Mersenne prime exponent is :

MersennePrimeExponent gives the Mersenne prime exponent:

is a Mersenne prime, where p is a Mersenne prime exponent:

If p is a Mersenne prime exponent, then is a perfect number:

Every even perfect number has the form , where p is a Mersenne prime exponent:

Check that in the representation above p is 5:

Triangular numbers of Mersenne primes are perfect numbers:

Hexagonal numbers related to Mersenne prime exponents are perfect numbers:

Find Mersenne prime exponents:

Expressions that represent Mersenne prime exponents but do not evaluate explicitly will give False:

It is necessary to use symbolic simplification first:

As of this version of the Wolfram Language, only 49 Mersenne prime exponents have definite ranking:

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

The minor planet 8191 Mersenne is named after Marin Mersenne:

The number is a Mersenne prime: