While any command in the package can be referred to using the long form, for example, NumberTheory:-IsMersenne, it is often easier to load the package and then use the short form command names.

Mersenne Primes are prime numbers that are one less than a power of 2. These are of the form:  $M_n=2^n-1$, where $n$ is a positive integer. The IthMersenne command returns the exponent for the Ith Mersenne prime number:

The top level isprime command determines if a given number is prime:

The IsMersenne command checks if a positive integer, n, is a Mersenne exponent, where 2^n-1 is a Mersenne prime:

There are 49 known Mersenne Primes.

NumberTheory