# Mersenne number

This article describes a sequence of natural numbers. The parameter for the sequence is a positive integer (or sometimes, nonnegative integer).
View other one-parameter sequences

## Definition

Let  be a natural number. The  Mersenne number, denoted , is defined as:

.

Sometimes the term Mersenne number is restricted to the case where  itself is a prime number.

If  itself is prime, it is termed a Mersenne prime. If  is prime, so is .

## Testing/listing

The ID of the sequence in the Online Encyclopedia of Integer Sequences is A000225
The ID of the sequence in the Online Encyclopedia of Integer Sequences is A001348