# Mersenne number

From 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

## Contents

## 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 .

## Relation with other properties

### Stronger properties

## Facts

### Number theory facts

- Mersenne number for prime or Poulet implies prime or Poulet
- Mersenne number is prime implies number is prime

### Facts in other branches of mathematics

## 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