# Difference between revisions of "Mersenne number"

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==Facts== | ==Facts== | ||

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+ | ===Number theory facts=== | ||

* [[Mersenne number for prime or Poulet implies prime or Poulet]] | * [[Mersenne number for prime or Poulet implies prime or Poulet]] | ||

* [[Mersenne number is prime implies number is prime]] | * [[Mersenne number is prime implies number is prime]] | ||

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+ | ===Facts in other branches of mathematics=== | ||

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+ | * [[Groupprops:Order is product of Mersenne prime and one more implies normal Sylow subgroup|Order is product of Mersenne prime and one more implies normal Sylow subgroup (fact about groups)]] | ||

==Testing/listing== | ==Testing/listing== |

## Latest revision as of 18:59, 2 January 2012

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