Mersenne number

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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 .

Relation with other properties

Stronger properties

Facts

Number theory facts

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