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 .

Relation with other properties

Stronger properties

• Sierpinski number

Facts

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

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