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
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
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
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