A number of the form 2p−1, where p is a prime number. Such a number which is itself prime is also called a Mersenne prime.
- Expressed in the form 2 p - 1, where the exponent p is itself prime, Mersenne numbers have characteristics that make it relatively easy to determine whether a candidate is prime.
- Written in the form 2 p - 1, where the exponent p is a prime number, Mersenne numbers hold a special place in the never-ending pursuit of larger and larger primes.
- One must be the Lucas Lehmer primality test which uses the Fermat congruence, and in particular his application to testing whether a Mersenne number was prime.
Late 19th century: named after Marin Mersenne (1588–1648), French mathematician.
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