Math 2.0

Number theory Definition

Mersenne prime

Builds on Mersenne numberPrime number

Definition

A Mersenne prime is a prime number of the form 2n−12^n - 1 for a natural number nn. That is, a Mersenne prime is a Mersenne number that is prime.

Remarks

The first Mersenne primes are 33, 77, 3131 and 127127, for n=2,3,5,7n = 2, 3, 5, 7. If 2n−12^n - 1 is prime, then nn is prime. The converse fails: 211−1=2047=23⋅892^{11} - 1 = 2047 = 23 \cdot 89. The Lucas–Lehmer test decides whether 2p−12^p - 1 is prime. It is not known whether there are infinitely many Mersenne primes.

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Divisibility, definition, no evidence levelDivisibilitydefinitionMersenne number, definition, no evidence levelMersenne numberdefinitionPrime number, definition, no evidence levelPrime numberdefinitionMersenne prime, definition, no evidence levelMersenne primedefinition
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  1. Divisibility definition
  2. Mersenne number definition
  3. Prime number definition
  4. Mersenne prime definition

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1 page builds on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Mersenne_prime, About Mersenne primes
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