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The 11 pages that link to Mersenne prime, each with the reason it gives.

• Prime numberBroader topic: Their form connects prime searches to efficient tests and perfect numbers.

• Marin MersenneBroader topic: These primes bear Mersenne’s name because he studied and listed many examples.

• Even numberRelated: Mersenne primes generate every even perfect number through Euclid's formula.

• Lucas sequenceRelated: The Lucas–Lehmer test uses a Lucas recurrence to test numbers of this form.

• Perfect numberRelated: Finding further such primes yields further even perfect numbers, but no odd ones.

• Édouard LucasRelated: Lucas devised a celebrated test for deciding whether numbers of this form are prime.

• Sophie Germain primeRelated: Some Sophie Germain primes yield Mersenne primes through a related factorization.

• Euclid–Euler theoremRelated: The theorem's formula produces an even perfect number exactly when this factor is prime.

• Aliquot sumRelated: Mersenne primes connect Euclid’s construction to the aliquot sums of perfect numbers.

• Catalan–Mersenne conjectureBroader topic: The conjecture asks whether repeated Mersenne operations eventually stop producing primes.

• Goormaghtigh conjectureBroader topic: Both known common values, 31 and 8191, are Mersenne primes.