Mersenne number

mathematics

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June 30, 2026

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A Mersenne number is a number of the form 2ⁿ − 1, where n is a natural number. When a Mersenne number is also a prime number, it is called a Mersenne prime. These primes are named after the French mathematician Marin Mersenne, who studied them in the 17th century.12

For a Mersenne number to be prime, the exponent n must also be a prime number, though not all Mersenne numbers with prime exponents are themselves prime. The search for Mersenne primes is an active area of research, often utilizing distributed computing projects like GIMPS, which enlists volunteers to use their computers to test large numbers for primality. The largest known Mersenne prime is 2^136,279,841 − 1, which contains over 41 million digits.13

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number game
Perfect numbers and Mersenne numbers
Most numbers are either “abundant” or “deficient.” In an abundant number, the sum of its proper divisors (i.e., including 1 but excluding the number itself) is greater than the number; in a deficient number, the sum of its proper divisors is less than…
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Most numbers are either “abundant” or “deficient.” In an abundant number, the sum of its proper divisors (i.e., including 1 but excluding the number itself) is greater than the number; in a deficient number, the sum of its proper divisors is less than…
Read More

Mersenne prime
…are a subset of the Mersenne numbers, M_n. The numbers are named for the French theologian and mathematician Marin Mersenne, who asserted in the preface of Cogitata Physica-Mathematica (1644) that, for n ≤ 257, M_n is a prime number only for 2, 3, 5, 7, 13, 17, 19, 31, 67,…
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…are a subset of the Mersenne numbers, M_n. The numbers are named for the French theologian and mathematician Marin Mersenne, who asserted in the preface of Cogitata Physica-Mathematica (1644) that, for n ≤ 257, M_n is a prime number only for 2, 3, 5, 7, 13, 17, 19, 31, 67,…
Read More

Marin Mersenne
…are now known as “Mersenne numbers,” his wider significance stems from his role as correspondent, publicizing and disseminating the work of some of the greatest thinkers of his age.
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…are now known as “Mersenne numbers,” his wider significance stems from his role as correspondent, publicizing and disseminating the work of some of the greatest thinkers of his age.
Read More