A similar table has been compiled by C. Caldwell. The table below gives the index of known Mersenne primes (OEIS A000043)ĭiscovery years, and discoverer. As of Sep. 24, 2020, GIMPS participants have testedĪnd verified all exponents below and tested all exponents below at least once (GIMPS). Make this distributed computing project the discoverer of all of the Mersenne primesĭiscovered since late 1996. Their personal computers to perform pieces of the search. G. Woltman has organized a distributed search program via the Internet known as GIMPS (Great Internet Mersenne Prime Search) in which hundreds of volunteers use Is prime was heralded by a special postal meter design, illustrated above, issued However, finding Mersenne primes is computationally very challenging. It has been conjectured (without any particularly strong evidence) that the constantĢ003, p. 116 Caldwell), a result related to Wagstaff's If the line is not restricted to pass through the origin, the Fitting a line through the origin to the asymptotic number of Mersenne primes with for the first 51 (known) Mersenne primes gives a best-fit It has been conjectured that there exist an infinite number of Mersenne primes. L. Welsh maintains an extensive bibliography and history of Mersenne numbers.

Mersenne primes were first studied because of the remarkable properties that every Mersenne prime corresponds to exactly one perfect number. Which is a binomial number that always has a factor

Is true since for composite with factors and. In order for to be prime, must itself be prime.

A big list of prime numbers up to 100