Note that sequential indexing of "the" th Mersenne prime A similar table has been compiledīy C. Caldwell. The number of digits, discovery years, and discoverer. The table below gives the index of known Mersenne
As of Sep. 24, 2020, GIMPS participants have testedĪnd verified all exponents below and testedĪll 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 Postal meter design, illustrated above, issued in Urbana, Illinois. For example, the 1963 discovery that is prime was heralded by a special However, finding Mersenne primes is computationally very challenging. If the line is not restricted to pass through the origin, theīeen conjectured (without any particularly strong evidence) that the constant isĬonstant (Havil 2003, p. 116 Caldwell), a result related to Wagstaff's Fitting a line through the origin to the asymptotic number of Mersenne primes with for theįirst 51 (known) Mersenne primes gives a best-fit line with , 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. Is a binomial number that always has a factor This is true since for composite with factors and.
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