A Mersenne prime is a Mersenne number that is prime. It is known that if 2p − 1 is prime then p is prime, so it makes no difference which Mersenne number definition is used. As of October 2009, 47 Mersenne primes are known. The largest known prime number (243,112,609 − 1) is a Mersenne prime. Since 1997, all newly-found Mersenne primes have been discovered by the “Great Internet Mersenne Prime Search” (GIMPS), a distributed computing project on the Internet.
Read more about Mersenne Prime: About Mersenne Primes, Searching For Mersenne Primes, Theorems About Mersenne Numbers, History, List of Known Mersenne Primes, Factorization of Mersenne Numbers, Perfect Numbers, Generalization, Mersenne Numbers in Nature and Elsewhere
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“Ye elms that wave on Malvern Hill
In prime of morn and May,
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—Herman Melville (1819–1891)