In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number that can be written in the form Mn = 2n − 1 for some integer n. They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century. The first four Mersenne primes (sequence A000668 in the OEIS) are 3, 7, 31, and 127. If n is a composite number then so is 2n − 1. (2ab − 1 is divisible by both 2a − 1 and 2b − 1.) The definition is therefore unchanged when written Mp = 2p − 1 where p is assumed prime.

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• In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number that can be written in the form Mn = 2n − 1 for some integer n. They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century. The first four Mersenne primes (sequence A000668 in the OEIS) are 3, 7, 31, and 127. If n is a composite number then so is 2n − 1. (2ab − 1 is divisible by both 2a − 1 and 2b − 1.) The definition is therefore unchanged when written Mp = 2p − 1 where p is assumed prime. More generally, numbers of the form Mn = 2n − 1 without the primality requirement are called Mersenne numbers. Mersenne numbers are sometimes defined to have the additional requirement that n be prime, equivalently that they be pernicious Mersenne numbers, namely those numbers whose binary representation contains a prime number of ones and no zeros. The smallest composite pernicious Mersenne number is 211 − 1 = 2047 = 23 × 89. Mersenne primes Mp are also noteworthy due to their . As of January 2016, 49 Mersenne primes are known. The largest known prime number 274,207,281 − 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. (en)
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• Regius, H.
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• A000668
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• Mersenne numbers
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• Mersenne prime
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• MersennePrime
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http://purl.org/linguistics/gold/hypernym
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• In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number that can be written in the form Mn = 2n − 1 for some integer n. They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century. The first four Mersenne primes (sequence A000668 in the OEIS) are 3, 7, 31, and 127. If n is a composite number then so is 2n − 1. (2ab − 1 is divisible by both 2a − 1 and 2b − 1.) The definition is therefore unchanged when written Mp = 2p − 1 where p is assumed prime. (en)
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• Mersenne prime (en)
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