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merase
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There are 6 letters in MERASE ( A1E1M3R1S1 )
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Merase might refer to |
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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 of 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 exponents n which give Mersenne primes are 2, 3, 5, 7, 13, 17, 19, 31, ... (sequence A000043 in the OEIS) and the resulting Mersenne primes are 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, ... (sequence A000668 in the OEIS). * If n is a composite number then so is 2n − 1. (2ab − 1 is divisible by both 2a − 1 and 2b − 1.) This definition is therefore equivalent to a definition as a prime number of the form Mp = 2p − 1 for some prime p. * 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 connection to perfect numbers. * A new Mersenne prime was found in December 2017. As of January 2018, 50 are now known. The largest known prime number 277,232,917 − 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. |