Mersenne prime

Etymology
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Noun

 * 1)  A prime number which is one less than a power of two (i.e., is expressible in the form $$2^n - 1$$; for example, $$31 = 2^5 - 1$$).
 * 2) * 2005, Jean-Claude Bajard, Laurent Imbert, Thomas Plantard, Modular Number Systems: Beyond the Mersenne Family, Helena Handschuh, M. Anwar Hasan (editors), Selected Areas in Cryptography: 11th International Workshop, SAC 2004, Revised Selected Papers, Springer, 3357, page 159,
 * Mersenne numbers of the form $$2^m - 1$$ are well known examples, but they are not useful for cryptography because there are only a few primes (the first Mersenne primes are 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, etc).
 * 1) * 2005, Jean-Claude Bajard, Laurent Imbert, Thomas Plantard, Modular Number Systems: Beyond the Mersenne Family, Helena Handschuh, M. Anwar Hasan (editors), Selected Areas in Cryptography: 11th International Workshop, SAC 2004, Revised Selected Papers, Springer, 3357, page 159,
 * Mersenne numbers of the form $$2^m - 1$$ are well known examples, but they are not useful for cryptography because there are only a few primes (the first Mersenne primes are 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, etc).