Mersenne prime

English Etymology en Marin Mersenne 1588 1648 French theologian, philosopher, mathematician and music theorist =. Pronunciation en /mɛə(ɹ)ˈsɛn ˈpɹaɪm/ en aɪm 3 Noun en number theory A prime number which is one less than a power of two (i.e., is expressible in the form ; for example, ). en Fermat prime Sophie Germain prime en 2004 Sheldon Axler 3: Mathematicians Versus the Silicon Age: Who Wins? David F. Hayes; Tatiana Shubin Mathematical Adventures for Students and Amateurs w:American Mathematical Society https://books.google.com.au/books?id=PD0clAlF8O4C&pg=PA20&dq=%22Mersenne+prime%22%7C%22Mersenne+primes%22&hl=en&sa=X&ved=0ahUKEwj8uPHJ9dncAhWEQd4KHSrQBHcQ6AEIQDAF#v=onepage&q=%22Mersenne%20prime%22%7C%22Mersenne%20primes%22&f=false 20 In addition to being the largest known Mersenne prime, this number is also currently the largest known prime number of any type. 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, LNCS 3357, page 159, Mersenne numbers of the form 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). en 2013 Louis Komzsik Magnificent Seven: The Happy Number https://books.google.com.au/books?id=Can4AAAAQBAJ&pg=PA71&dq=%22Mersenne+prime%22%7C%22Mersenne+primes%22&hl=en&sa=X&ved=0ahUKEwj8uPHJ9dncAhWEQd4KHSrQBHcQ6AEIogEwGQ#v=onepage&q=%22Mersenne%20prime%22%7C%22Mersenne%20primes%22&f=false 71 Trafford Publishing Mersenne primes, named after the French priest first describing them in the 17th century, are of the form of , where the exponent is a prime itself. Obviously is a Mersenne prime, since , and is a prime. The interesting twist comes in the fact that there are certain primes that are double Mersenne primes. These are of the form , meaning that the exponent now is not just a prime, but it is itself a Mersenne prime. Since , is the very first double Mersenne prime. Related terms en Mersenne number en Mersenne twister Translations prime number which is one less than a power of two Bulgarian: bg про́сто число́ на Мерсе́н n Polish: pl liczba Mersenne'a f See also en perfect number Further reading Fermat number Fermat's little theorem Great Internet Mersenne Prime Search Perfect number Euclid–Euler theorem