Dictionary

Mersenne prime en · NOUN

Pronunciation

• /mɛə(ɹ)ˈsɛn ˈpɹaɪm/

Etymology

Named after French theologian, philosopher, mathematician, and music theorist Marin Mersenne (1588–1648).

Meanings

1. A prime number which is one less than a power of two (i.e., is expressible in the form 2ⁿ-1; for example, 31=2⁵-1).
   • Mersenne primes, named after the French priest first describing them in the 17th century, are of the form of 2ᵖ-1, where the exponent p is a prime itself. Obviously 7 is a Mersenne prime, since 2³-1#61;7, and 3 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 2#123;2ᵖ-1#125;-1, meaning that the exponent now is not just a prime, but it is itself a Mersenne prime. Since 2#123;2²-1#125;-1#61;7, 7 is the very first double Mersenne prime. 2013, Louis Komzsik, Magnificent Seven: The Happy Number, Trafford Publishing, page 71:
   • In addition to being the largest known Mersenne prime, this number is also currently the largest known prime number of any type. 2004, Sheldon Axler, “3: Mathematicians Versus the Silicon Age: Who Wins?”, in David F. Hayes, Tatiana Shubin, editors, Mathematical Adventures for Students and Amateurs, American Mathematical Society, page 20:
   • 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 2ᵐ-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).

Forms

Coordinates

Fermat prime · Sophie Germain prime

Relateds

Mersenne twister · Mersenne number · perfect number

Translations (2)

bg про́сто число́ на Мерсе́н (prime number which is one less than a power of two) · pl liczba Mersenne'a (prime number which is one less than a power of two)