Mersenne prime
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English[edit]
Etymology[edit]
Named after Marin Mersenne (1588–1648), French theologian, philosopher, mathematician, and music theorist.
Pronunciation[edit]
- IPA^{(key)}: /mɛə(ɹ)ˈsɛn ˈpɹaɪm/
Noun[edit]
Mersenne prime (plural Mersenne primes)
- (number theory) 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).
- 2004, Sheldon Axler, 3: Mathematicians Versus the Silicon Age: Who Wins?, David F. Hayes, Tatiana Shubin (editors), Mathematical Adventures for Students and Amateurs, Mathematical Society of America, page 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).
- 2013, Louis Komzsik, Magnificent Seven: The Happy Number, Trafford Publishing, page 71,
- 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.
- 2004, Sheldon Axler, 3: Mathematicians Versus the Silicon Age: Who Wins?, David F. Hayes, Tatiana Shubin (editors), Mathematical Adventures for Students and Amateurs, Mathematical Society of America, page 20,
Related terms[edit]
See also[edit]
Further reading[edit]
- Fermat number on Wikipedia.Wikipedia
- Fermat's little theorem on Wikipedia.Wikipedia
- Great Internet Mersenne Prime Search on Wikipedia.Wikipedia
- Perfect number on Wikipedia.Wikipedia
- Euclid–Euler theorem on Wikipedia.Wikipedia