A 'Mersenne Prime' is prime number one less than a power of two. That is, a prime number of the form
M = 2^{n} - 1 for some integer *n*. They're named after Marin Mersenne
(1588-1648), a French friar, who
studied them in the early 19th century. If *n* is composite (not prime), then M is also composite.
If *n* is prime, M may or may not be prime.

The smallest composite Mersenne number with a prime exponent *p* is 2^{11} − 1 = 2047 = 23 × 89.

The largest known prime number, 2^{82,589,933} − 1, is a Mersenne prime.

See "Mersenne Prime" in Wikipedia.

Also see the "Online Encyclopedia of Integer Sequences: Mersenne Primes here.

Nth Number | P | Mersenne Number (M) | Prime? |
---|---|---|---|

1 | 2 | 3 | Prime |

2 | 3 | 7 | Prime |

3 | 5 | 31 | Prime |

4 | 7 | 127 | Prime |

5 | 11 | 2,047 | Prime |

6 | 13 | 8,191 | Prime |

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