A number of the form

(1) |

The number of digits in the Mersenne number is

(2) |

(3) |

In order for the Mersenne number to be Prime, must be Prime. This is true since for Composite with
factors and , . Therefore, can be written as , which is a Binomial Number and can be
factored. Since the most interest in Mersenne numbers arises from attempts to factor them, many authors prefer to define a
Mersenne number as a number of the above form

(4) |

The search for Mersenne Primes is one of the most computationally intensive and actively pursued areas of advanced and distributed computing.

**References**

Pappas, T. ``Mersenne's Number.''
*The Joy of Mathematics.* San Carlos, CA: Wide World Publ./Tetra, p. 211, 1989.

Shanks, D. *Solved and Unsolved Problems in Number Theory, 4th ed.* New York: Chelsea, pp. 14, 18-19, 22,
and 29-30, 1993.

Sloane, N. J. A. Sequence
A000225/M2655
in ``An On-Line Version of the Encyclopedia of Integer Sequences.''
http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.
*The Encyclopedia of Integer Sequences.* San Diego: Academic Press, 1995.

© 1996-9

1999-05-26