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Math Trek

Priming Upward

11:17am, June 3, 2004

In 1644, French cleric and mathematician Marin Mersenne (1588–1648) proposed that the numbers 2n – 1 are prime for the values n = 2, 3, 5, 7, 13, 17, 19, 31, 67, 127, and 257, and they are composite for all other positive integers greater than 257. A prime is a whole number evenly divisible only by itself and 1.

Mersenne was certainly correct about the smaller numbers. For example, when n = 7, (27 – 1) = 127, which is a prime number. However, Mersenne could not have tested all the candidates. It turns out that he was wrong about two of them (for n = 67 and 257, the numbers are composite) and also missed a few (for n = 61, 89, and 107, the numbers are prime).

Nonetheless, it's Mersenne's name that's now associated with numbers of the form 2n – 1. And the Great Internet Mersenne Prime Search (GIMPS) continues to unearth new Mersenne primes.

The latest entry—the 41st known Mersenne pr

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