Priming Upward | Science News



Support credible science journalism.

Subscribe to Science News today.

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

This article is available only to subscribing members. Join the Society today or Log in.

Get Science News headlines by e-mail.

More from Science News

From the Nature Index Paid Content