MathWorld Headline News

New Mersenne Prime (Probably) Discovered

By Eric W. Weisstein

November 14, 2001--The Mersenne prime mailing list (Woltman, Nov. 14, 2001) has reported that a new Mersenne number has passed the Lucas-Lehmer test, identifying it as a prime number. Mersenne numbers are numbers of the form M_n = 2ⁿ - 1. For example, M₇ = 2⁷ - 1 = 127 is a Mersenne number.

The study of such numbers has a long and interesting history, and the search for Mersenne numbers that are prime (so-called Mersenne primes) has been a computationally challenging exercise requiring the world's fastest computers. The complete list of indices n for previously known Mersenne primes is given by n = 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, and 6972593 (Sloane's A000043). The last of these has a whopping 2,098,960 digits. However, the region between the last two previously known Mersenne primes has not been completely searched, so it is not known if M_6972593 is actually the 38th Mersenne prime.

The four largest known Mersenne primes have been discovered by an international collaboration of volunteers known as the Great Internet Mersenne Prime Search (GIMPS). In an email sent to members, this group recently reported that an even larger Mersenne prime has now been found.

The candidate prime was flagged prime by a GIMPS volunteer running George Woltman's prime95 code on an x86-compatible PC. However, the number has yet to be verified as prime by independent software running on different hardware. The verification is currently being completed by Paul Novarese of Compaq using a program written by Ernst Meyer (ftp://hogranch.com/pub/mayer/README.html) running on a 667MHz Alpha 21264 CPU (Meyer, Dec. 3, 2001). Assuming the initial result is confirmed, GIMPS will make an official announcement with press release which will reveal the number and the name of the lucky discoverer. An official announcement of the exact exponent for the new Mersenne prime is currently planned for December 6 or 7 (Woltman, Nov. 21, 2001), and search organizers have already reported that the number itself has more than 3.5 million digits!