Once again the record for the largest prime number has been shattered. As with all recent records, the new number is a Mersenne prime, a number of the form

*M*_{p}* = * 2^{p}* – * 1

where *p* itself is a prime. Participants in a distributed computing project called GIMPS (Great Internet Mersenne Prime Search) continue without rest to search for ever-larger primes of this form.

Most of the recent large primes have been found in the GIMPS project (for an earlier post on GIMPS, click Mersennery Quest. The project uses a search algorithm called the Lucas-Lehmer primality test, which is particularly suitable for finding Mersenne primes. The test, which was originally devised by Edouard Lucas in the nineenth century and extended by Derek Lehmer in 1930, is very efficient on binary computers.