### May 15, 2004

Largest Known Prime Number Discovered

Josh Findley discovered the 41st Mersenne prime, 2^{24,036,583} - 1. He found it using a 2.4-GHz Pentium 4 computer. A Mersenne prime number is one less than a power of two expressed as M_{n} = 2^{n} - 1. For this to be true, the exponent n must also be prime. Mersenne primes have a close connection to perfect numbers, which are equal to the sum of their proper divisors. The study of Mersenne primes was motivated by this connection. In the 4th century B.C. Euclid demonstrated that if M is a Mersenne prime, then M(M+1)/2 is a perfect number. In the 18th century, Leonhard Euler proved that all even perfect numbers have this form. No odd perfect numbers are known and it is suspected that none exist. It is currently unknown whether an infinite number of Mersenne primes exist.