Perfect Numbers
There is a theorem that states that if
2^N  1 is prime, then (2^N  1) * 2^(N1)
is perfect. A perfect number is, by definition, a number that is the sum of all its divisors, excluding itself. The numbers 6 and 28 are the first two perfect numbers. By finding the 40th Mersenne prime, GIMPS also has found what must be the largest known perfect number, namely:
(2^20,996,011  1 ) * 2^20,996,010
