Thread: Perfect Numbers
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Old 2003-12-12, 20:40   #1

16508 Posts
Default Perfect Numbers

There is a theorem that states that if
2^N - 1 is prime, then (2^N - 1) * 2^(N-1)
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