ImperialViolet

Mersenne Primes and Perfect Numbers (09 Sep 2002)

Mersenne (named after a french monk) primes are of the form 2n-1 where n is an integer, greater then 0. There is a distributed.net like effort to find them called GIMPS (search Google).

A perfect number is a number where the sum of its divisors (excluding itself, but including 1) equals that number. For example 6 is perfect because (1 + 2 + 3) = 6. Thus the sum of all the divisors is twice the number.

Now, I read a while back in a book that (2n-1)(2n-1) was proven to be a perfect number, but the book didn't have the proof. Thankfully, I ran across the proof today. That proof leaves out a number of steps thou, so here's a better one:

One from The Book