__Background__: In number theory, a perfect number is a positive integer that is equal to the sum of its positive divisors, excluding itself. The definition of the perfect number dates back to Euclid's

*Elements*. For example, 6, 28, 496, and 8128 are all perfect numbers. It is not known whether odd perfect numbers exist, and there is no current proof of the existence of infinitely even perfect numbers. Euclid proved that

*Mersenne primes*tie directly to even perfect numbers, but this does not hold true for all perfect numbers.

__YOUR TASK__: Investigate Mersenne primes & perfect numbers. The number theory involved is dense, so a simple pen-and-paper may not suffice. You tell us:

*Are there infinitely many perfect numbers? Are there any odd perfect numbers at all?*Comment your opinions below. Let's get thinking!

http://en.wikipedia.org/wiki/Perfect_number