A perfect number is an integer (whole number) equal to the sum of its proper divisors (whole number factors).
One of the properties of perfect numbers, is that it can be shown mathematically, (e.g. at my personal website, http://www6.50megs.com/bearnol ) that each is of the form 2^(p-1)*(2^p-1), whenever 2^p-1 is prime. This latter is called a "Mersenne" prime. The best tools we have available at the moment for finding Mersenne primes (and hence perfect numbers) are summarized, and exemplified at sites such as the GIMPS project on the world-wide web. GIMPS stands for Great Internet Mersenne Prime Search. I can heartily recommend this site (http://www.mersenne.org or thereabouts) and urge you to participate by turning over any spare MIPS you have to offer to the cause!!