Do perfect numbers have any relation to the real world, or any type of use at all? It seems that they aren't so perfect, just because base 10 doesn't really occur in nature--ever. Is there any sort of importance of these numbers, or is it just some phenomena that happens that mathematicians like to look at? :P Thanks for responses. :)
Perfect numbers have nothing to do with base 10. Most mathematics is about what mathematicians like to look at.
I don't suppose they have any real use, but the Greeks gave them importance and were believers in numerology. The matter can be generalized some to Amicable Numbers, such as 284 and 220, where each has divisors less than itself that sum up to the other. 220 = (2^2)x5x11, and the sum of the divisors less than itself is: (1+2+4)(1+5)(1+11)-220 = 7x6x12-220 = 284. While 284 =4x71, and the divisors (1+2+4)(71+1)-284=220. These numbers were given importance even in things like marrage. Fermat and Descartes both discovered new sets of amicable numbers.
Ok, I see. So they're just numbers that are very "nice" numbers. The only time I've seen perfect numbers are in base 10. I wasn't thinking, though... because it doesn't matter what the base is, they're going to be perfect no matter what. D'oh. >_< Thanks for the replies.