A **perfect number** is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself. For example, 1 + 2 + 3 = 6 implies 6 is a perfect number.

**Unsolved Problem***: Are there any odd perfect numbers? *

The belief, by some, that there are none goes back over 500 years (wikipedia).

If you want to check out some recent research into this problem, see oddperfect.org.

*(Another unsolved problem: Are there an infinite number of even perfect numbers?)*