Numbers like e and π have mathematical ties and relationships that are endless, but they don't quite compare in the beauty and simplicity of the properties like that of perfect numbers. Perfect numbers are integers who proper divisors add up to the integer itself. But what are proper divisors? The proper divisors of a number are all the divisors of the number, excluding itself. Perfect numbers are extraordinary in that their proper divisors add up to no more or no less then itself, there is none to little and none to much. "The number 6 is unique in that 6 = 1+2+3, where 1, 2, and 3 are all of the proper divisors of 6. The number 28 also shares this property, for 28 = 1+2+4+7+14. These "perfect" numbers have seen a great deal of mathematical study - indeed, many of the basic theorems of number theory stem from the investigation of the Greeks into the problem of perfect and Pythagorean numbers" (Voight).

        For more information about the history of perfect numbers, the explanation of the mathematics, significance and applications of perfect numbers or for applets and videos on perfect numbers, click the links on the left. For a synopsis of perfect numbers, watch the video below.
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