Perfect Numbers

A perfect number equals the sum of its proper divisors. Six is perfect: 1 + 2 + 3 = 6. Twenty-eight is perfect: 1 + 2 + 4 + 7 + 14 = 28. Euclid proved that if 2ⁿ − 1 is prime, then 2ⁿ⁻¹(2ⁿ − 1) is perfect. The ancients thought perfect numbers had mystical significance. Today only 51 even perfect numbers are known — all following Euclid's formula. Whether any odd perfect number exists is one of mathematics' oldest unsolved problems.