The number six is perfect because its proper divisors of one, two, and three add up to six.

The longer version

A proper divisor is a whole number that divides in evenly, excluding the number itself. For six those are one, two, and three, and their sum returns exactly six. Nothing is left over and nothing is missing, which is the whole definition of being perfect.

The next examples are twenty-eight, four hundred ninety-six, and eight thousand one hundred twenty-eight, and a rule links them to primes of the form two to a power minus one. Whether any odd perfect number exists remains unsettled after more than two millennia of attention. Deficient and abundant numbers fill the gaps between these rare hits.

Where this entry sits

This section collects odd corners of mathematics, from stubborn prime numbers to counting systems older than modern schools. Expect famous constants, probability puzzles, shapes that break everyday intuition, and numbers far too large to picture. The full list sits on the Numbers and Math page, where every entry is listed in order.