### Perfect Numbers

Perfect numbers are quite rare. The first five are -
6, 28, 496, 8128, 33550336 ...
The tenth perfect number is more than 50 digits long.

A perfect number is defined as a number that equals the sum of its factors, apart from itself. The factors of 28 are 1, 2, 4, 7 and 14, adding these up makes 28, and so 28 is a perfect number.

Perfect numbers have been known for many thousands of years and have often been treated with reverence. Jewish and Christian writers stressed that the world was created in six days and that there are 28 days in a lunar month.

All known perfect numbers are even numbers and are triangular numbers. They all end with either a '6' or an '8'.

Whenever someone discovers a new Mersenne prime number they also automatically discover a new perfect number.

Based on the book Numbers: Facts, Figures & Fiction.

Website copyright © Cambridge University Press (text), University of Nottingham & Richard Phillips (illustrations) 1994/2003.

Updated 1 June 2003.