Perfect+Number+Theory

__Perfect Number Theory__ A perfect number is a whole number, an integer greater than zero and when you add up all of the factors less than that number, you get that number. For example....

The factors of 6 are: 1,2,3,6. 1+2+3=6

The factors of 28 are: 1,2,4,7,14,28. 1+2+4+7+14=28

Before one billion, there are only 5 perfect numbers. These are: 6, 28, 496, 8128, 33550336. All of these numbers follow a pattern. There are all of the powers of 2 from 1 up to a certain number, and then a prime number that is equal to DOUBLE the last power of two, minus 1. A bit confusing!!! So I will try to explain it to you. Lets use 6 as an example. 1*2=2, (thats the first part) and then you take 2 (because its the last number) double it and minus 1. That comes to 3. You then do 2 two the power of 3 which comes to 6.

You can use this to make a formula: it is (2*n)*(2*n-1) (The * means multiply)

//If you are still confused come talk to me (Chloe) and I will explain it to you !!!//