*6 is a perfect number, and it is the first perfect number.*

## Perfect Numbers

The next perfect number is 28, and the next one after that is 496, and after that, they keep getting bigger and bigger--as you can imagine it's really hard to find perfect numbers because it would take us forever to just go around checking the sums of all the factors of all the numbers!

But fear not! Mathematicians have found a way to generate perfect numbers, and if you're curious about that method, you can read the Wikipedia article on Mersenne primes. It has a section about the generation of perfect numbers. The mathematician Euler proved that this formula generates all even perfect numbers. As of yet, we haven't found an odd perfect number, but we don't know for sure that there aren't any. So if you find one, you could be famous! (At least in the math world...)

## Prime Numbers

Prime numbers are numbers who have only two factors: 1 and the number itself. Given this definition, 1 is not a prime because it has only one factor: 1. This means that 1 is actually in a class all by itself because it's the only number with only one factor!

So 2 (with factors 1 and 2) is the first prime number. It is also the only even prime because every even number after 2 has 2 as a factor--that's the definition of being even.

After two, we have a lot of primes early on: 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43... And the prime numbers go on forever. We'll show the proof for that in one of our Elegant Math posts.

Another curious thing about prime numbers is that even though for the most part they seem to keep getting farther apart, we keep seeing primes that are right next to each other (except for an even number in between): 11 and 13, 17 and 19, 29 and 31, 41 and 43... No one knows if these "twin primes" keep going on forever. If you can figure that one out, you'll be rich

*and*famous!

The only triplet primes are 3, 5 and 7. Can you figure out why?

## Composite Numbers

## What's the big deal?

I guess another answer to his question (and probably the true answer) is that mathematicians just like to look at numbers and how they behave, and prime numbers behave in very interesting ways!