Primes are numbers that can only be evenly divided by themselves and 1. For example, 7 is a prime number since I'm left with a remainder or a fractional component if I divide 7 by anything other than itself or 1. 6 is not a prime because I can divide 6 by 2 and get 3.

One of the reasons primes are important in number theory is that they are, in a certain sense, the building blocks of the natural numbers. The fundamental theorem of arithmetic (the name of which indicates its basic importance) states that any number can be factored into a unique list of primes. 12 = 2 x 2 x 3, 50 = 5 x 5 x 2, 69 = 3 x 23.

Studying numbers, then, basically amounts to studying the properties of prime numbers. Mathematicians have, over the millennia, figured out quite a bit about the prime numbers. One of Euclid's most famous proofs shows that there are infinitely many primes.

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