= Primes =

A Prime is a natural number that is only divisible by one and itself.

== Prime factorization ==

Everynumber is either a Prime or a product of several primes together. This is
called prime factorization.

== Euclid's Proof ==

Euclid Prooved that that are infinitely many primes in existance. The proof is
as follows

1) Let p,,1,, , p,,2,, , p,,3,, , etc be an infinite list of primes
2) Let P be the product of all of those primes, and q be P + 1
3) If q is a prime then there is at least one more prime that is not in the
   list, namely, q 
4) If q is not prime, then some prime factor p divides into q. If this factor p
   were in the list, then it would divide P; However p also divided P+1=q. If p
   divides P and also q, then p must also divide the difference of the two
   numbers, which is (P+1)-P, or 1. Since no prime divides 1, p cannot be on
   the list. This means at least one more prime exists beyond those in the list