Euclid's Infinitude of Primes
There exist an infinite number of primes
Proof:
Suppose there are a finite number, n of primes, p1…pn.
Let P=p1p2p3p4…pn + 1
P is not divisible by any of the n primes, so either it is divisible by a prime larger than pn, or it is itself prime
=> there are more than n primes