euclid'sinfinitudeofprimes

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