We are going to use proof by contradiction to show that there are infinitely many primes. Proof by contradiction assumes a theorem is false and then derives something false from it. Thus the theorem must be true.

Assume there are finitely many primes. Multiply them together and add 1. The result, by the division algorithm, does not have any lesser prime factors. Thus it is prime, but is strictly larger than every prime number. This is a contradiction.

Apr 19th, 2015

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