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Question 738228: Show that there are infinitely many positive primes.
Answer by tommyt3rd(5050)   (Show Source):
You can put this solution on YOUR website! Suppose that there are only n-prime numbers and denote the product of all of the primes as A. Next let B be the product of all of the primes plus 1. Now 1 is not a prime number by definition so for any particular prime p>1. By the fundamental theorem of algebra, our p had to be a divisor of A as well as a divisor of B. Furthermore it also must divide their difference, B-A - which is 1. Since the difference is 1, p must be a divisor of 1 and this is impossible.
Our contradiction tells us that our first statement must be false. There are infinitely many primes.
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