document.write( "Question 727768: . I need to proof that \"There are infinitely many primes\"
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Algebra.Com's Answer #454746 by tommyt3rd(5050) $\"\"$ $\"About$

You can put this solution on YOUR website!
I answered this before, here is what I wrote:
\n" ); document.write( "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.
\n" ); document.write( "Our contradiction tells us that our first statement must be false. There are infinitely many primes. \n" ); document.write( "

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