revolutionx897 wrote:One proof that there's an infinite number of primes is to:
1- Assume a finite number of primes
2- Take the product of all primes (p1, p2,...,pn with p1 as the 1st prime and pn as the last) and add 1
3- This number cannot be divisible by any of the primes in the list, so it must either be prime or divisible by a prime larger than pn, and therefore the original assumption of a finite number of primes is invalid
This seems to be the proof Randall is using, but I'm not exactly sure what the divisors part is meant to be. Bad wording?
The proof of the infinitude of the primes irks me more than any other! People always tack on a little superfluous (false) information right at the end, or even worse, just state that p1p2...pn+1 is prime.