And if the Riemann Zeta function goes to infinity, then the sum and product are divergent. So we need s = 2.
Assume there are finitely many primes.
But we know
Therefore, we have reached a contradiction. Correct?
Yes it's correct... but what I had in mind is that the 'infinite sum' when is the 'armonic sum' which diverges to . If the 'discovery' of Leonhard Euler is true, then the product diverges to and that means that the product diverges to 0. Bur none of the terms is zero, so that necessarly there are infinite factors , i.e. there are infinite primes...
Last edited by chisigma; June 22nd 2011 at 01:03 PM.