Does any one know of a link to the proof that there are infinitely many primes using the Riemann Zeta function or would be willing to produce it?

Thanks.

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- Jun 21st 2011, 07:19 PMdwsmithInfinitely many primes (Riemann Zeta)
Does any one know of a link to the proof that there are infinitely many primes using the Riemann Zeta function or would be willing to produce it?

Thanks. - Jun 21st 2011, 08:54 PMchisigmaRe: Infinitely many primes (Riemann Zeta)
One of the most 'wonderful' discoveries of the Swiss mathematician Leonhard Euler was the 'product'...

(1)

Now if s tends to 1, then tends to infinity... what's the consequence?...

Kind regards

- Jun 22nd 2011, 09:33 AMdwsmithRe: Infinitely many primes (Riemann Zeta)
- Jun 22nd 2011, 11:46 AMchisigmaRe: Infinitely many primes (Riemann Zeta)
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...

Kind regards

- Jun 22nd 2011, 07:43 PMdwsmithRe: Infinitely many primes (Riemann Zeta)
What is the product of since the the sum is divergent?

- Jun 22nd 2011, 08:50 PMchisigmaRe: Infinitely many primes (Riemann Zeta)
Even if with non precise speaking is ...

Kind regards