MHB Euler/Riemann Point of Departure in Riemann's 1859 paper containing RH

[Greg]

In his 1859 paper entitled "On the Number of Primes Less than a Given Magnitude", Riemann gives as his point of departure the equation

$$\prod\frac{1}{1-\frac{1}{p^s}}=\sum\frac{1}{n^s}$$[/size]

where $p$ is all primes and $n$ is all natural numbers. The function of the complex variable $s$, wherever these expressions converge, is called by Riemann $\zeta(s)$.

Any thoughts on how to prove this equation?

All comments welcome. :)

 

[I like Serena]

It is called the Euler product formula for the Riemann zeta function.

Wiki gives 2 proofs here.