Zeta of 2 as Product of Fractions with Prime Numerators

Theorem
where:
 * $\zeta$ denotes the Riemann zeta function
 * $\displaystyle \prod_p$ denotes the product over all prime numbers.

Proof
By definition of Riemann zeta function:
 * $\displaystyle \zeta \left({z}\right) = \prod_p \frac 1 {1 - p^{-z}}$

where $p$ ranges over the prime numbers.

Thus:

which is the result required.