# Number TheoryEuler/Riemann Point of Departure in Riemann's 1859 paper containing RH

#### Greg

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

$$\displaystyle \prod\frac{1}{1-\frac{1}{p^s}}=\sum\frac{1}{n^s}$$

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?