How does the Riemann Hypothesis/Riemann Zeta function even work?

I understand that $\zeta(s)=\sum_{n=1}^{\infty}\frac{1}{n^s}=\frac{1}{1^s}+\frac{1}{2^s}+\frac{1}{3^s}\cdots$ I understand what an infinite series is. I know n goes on to infinity and that s is the function input. I just don't know how the heck this finds primes? Can someone explain? I have... Read more