How exactly is the Riemann hypothesis related to the distribution of prime numbers?

The Riemann zeta function is an EXTREMELY important function in analytical number theory. As explained here:


http://en.wikipedia.org/wiki/Riemann_hyp鈥?/a>


the Riemann hypothesis may look unrelated to number theory, but it is equivalent to many results related to 蟺(x), the prime-counting function.