I am trying to prove that lim as x->infinity of pi(x)/x =0
pi(x) is the counting function that describes the number of prime numbers equal to or less than x and greater than 1.
The Attempt at a Solution
I'm really stuck about where to start here. So far I have made tables and whatnot. I wrote a program that shows an approximation of this up to 10^9, so I am certain that this is accurate. Also I have looked at the theorems that I have: infinitude of primes, infinitude of 1 (mod 4) and 3 (mod 4) primes. pi(x)~~x/ln(x) (but I'm not allowed to use this in the proof). There really aren't any solid, proveable theorems that I can use here. Any advice?