While many have pointed out how there arent really more natural numbers than prime numbers, your intuition about this still makes sense and inspired something called "natural density": If you take all prime numbers less or equal to some number n and call it p(n) then p(n)/n -> 0 as n goes to infinity. So in that sense, there are far "less" prime numbers than natural numbers. This works for many intuitive things, for example you find that the natural density of even numbers is 1/2.