# Existence of a function for the n-th prime

 P: 7 There is a function $\pi$(x) that takes the natural numbers as its input and outputs the number of primes less than or equal to x. There are some nice properties of this function. For instance, the growth rate as x approaches infinity approaches x/lnx
 Quote by Jack Jenkins There is a function $\pi$(x) that takes the natural numbers as its input and outputs the number of primes less than or equal to x. There are some nice properties of this function. For instance, the growth rate as x approaches infinity approaches x/lnx
Unless $\pi$(x) is viewed as an approximation only, there is no simple way known to calculate it, just as there is no known way to simply output the nth prime, given n.