Project Euler/7

Project Euler, question 7: https://projecteuler.net/problem=7

The Question

By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.

What is the 10,001st prime number?

https://projecteuler.net/problem=7

Approach

Start with the prime number distribution function pi(x),

$ \pi(x) \approx \dfrac{x}{\ln{(x)}} $

This gives us a ballpark estimate of how many numbers we will need to look at to find the 10,001st prime number: just solve

$ \dfrac{x}{ln{(x)}} = 10,001 $

or,

$ x \approx 116,000 $