Project Euler/7

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

Solution: https://git.charlesreid1.com/cs/euler/src/master/007

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,

$x\approx 116,000$