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Project Euler, question 7: https://projecteuler.net/problem=7
 
Project Euler, question 7: https://projecteuler.net/problem=7
  
Solution: https://charlesreid1.com:3000/cs/euler/src/master/007
+
Solution: https://git.charlesreid1.com/cs/euler/src/master/007
  
 
==The Question==
 
==The Question==

Latest revision as of 03:50, 9 October 2019

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