# Project Euler #7 - 10001st prime

### Peter Kim Frank ・1 min read

Project Euler (7 Part Series)

1) Project Euler #1 - Multiples of 3 and 5
2) Project Euler #2 - Even Fibonacci numbers
3 ... 5
3) Project Euler #3 - Largest Prime Factor
4) Project Euler #4 - Largest Palindrome Product
5) Project Euler #5 - Finding the Smallest Multiple
6) Project Euler #6 - Sum Square Difference
7) Project Euler #7 - 10001st prime

Continuing the wonderful community solutions to Project Euler.

This is Problem 7, 10001st prime.

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?

Classic DEV Post from Aug 25 '19

JS

Python

JavaScript:

If some is wondering what in the world I'm doing to compute

`n`

, it's about this: every prime number larger than 3 is of the form 6k± 1. With a little manipulation it could be rewritten as 3/2 + 3h+ (-1)^{h + 1}/ 2.Rust Solution: Playground

Got it to 17s, from 34s using the lazy iterators, was still using

`2..(n/2)`

for checking primes.Got it down to 0.9s by changing the prime check to

`2..(sqrt(n)+1)`

The iterator for checking prime uses

`any(|i| n % i == 0)`

instead of`all(|i| !n % i == 0)`

, so that it may short-circuit when any case returns true. Similar to using a loop with break condition.Still is a brute force technique.

Using sieve of Eratosthenes method

like

@peter I think it is asked on the Project Euler page that solutions are not posted on blog posts, etc. outside the Project forum. I think we should respect that.

Hey, I want to make sure we're following their rules and guidelines. I had reviewed the copyright page (and the related license) and I was confident we were following their preferred attribution requests and other specifications.

Can you point me in the right direction here if I'm missing something?

Read through their about page. They have a few points addressing sharing questions & solutions. Specifically, question 13 and the disclaimer at the bottom.

I know that in the past, they were "blocking" people who shared solutions online. It seems like they have realized that that is not a feasible goal, but it is still important to respect their objectives.

Found it!

Thanks for this. The "logged-out" version of the page wasn't showing this question+answer for some reason.

In recognition of this preferred policy, I'll discontinue the series here on DEV.

Thanks to you, @brandelune , and @gcvancouver for making me aware of this policy. I'll start posting questions from a different source in the coming days.

Peter, I was actually glad that you started that thread, I had started the Project Euler problems to go back to some sort of fun programing and stopped after I could not find an algorithm that made my code faster for problem 10 I think. So seeing your thread made me want to go back to it.

There are probably ways to promote Project Euler here while respecting their intentions. It may be less interactive but still worth it.

I like that problem! Have no fast solution yet.