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Project Euler #7 - 10001st prime

peter profile image Peter Kim Frank ・1 min read

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?


Editor guide
karataev profile image
Eugene Karataev


function getPrimes(max) {
  let arr = new Array(max).fill(undefined);
  for (let i = 2; i < max; i++) {
    if (arr[i] === undefined) {
      arr[i] = true;
      for (let j = i + i; j < max; j += i) {
        arr[j] = false;
  return arr
    .map((item, i) => item ? i : false)

let primes = getPrimes(150000);
aspittel profile image
Ali Spittel


def is_prime(n):
    nums_to_check = range(2, int(n**.5) + 1)
    for i in nums_to_check:
        if n % i == 0:
            return False
    return True

def prime_at_index(idx):
    n_primes = 1
    n = 2
    while n_primes < idx:
        if is_prime(n):
            n_primes += 1
    return n

maxart2501 profile image
Massimo Artizzu


const primes = [ 2, 3 ];
function isPrime(n) {
  return primes.every(d => n % d > 0);

let i = 1;
while (primes.length < 10001) {
  const n = i * 3 + 1.5 + .5 * (-1) ** (i + 1);
  if (isPrime(n)) primes.push(n);

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 6 k ± 1. With a little manipulation it could be rewritten as 3/2 + 3 h + (-1)h + 1 / 2.

crownedprinz profile image
Ademola John

Here is a javascript solution

function nthPrime(n) {
    let primes = [2];
    let higherDivisorLimit;
    let isPrime;
    for(let i = 3; primes.length < n; i+=2) {
      higherDivisorLimit = Math.sqrt(i) + 1;
      isPrime = true;
      for(let j = 0; primes[j] < higherDivisorLimit; j++) {
        if(i % primes[j] === 0) {
          isPrime = false;
      if(isPrime) primes.push(i);
    return primes[primes.length - 1];

flrnd profile image
Florian Rand

Using sieve of Eratosthenes method

package main

import (

func primeEratosthenes(a []bool, n int) []bool {
    for i := 2; i < int(math.Sqrt(float64(n))); i++ {
        if a[i] {
            for j := i * i; j < n; j += i {
                a[j] = false
    return a

func main() {
    a := make([]bool, n+1)
    for i := range a {
        a[i] = true

    primes := primeEratosthenes(a, 100000)
    var pList []int

    for i, v := range primes {
        if v {
            pList = append(pList, i)
    pList = pList[2:]
vitalipom profile image
Vitali Pomanitski


Set i 0
Set num 3
While (true)
  If (IsPrime(num))
    Set i `eval(i+1)`
    If (i == 1001 or i == 6)
      echo num 
  Set num `eval(num + 1)`
IsPrime.fn << curl
jay profile image

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.

fn main() {
    println!("{}", get_nth_prime(10001));

fn get_nth_prime(n: usize) -> u32 {
    (1..).into_iter().filter(|&num| is_prime(num)).nth(n - 1).unwrap_or_default()

fn is_prime(n: u32) -> bool {
    match n {
        1 => false,
        2 => true,
        n if n % 2 == 0 => false,
        _ => !(2..(n as f32).sqrt() as u32 + 1).any(|i| n % i == 0),
brandelune profile image
Jean-Christophe Helary

@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.

peter profile image
Peter Kim Frank Author

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?

gcvancouver profile image

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.

flrnd profile image
Florian Rand

Found it!

I learned so much solving problem XXX so is it okay
to publish my solution elsewhere?

It appears that you have answered your own question. There is nothing quite like that "Aha!" moment when you finally beat a problem which you have been working on for some time. It is often through the best of intentions in wishing to share our insights so that others can enjoy that moment too. Sadly, however, that will not be the case for your readers. Real learning is an active process and seeing how it is done is a long way from experiencing that epiphany of discovery. Please do not deny others what you have so richly valued yourself.

Thread Thread
peter profile image
Peter Kim Frank Author

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.

Thread Thread
brandelune profile image
Jean-Christophe Helary

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.

nilzoft profile image

My solutions in .C


vitalipom profile image
Vitali Pomanitski

I like that problem! Have no fast solution yet.