freeCodeCamp/guide/english/certifications/coding-interview-prep/project-euler/problem-7-10001st-prime/index.md

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Problem 7: 10001st prime

Problem 7: 10001st prime

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Problem Explanation

• A prime number is a number which is divided by 1 and itself.
• We can find a number is prime if it's not divisible by other prime numbers smaller than itself.

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Solutions

Solution 1 (Click to Show/Hide)

function nthPrime(n) {
  //Primes array which will store all the prime numbers
  const primes = [2];

  //Num is the number we want to check
  let num = 3,
    isPrime = true;

  //Looping until primes array is equal to n
  while (primes.length < n) {
    //All the primes numbers of a number is always <= its square root
    let max = Math.ceil(Math.sqrt(num));

    for (let i = 0; primes[i] <= max; i++) {
      if (num % primes[i] == 0) {
        //Looping till we find the prime
        isPrime = false;
        break;
      }
    }

    //if Prime found, push it to the array
    if (isPrime) primes.push(num);
    isPrime = true;

    //An optimization technique, since we know of all even numbers only 2 is a prime number, we can skip the rest
    num += 2;
  }

  //Returning the last number
  return primes[primes.length - 1];
}

Relevant Links

• Wikipedia