freeCodeCamp/guide/english/certifications/coding-interview-prep/project-euler/problem-10-summation-of-primes/index.md

title
Summation of primes

Problem 10: Summation of primes

Method:

• In this challenge we need to find sum of all prime numbers up to n.
• Example:
  • If n = 10 then prime numbers before it are 2, 3, 5, 7 and their sum is 17.
• We've used Sieve of Eratosthenes algorithm to find prime numbers in the below solution.

Solution:

function primeSummation(n) {
  
  // Initializing the array and sum which hold all prime numbers and the total sum, respectively
  let nums = []
  let sum = 0;
  
  // Upperbound of `n`
  const upperBound = Math.ceil(Math.sqrt(n));
  
  // Making an array of `n` numbers
  for (let i = 0; i < n; i++){
    nums.push(i);   
  }
  nums[1] = 0;
  
  // Looping until the upperbound
  for (let i = 2; i <= upperBound; i++){
    
    // Skipping if the number is already 0
    if (nums[i] !== 0){
    
      // Explcitly marking all multiples of `i` 0 
      for (let j = i*i; j < n; j += i){
        if (nums[j] % i == 0) {
          nums[j] = 0;
        }
      }
    }
  }
  
  // Sum and return all values in the array up to `n`
  for (let i = 0; i < n; i++){
    sum += nums[i];
  }
  return sum;
}

• Run Code

References:

• Sieve of Eratosthenes Wikipedia