# Problem 10: Summation of primes

## Problem Explanation

• 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.

## Solutions

Solution 1 (Click to Show/Hide)
``````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;
}
``````