Summation of Primes

Problem

Problem Link

The sum of the primes below $10$ is $2+3+5+7=17$.

Find the sum of all the primes below two million.

Solution

CodeCPP fileDownload

#include <iostream>
#include <vector>
 
int main(void) {
  std::vector<bool> prime(2000001, true);
  prime[0] = prime[1] = false;
  for (int i = 2; i * i <= 2000000; ++i) {
    if (prime[i]) {
      for (int j = i * i; j <= 2000000; j += i) {
        prime[j] = false;
      }
    }
  }
 
  long long sum = 0;
  for (int i = 1; i <= 2000000; ++i) {
    if (prime[i]) {
      sum += i;
    }
  }
  std::cout << sum << std::endl;
}