find all the primes from 1 to n quickly.

findPrimes.cpp

/*  the Sieve of Eratosthenes */
#include <cmath>
#include <vector>

using namespace std;

bool[] findPrimes(int n) {
  vector<bool> isPrimes(n + 1, true);
  isPrimes[0] = false;
  isPrimes[1] = false;
  
  int m = sqrt(n);
  
  for (int i = 2; i <= m; i++) {
    if (isPrimes[i]) {
      for (int k = i * i; k <= m; k += i) {
        isPrimes[k] = false;
      }
    }
  }
}