What can be done to enhance this code. Like its gotta be bug free and efficient enough

Code:
#include <iostream>
#include <cmath>
#include <fstream>
using namespace std;
int main (int argc, char* argv[])
{
 //Create the various different variables required
 int limit = 1000000;
 int root = ceil(sqrt(limit));
 bool sieve[limit];
 int primes[(limit/2)+1];
 int insert = 2;
 primes[0] = 2;
 primes[1] = 3;
 for (int z = 0; z < limit; z++) sieve[z] = false; //Not all compilers have false as the default boolean value
 for (int x = 1; x <= root; x++)
 {
 for (int y = 1; y <= root; y++)
 {
 //Main part of Sieve of Atkin
 int n = (4*x*x)+(y*y);
 if (n <= limit && (n % 12 == 1 || n % 12 == 5)) sieve[n] ^= true;
 n = (3*x*x)+(y*y);
 if (n <= limit && n % 12 == 7) sieve[n] ^= true;
 n = (3*x*x)-(y*y);
 if (x > y && n <= limit && n % 12 == 11) sieve[n] ^= true;
 }
 }
 //Mark all multiples of squares as non-prime
 for (int r = 5; r <= root; r++) if (sieve[r]) for (int i = r*r; i < limit; i += r*r) sieve[i] = false;
 //Add into prime array
 for (int a = 5; a < limit; a++)
 {
 if (sieve[a])
 {
 primes[insert] = a;
 insert++;
 }
 }
 //The following code just writes the array to a file
 ofstream file;
 char filename[100];
 sprintf(filename, "primes_%d.txt", limit);
 file.open(filename);
 for (int a = 0; a < insert; a++) file << primes[a] << ((a == insert-1) ? "" : "\n");
 file.close();
 cout << "Written to file.\n";
 return 0;
}