problem 35

/*e number, 197, is called a circular prime because all rotations of the digits: 197, 971, and 719, are themselves prime.

There are thirteen such primes below 100: 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, and 97.

How many circular primes are there below one million?
*/
#include <iostream>
#include<math.h>
#include<string>
#include <algorithm> 
#include<vector>
using namespace std;

bool prime(int num){
  for(int i = 2; i <= pow(num, .5); i++)
  if(num % i == 0){
    return false;
  }
  return true;
}

int swap(vector<int> primes){
  int counter = 4;
  for(auto n : primes){
    int num1 = n;
   int shift = 1;
   while(n > shift * 10){
     shift = shift * 10;
   }
   do{
      int first_digit = num1 % 10;
      num1 = num1 / 10;
      num1 += first_digit * shift;
      if(!prime(num1)){
        break;
      } 
    }while(num1 != n);
    if(num1 == n){
     counter++;
    }
  }
 return counter;
}

int main() {
 vector<int> primes;
 for(int i = 11; i < 1000000; i+= 2){
   if(prime(i)){
     primes.push_back(i);
    }
  }
  cout << swap(primes) << endl;
 // cout << counter << endl;
 //cout << prime(97) << endl;
 return 0;
}