Check if number is perfect prime recursively c++ - c++

Question

I've been assigned to write a program that checks if a number is perfect prime or not (the sum of its digits is prime, the sum of the sum of its digits is prime...). I've stumbled upon two extreme cases that break my program:
INPUT: 20328307 OUTPUT: true (expected false)
INPUT: 587899597 OUTPUT: true (expected false)
The code:
#include <iostream>
using namespace std;
bool is_prime(int n) {
if (n == 0 or n == 1) return false;
if (n == 2) return true;
if (n % 2 == 0) return false;
for (int i = 3; i * i == n; i += 2) {
if (n % i == 0) return false;
}
return true;
}
int sum_of_digits(int n) {
int sum = 0;
while (n > 0) {
sum += n % 10;
n /= 10;
}
return sum;
}
bool is_perfect_prime(int n) {
if (sum_of_digits(n) >= 10) is_perfect_prime(sum_of_digits(n)); //cas recursiu
return is_prime(n); //cas base
}
int main() {
int n;
while (cin >> n) cout << (is_perfect_prime(n) ? "true" : "false") << endl;
}
I can't see where this script fails for these two values, and why it doesn't fail for smaller numbers.

Answer 1

First of all your for loop is incorrect, it should be instead:
for (int i = 3; i * i <= n; i += 2) {
if (n % i == 0) return false;
}
otherwise you return true almost on every non even number. Second you ignore result of recursive call, possible solution is:
bool is_perfect_prime(int n) {
if ( n >= 10 and not is_perfect_prime(sum_of_digits(n)) )
return false;
return is_prime(n); //cas base
}

Answer 2

Finally I've got it to work. The problem was in the is_prime() for loop and in the recursive case of is_perfect_prime(). This is what I've come up with:
bool is_prime(int n) {
if (n == 0 or n == 1) return false;
if (n == 2) return true;
if (n % 2 == 0) return false;
for (int i = 3; i * i <= n; i += 2) {
if (n % i == 0) return false;
}
return true;
}
int sum_of_digits(int n) {
int sum = 0;
while (n > 0) {
sum += n % 10;
n /= 10;
}
return sum;
}
bool is_perfect_prime(int n) {
if (n < 10) return is_prime(n);
if (! is_prime(n)) return false;
return is_perfect_prime(sum_of_digits(n));
}
Thanks for your answers.