【PAT (Advanced Level) Practice】1015 Reversible Primes (20 分)

A reversible prime in any number system is a prime whose “reverse” in that number system is also a prime. For example in the decimal system $73$ is a reversible prime because its reverse $37$ is also a prime.

Now given any two positive integers $N (<10^5 )$ and $D (1<D≤10)$, you are supposed to tell if $N$ is a reversible prime with radix $D$.

Input Specification:
The input file consists of several test cases. Each case occupies a line which contains two integers $N$ and $D$. The input is finished by a negative $N$.

Output Specification:
For each test case, print in one line Yes if $N$ is a reversible prime with radix $D$, or No if not.

Sample Input:

73 10
23 2
23 10
-2

Sample Output:

Yes
Yes
No

---

#include<iostream>

using namespace std;

bool is_prime(int n){
    
    if(n < 2) return false;
    for(int i = 2; i <= n / i; i++)
        if(n % i == 0) return false;
    
    return true;
}


bool check(int x, int d){
    
    if(!is_prime(x)) return false;
    
    int res = 0;
    
    while(x){
        res = res * d + x % d;
        x /= d;
    }
    
    return is_prime(res);
}

int main(){
    
    int n, d;
    
    while(cin >> n >> d, n > 0){
        
        if(check(n, d)) puts("Yes");
        else puts("No");
    }
    
    return 0;
}