The Program in C++ Program to check if a given number is circular prime or not is given below:

#include <iostream>
#include <cmath>
#include <vector>
#include <algorithm>

using namespace std;

bool isPrime(int n) {
    if (n <= 1) {
        return false;
    }
    for (int i = 2; i <= sqrt(n); i++) {
        if (n % i == 0) {
            return false;
        }
    }
    return true;
}

vector<int> rotate(int num) {
    vector<int> rotations;
    string numStr = to_string(num);
    for (int i = 0; i < numStr.length(); i++) {
        rotate(numStr.begin(), numStr.begin() + 1, numStr.end());
        rotations.push_back(stoi(numStr));
    }
    return rotations;
}

bool isCircularPrime(int n) {
    vector<int> rotations = rotate(n);
    for (int i : rotations) {
        if (!isPrime(i)) {
            return false;
        }
    }
    return true;
}

int main() {
    int n;
    cout << "Hello Codeauri Family,Enter a number here to check whether it is a circular prime number or not!:\n ";
    cin >> n;
    if (isCircularPrime(n)) {
        cout << n << " is a Circular Prime." << endl;
    } else {
        cout << n << " is not a Circular Prime." << endl;
    }
    return 0;
}

Output:

Hello Codeauri Family,Enter a number here to check whether it is a circular prime number or not!:
1193
1193 is a Circular Prime.

Pro-Tips💡

This program implements a function isPrime to check if a number is prime.

The function returns false if the number is less than or equal to 1 or is divisible by any number between 2 and the square root of n.

The function rotate uses the to_string function to convert num to a string, then uses the rotate algorithm to rotate the first character of the string to the end, repeating the process numStr.length() times.

The rotate function returns a vector of the rotated numbers. The isCircularPrime function uses the rotate function to find all rotations of n and uses the isPrime function to check if each rotation is prime.

If all rotations are prime, the function returns true, indicating that n is a Circular Prime.

The main function prompts the user to enter a number and calls the isCircularPrime function with the input.

If the function returns true, the number is a Circular Prime and the program prints a message to that effect.

If the function returns false, the number is not a Circular Prime and the program prints a message to that effect.