A number is said to be a **circular prime** if all its possible rotations are also prime numbers.

## Algorithm

* First, divide the number into its digits.
* Then, make all possible rotations with those digits.
* Now, check whether or not each possible rotation is a prime number.

## Code

In the code below, we have used the `is_prime()` method to check whether or not a number is prime. In order to get our new rotation, we simply get the last digit of the number and place it at the start. 

# Function to check a number is a circular
# prime or not
# number is passed as a string, so number of
# digits is evaluated easily.
def is_circular_prime(number):
    i = remainder = value = total = 0
    digits = len(number)
    num = int(number)
    # Here we will pick the last digit and
    # place it at the start in order to form
    # a new rotation.
    # 199 -> 919 -> 991    
    while i < digits:
        # Dividing the number in digits
        # 199 % 10 = 9(last digit)
        remainder = int(num % 10)
        num = int(num / 10)
        num = int((remainder * (10 ** (digits - 1)) + num))
        print(num)
        value = is_prime(num)
        total += value
        i += 1
    if total is digits:
        print("Circular Prime")
    else:
        print("Non-Circular Prime")

# Function to check number is a prime or not
def is_prime(num):
    count = 0
    for i in range(1,num+1):
        if num % i is 0:
            count += 1
    if count is 2:
        return 1
    else:
        return 0

# Driver Function
is_circular_prime("199")

Python

class CircularPrime
{
    // main driver function
    public static void main(String[] args)
    {
        IsCircularPrime(199);
    }
    // Function to check a number is a circular
    // prime or not
    static void IsCircularPrime(int n){
        boolean flag = true;
        int num, remainder, c = 0;
        num = n;
        // calculating the number of digits.
        while (num > 0)
        {
            remainder = num % 10;
            c++;
            num = num / 10;
        }
        num = n;
        // Here we will pick the last digit and
        // place it in the start, in order to form
        // a new rotation.
        // 199 -> 919 -> 991
        for (int i = 1; i <= c; i++)
        {
            // Dividing the number in digits
            // 199 % 10 = 9(last digit)
            remainder = num % 10;
            num = num / 10;
            num = (remainder * (int) Math.pow(10, c - 1)) + num;
            System.out.println(num);
            if(!IsPrime(num))
            {
                flag = false;
                break;
            }
        }
        
        if(flag)
        {
            System.out.println("Circular Prime");
        }
        else
        {
            System.out.println("Not Circular Prime");
        }
    }
    
    // Function to check number is a prime or not
    static boolean IsPrime(int n)
    {
        int i = 2;
        boolean flag = true;
        while (n > i)
        {
            if (n % 2 == 0)
            {
                flag = false;
                break;
            }
            i++;
        }
        return flag;
    }
}

What is a circular prime?

Algorithm

Code