How To Check Whether a Number is an Empire Number or Not in Java?

What is Empire Number?

A number is said to be an Empire number if it is a prime number, and when we reverse that number, we should get another prime number. For example, let's consider the number 17. We know that 17 is a prime number, and if we reverse this number, we get 71, which is also a prime number. Therefore, 17 is known as an empire number.

Here are some other examples of prime numbers such as 11, 13, 17, etc.

Input & Output Scenarios

Below are a few input and output scenarios that help to understand the problem implementation:

Scenario 1

Suppose the given number is 13:

Input: n = 13
Output: Yes

Calculation:
Reverse of 13 is 31.

Since both the number 13 and its reverse, 31, are prime numbers, 13 is considered an empire number.

Scenario 2

Suppose the input number is 53:

Input: n = 53
Output: No

Calculation:
Reverse of 53 is 35.

Since both the number 53 and its reverse, 35, are not prime numbers, 53 is not an empire number.

Example 1

The following program checks whether the number 31 is an Empire number. After reversing the number, if the resultant number (i.e., 13) is also a prime number, then the number is called an empire number:

public class empireNumber {
   //method to check for prime number
   public static boolean checkPrime (int n) {
      if (n <= 1){
         return false;
      }
      for (int i = 2; i < n; i++)
      if (n % i == 0){
         return false;
      }
      return true;
   }
   public static void main (String args[]) {
      int num = 13;
      System.out.println("The given number is: " + num);
      if (checkPrime(num) == false){
         System.out.println("No! " + num + " is not a empire number");
      }
      int reverse = 0;
      while (num != 0) {
         int digit = num % 10;
         reverse = reverse * 10 + digit;
         num = num / 10;
      }
      boolean result = checkPrime(reverse);
      if(result){
         System.out.println("Yes! " + reverse + " is a number a empire number");
      }
      else{
         System.out.println("No! " + reverse + " is a number a empire number");
      }
   }
}

Following is the output of the above program:

The given number is: 13
Yes! 31 is a number a empire number

Example 2

In the example below, we define a method named checkEmpire(), which reverses the given number 89 and checks whether the reversed number is prime or not if it is a prime number is an empire or not:

public class empireNumber {

   //method to check for prime number
   public static boolean checkPrime (int n) {
      if (n <= 1){
         return false;
      }
      for (int i = 2; i < n; i++)
      if (n % i == 0){
         return false;
      }
      return true;
   }
   //method to check empire number
   public static boolean checkEmpire(int num){
      if (checkPrime(num) == false){
         System.out.println("No! " + num + " is not a empire number");
      }
      int reverse = 0;
      while (num != 0) {
         int digit = num % 10;
         reverse = reverse * 10 + digit;
         num = num / 10;
      }
      boolean result = checkPrime(reverse);
      if(result){
         return true;
      }
      return false;
   }
   public static void main (String args[]) {
      int num = 89;
      System.out.println("The given number is: " + num);
      //calling the checkEmpire() method to check empire number
      System.out.println("Is the number " + num + " is empire number? " + checkEmpire(num));
   }
}

The above program produces the following output:

The given number is: 89
Is the number 89 is empire number? false