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

What is a Mersenne Number?

A Mersenne number is a positive integer that is obtained using the expression M(n)= 2n-1, where 'n' is an integer. If you keep any value of n (e.g., 0, 1, 2, 3) in the above expression, the result will be a Mersenne number.

For example, consider n = 2 and calculate the expression 2² - 1. The result is 3, which is a Mersenne number. Not all Mersenne numbers are prime (e.g., 2⁴ - 1 = 15) is a mersenne number, which is not prime.

Here are some other examples of Mersenne numbers:

• 2³ - 1 = 7
• 2⁴ - 1 = 15
• 2⁵ - 1 = 31
• 2⁶ - 1 = 63

To find the next Mersenne number, you just need to multiply 2 by the current Mersenne number and add 1.

Input & Output Scenarios

Below are some input and output scenarios that provide a clear understanding of the problem and calculation to check the Mersenne number:

Scenario 1

Suppose the input number is 3:

Input: 3
Output: Yes

Calculation: M(n) = M(3) = 2n-1 = (2^3)-1 = 7

As you can see, the result of expression 2ⁿ-1 is a prime number (i.e., 7). Hence, 3 is a Mersenne number.

Scenario 2

Let's suppose the given number is 4:

Input: 304
Output: No

Calculation:
For any value of 'n' we never get the 2n-1 as 304.

The number 304 is not a Mersenne number.

Since we need to calculate the power of any number raised to the power of another number, we will use an inbuilt java.lang.Math.pow() method. Here is the syntax:

power = Math.pow(inputValue, 2)

Here, inputValue is the value of which power that will be calculated.

Example 1

The following is a basic example of checking whether the number 3 is a Mersenne number or not by comparing the value of the expression 2ⁿ-1 with the given number:

public class checkMersenne {
   public static void main(String args[]) {
      int num = 3;
      System.out.println("The given number is: " + num);
      //increase the value of num  by one and assign it into another temp variable
      int temp = num  + 1;
      int p = 0, res = 0;
      
      //loop to check whether by taking any value of n we are getting the original number or not
      for(int i = 0; ;i++) {
         
         //calculate the power value
         p = (int)Math.pow(2, i);
         
         if(p > temp) {
            break;
         }
         else if(p == temp) {
            System.out.println("Yes! " + num +" is a Mersenne number.");
            res = 1;
         }
      }
      if(res == 0) {
         System.out.println("No! " + num + " is not a Mersenne number.");
      }
   }
}

The above program produces the following output:

The given number is: 3
Yes! 3 is a Mersenne number.

Example 2

In the example below, we define a method named isMersenneNumber(), which calculates the power of the number and compares the expression 2ⁿ - 1 with the given number 10 to check whether the number is Mersenne:

import java.util.Scanner;
public class checkMersenne {
   //method to calculate the Mersenne number
   public static boolean isMersenneNumber(int num){
      int temp = num  + 1, p = 0;
   
      //loop will stop only when break statement is used...
      for(int i = 0; ;i++) {
      
         //calculate the power value
         p = (int)Math.pow(2, i);

         if(p > temp) {
            break;
         }
         else if(p == temp) {
            return true;
         }
      }
      return false;
   }
   public static void main(String args[]) {
      int num = 10;
      System.out.println("The given number is: " + num);
      
      //calling the isMersenneNumber() to check 
      System.out.println("Is the number " + num + " is a Mersenne? " + isMersenneNumber(num));
   }
}

Below is the output of the above program:

The given number is: 10
Is the number 10 is a Mersenne? false