Twin Prime Number in Java

Previous we developed the prime number program in java to check the given number is a prime number or not. Now, based on that program we will develop a twin prime number program in Java to check the given two numbers are prime twin numbers or not.

A pair of prime numbers having a difference of 2 is called a twin prime number. Sometimes it is also called a prime twin or prime pair. Example of prime twin are:- (3,5), (5,7), (11,13) e.t.c.

The even numbers are divisible by 2, so they can not be a prime number. Due to this reason, the prime twin can’t have an even number. In the given number if any number is even number then it can not be a prime twin. Since 2 is the only prime number which is even, and (2,4) is not a twin prime.

From the prime number program in java, we know that every prime number can be represented as 6n-1 or 6n+1. The twin prime number has a difference of 2. So, every twin prime except(3,5) in the form of (6n-1, 6n+1) for some natural number; that is the number between the twin prime number is a multiple of 6 (6n).

Java program to check twin prime number

import java.util.Scanner;

public class TwinPrimeNumber {

  public static boolean isPrime(int number) {

     // negative numbers, 0 and 1 are 
     // not a prime number
     if( number <= 1 ) return false;

     // 2 and 3 are prime numbers
     if( number <= 3 ) return true;

     // numbers divisible by 2 and 3
     // are not prime number
     if(number%2==0 || number%3==0)
        return false;

     // logic for remaining numbers
     for(int i=5; i<=Math.sqrt(number); i=i+6){
        if(number%i == 0 || number%(i+2) == 0) 
            return false;

     return true;

  public static boolean isTwinPrime(int a, int b){

     // if difference is not 2 then
     // it is not twin prime
     if(Math.abs(b-a) != 2) return false;

     // check both are prime number or not
     if(isPrime(a) && isPrime(b)) return true;
     // else return false  
     return false;

   public static void main(String[] args) {

     // declare variables
     int n1 = 0, n2 = 0;

     // create Scanner class object to read input
     Scanner scan = new Scanner(;

     // read number
     System.out.print("Enter two numbers:: ");
     n1 = scan.nextInt();
     n2 = scan.nextInt();

     // check twin prime and display result
     if(isTwinPrime(n1, n2))
        System.out.println(n1+" and "+ n2 + 
                 " are twin prime");
        System.out.println(n1+" and "+ n2 + 
                 " are not twin prime");

     // close Scanner class object

The output for different test-cases:-

Enter two numbers:: 2 3
2 and 3 are not twin prime

Enter two numbers:: 3 5
3 and 5 are twin prime.

Enter two numbers:: 5 7
5 and 7 are twin prime

The logic for the isTwinPrime() method also can be written in one line as,

public static boolean isTwinPrime(int a, int b){
   return ( (Math.abs(b-a) == 2) &&
          isPrime(a) && isPrime(b) );

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