Twin Prime Numbers

The Twin Prime numbers are the two Prime numbers having a difference of 2 between both of them. A prime having a prime gap of two is referred to as a twin prime. The twin prime term is used for a pair of twin primes. The twin primes are also known as prime pair or prime twin.

The pair (2, 3) is generally not considered as a pair of twin prime because 2 is the only even prime, and the pair is the only pair of prime numbers that differ from one.

Let's take some examples of Twin Prime numbers.

The pair (3, 5) is a pair of Twin Primes numbers because the difference between both the numbers is 2.
The pair (3, 7) is not a pair of Twin Primes number because the difference of both the numbers is not 2.
The pair (71, 73) is a pair of Twin Primes numbers because the difference between both the numbers is 2.

These are some of the twin prime pairs:

(3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73), (101, 103), (107, 109), (137, 139), ...etc.

Note: Each and every pair of twin prime except (3, 5) is of the form (6n - 1, 6n + 1) for natural number.

Steps to check twin prime numbers

In order to check whether the numbers are twin prime or not, we have to follow the following steps:

Get pair of numbers from the user to check whether it is twin prime or not.
Check whether both the numbers are prime or not.
Find the difference between both numbers.
If both the numbers are prime and the difference of both the number is 2, print "numbers are the twin prime numbers".
If not, then print "numbers are not the twin prime numbers."

Let's implement the code to check whether the numbers are twin prime numbers or not.

TwinPrimeNumbers.java

//import required classes and packages
import java.io.*;
import java.util.*;

//create TwinPrimeNumbers class to check whether the numbers are twin prime or not
class TwinPrimeNumbers {
 
    // create checkPrimeNumber() method to check whether the number is prime or not
    static boolean checkPrimeNumber(int number)
    {
        int i;
		int m = 0;
		int flag = 0;      
		m = number/2;      
		if(number == 0 || number == 1){  
			return false;      
		}else{  
			for(i = 2; i <= m ;i++){      
				if(number%i == 0){      
					flag=1;      
					return false;     
				}      
			}      
			if(flag == 0)  
			{ 
				return true;
			}  
		}
		return false;
    }
 
    // create checkTwinPrimeNumber() to check whether the numbers are twin prime or not
    static boolean checkTwinPrimeNumber(int number1, int number2)
    {
        if(checkPrimeNumber(number1) && checkPrimeNumber(number2) && Math.abs(number1 - number2) == 2)
			return true;
		else
			return false;
    }
 
    /* Driver program to test above function */
    public static void main(String[] args)
    {
         int number1, number2;
		
		//create scanner class object to get input from user
		Scanner sc = new Scanner(System.in);
		
		//show custom message
		System.out.println("Enter first number");
		
		//store user entered value into variable n1
		number1 = sc.nextInt();
		
		//show custom message
		System.out.println("Enter second number");
		
		//store user entered value into variable n2
		number2 = sc.nextInt();
		
        if (checkTwinPrimeNumber(number1, number2)) 
            System.out.println("("+number1 +", "+number2+ ") is a pair of twin primes"); 
        else
            System.out.println("("+number1 +", "+number2+ ") is not a pair of twin primes"); 
        
    }
} 

Output:

FindAllTwinPrimeNumbers.java

//import required classes and packages
import java.io.*;
import java.util.*;

//create FindAllTwinPrimeNumbers class to get all the twin prime numbers in the given range
class FindAllTwinPrimeNumbers {
 
    // create checkPrimeNumber() method to check whether the number is prime or not
    static boolean checkPrimeNumber(int number)
    {
        int i;
		int m = 0;
		int flag = 0;      
		m = number/2;      
		if(number == 0 || number == 1){  
			return false;      
		}else{  
			for(i = 2; i <= m ;i++){      
				if(number%i == 0){      
					flag=1;      
					return false;     
				}      
			}      
			if(flag == 0)  
			{ 
				return true;
			}  
		}
		return false;
    }
 
    // create checkTwinPrimeNumber() to check whether the numbers are twin prime or not
    static boolean checkTwinPrimeNumber(int number1, int number2)
    {
        if(checkPrimeNumber(number1) && checkPrimeNumber(number2) && Math.abs(number1 - number2) == 2)
			return true;
		else
			return false;
    }
 
    /* Driver program to test above function */
    public static void main(String[] args)
    {
        int startRange, endRange;
		
		//create scanner class object
		Scanner sc=new Scanner(System.in);
		
		//show custom message
		System.out.println("Enter start value");
		
		//store user entered value into variable startRange
		startRange = sc.nextInt();
		
		//show custom message
		System.out.println("Enter last value");
		
		//store user entered value into variable endRange
		endRange = sc.nextInt();
		
		System.out.println("The pairs of twin primes between" + startRange + " and " + endRange + "are:");
		
		for (int i = startRange; i < endRange; i++) {
            if (checkTwinPrimeNumber(i, (i + 2))){
                System.out.printf("(%d, %d)\n", i, i + 2);
            }
        }
    }
}

Output: