In this java program, we will learn about how to check whether a number can be expressed as sum of two prime numbers. We will also learn to check whether a number is prime number or not.

First of all, we have to understand fundamentals of prime numbers.

- A Prime number is a positive number greater than 1 that is only divisible by either 1 or itself.
- Any non-prime number can be expressed as a factor of prime numbers.

## How to check whether a number is prime number or not ?

Let N be the number for primality testing. Here, we will use brute force approach by testing whether N is a multiple of any integer between 2 and N/2. This is the most basic method of checking the primality of a given integer N and is called trial division method. Here is a java method to test prime numbers. It returns true of given number is prime number otherwise false.

static boolean IsPrime(int num) { boolean isPrimeNumber = true; for (int i = 2; i <= num / 2; ++i) { if (num % i == 0) { isPrimeNumber = false; break; } } return isPrimeNumber; }

To understand this java program, you should have understanding of the following Java programming concepts:

## Java Program to Check Whether a Number can be Expressed as Sum of Two Prime Numbers

public class PrimeSum { public static void main(String[] args) { int N; boolean isPrimeSum = false; Scanner scanner = new Scanner(System.in); System.out.println("Enter a number"); N = scanner.nextInt(); for (int i = 2; i <= N / 2; i++) { // Check if i is prime number if(IsPrime(i)) { // Check if N-i is prime number also if(IsPrime(N-i)) { System.out.format("%d = %d + %d\n", N,i,N-i); isPrimeSum = true; } } } if (!isPrimeSum) { System.out.format("%d cannot be expressed as sum of two prime numbers."); } } // Returns true if num is prime otherwise false. static boolean IsPrime(int num) { boolean isPrimeNumber = true; for (int i = 2; i <= num / 2; ++i) { if (num % i == 0) { isPrimeNumber = false; break; } } return isPrimeNumber; } }Output

Enter a number 24 24 = 5 + 19 24 = 7 + 17 24 = 11 + 13

- In above java program, we created a method called "IsPrime" to check whether a given number is prime number or not. This method returns true if number is prime otherwise false.
- For a given number N, a for loop will iterate from 2 to N/2 and for every number i it check whether i is prime number of not.
- If i is prime number then we check whether N-i is prime or not.
- If N-i is also prime number then, N can be expressed as sum of two prime numbers i and N-i.