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

Example: Represent a number as Sum of Two Prime Numbers

public class Main {

  public static void main(String[] args) {
    int number = 34;
    boolean flag = false;
    for (int i = 2; i <= number / 2; ++i) {

      // condition for i to be a prime number
      if (checkPrime(i)) {

        // condition for n-i to be a prime number
        if (checkPrime(number - i)) {

          // n = primeNumber1 + primeNumber2
          System.out.printf("%d = %d + %d\n", number, i, number - i);
          flag = true;
        }

      }
    }

    if (!flag)
      System.out.println(number + " cannot be expressed as the sum of two prime numbers.");
  }

  // Function to check prime number
  static boolean checkPrime(int num) {
    boolean isPrime = true;

    for (int i = 2; i <= num / 2; ++i) {
      if (num % i == 0) {
        isPrime = false;
        break;
      }
    }

    return isPrime;
  }
}

Output

34 = 3 + 31
34 = 5 + 29
34 = 11 + 23
34 = 17 + 17

In the above example, we have created the checkPrime() method to find whether a number is prime or not. The method returns true if the passed number is prime.

Here, we have a number 34. The program tries to check if 34 can be represented as the sum of two prime numbers.

Working of Program

• First, we run a for loop from i = 2 to number / 2.
• Inside the for loop, we used two if statements. The first statement checks if i is prime or not.
  
  If true, the second if statement checks if number - i is prime or not. This is because the sum of i and number - i is equal to number.
• If the second statement is also true, then we can say the number 34 is a valid sum of two prime numbers.