GoldBach Number in JAVA

Goldbach Number in JAVA

A Goldbach number is a positive even integer that can be expressed as the sum of two odd prime numbers.

All even integers greater than 4 are Goldbach numbers. 

The expression of a given even number as a sum of two primes is called a Goldbach partition of that number.

Examples of Goldbach Numbers are :-

6 = 3 + 3 

8 = 3 + 5  

10 = 3 + 7 = 5 + 5 

12 = 7 + 5

Example 1:
INPUT:
N = 14
Prime pairs are:
3, 11
7, 7 

Output : It is a GoldBach Number

INPUT:
N = 28
Prime pairs are:
3, 11
7, 7 

Output : It is a GoldBach Number

Algorithm and Program  given Below :-

Algorithm :-

• Input number in a variable
• Store the input number in another variable
• define two arrays used for storing and calculating odd prime numbers
• Now use if statement to check if the entered number is odd or not.
• If it is odd Display "Entered number is Invalid"
• Else using for loops find each prime numbers till the entered number
• Now use if statement and store only odd prime numbers in both the arrays
• Now Display "Prime Pairs are:-"
• Using for loop store sum of two odd prime numbers in a variable (say 's')
• Using if condition compare the sum with the original number
• If it satisfy the condition than display the prime pairs.
• Compile and run the program.

Program :-

import java.io.*;
import java.util.*;
class Goldbach
{
    public static void main(String args[])
    {
        Scanner in= new Scanner(System.in);
        int i,j,n,p,b=0,c=0,s=0;
        System.out.println("Enter Number");
        n=in.nextInt(); // Input Number
        p=n; // Storing input number
        int ar[]=new int[n];// array defined with capacity equal to number
        int br[]=new int[n];// array defined with capacity equal to number
        if(n%2!=0)// if number is odd
        {
            System.out.println("Invalid Input, Number is Odd "+n); // printing Invalid
        }
        else
        {
            for(i=1;i<=n;i++) //loop used for finding prime number
            {
                for(j=1;j<=i;j++)
                {
                    if(i%j==0) //condition if number is divisible
                    {
                        c++; // increasing value of c initially it is 0
                    }
                }
                if((c==2)&&(i%2!=0)) // condition for odd Prime numbers
                {
                    ar[b]=i; // storing odd prime number
                    br[b]=i; // storing odd prime number
                    b++; // increasing value of b
                }
                c=0; // initializing c=0 again.
            }
            System.out.println("Prime Pairs are :- ");
            for(i=0;i<b;i++)
            {
                for(j=i;j<b;j++)
                {
                    s=ar[i]+br[j]; //storing sum of two odd prime numbers
                    if(s==p) // condition if the sum is equal to the number
                    {
                        System.out.print(ar[i]+" , "+br[j]); // printing prime pairs
                        System.out.println();
                    }
                }
            }
            System.out.println("It is GoldBach Number "+p);
        }
    } // end of main method
} // end of class

 
All the Best :)
Keep Learning :)