Goldbach Number in Java

In this section, we will learn what is a Goldbach number and also create Java programs to check if the given number is Goldbach or not. The Goldbach number Java program frequently asked in Java coding tests to check the logic of the programmer.

In 1742, German mathematician Christian Goldbach proposed speculation that all prime numbers that are greater than 2 can be expressed as the sum of 2 odd prime numbers. It is speculation because there is no proof for the same.

Goldbach Number

A positive and even number is called a Goldbach number if the number can be expressed as the sum of two odd prime numbers. Note that all even integers greater than 4 are Goldbach numbers.

Goldbach Number Example

Consider the following numbers:

6 = 3 + 3

14 = 7 + 7 and 11 + 3

30 = 23 + 7, 11 + 19, and 13 + 17

28 = 11 + 17

12 = 7 + 5

10 = 5 + 5 and 7 + 3

We see that the numbers are positive and even, expressed as the sum of odd numbers.

Steps to Find Goldbach Number

Read or initialize a number N.
Store it in another variable.
Check if the given number N is even or not.
If the number is odd, print "Invalid input".
If the number is even, follow the procedure given below:
- Define two arrays one for storing the prime numbers and the other for calculating the prime number.
- Find all prime numbers till the entered number using a for loop and store it in an array.
- In the second array, store only odd prime numbers using if statement.
- Display the odd prime pairs.
By using the for loop, store the sum of two odd prime numbers in a variable (sum).
Using the if statement, compare the sum with the original number N. If the sum is equal to the original number, the given number N is Goldbach Number, else not.

Let's implement the above steps in a Java program.

Goldbach Number Java Program

We will solve the problem using recursion. In the following program, we have defined a method isPrime() to check if the number is prime or not.

GoldbachNumberExample1.java

import java.io.*; 
import java.util.*; 
public class GoldbachNumberExample1
{     
public static void main(String args[])     
{         
Scanner sc= new Scanner(System.in);         
int i, j, n, k, b=0, c=0, sum=0;         
System.out.println("Enter the Number: ");         
//reads an integer from the user
int num=sc.nextInt(); 
//assigning the variable to another variable k
k=num; 
//defining two arrays with capacity equal to the number
int arr1[]=new int[num];      
int arr2[]=new int[num];        
//checks if the number is even or not
if(num%2!=0) 
{
//prints if the number is not even    
System.out.println("Invalid Input, Number is Odd.");   
}       
//executes if the number is even
else        
{             
//loop used for finding prime numbers    
for(i=1;i<=num;i++)             
{                 
for(j=1;j<=i;j++)                 
{     
//condition if number is divisible     
if(i%j==0)                    
{                         
//increments the value of c, initially it is 0    
c++;                   
}                 
}  
//condition for odd Prime numbers
if((c==2)&&(i%2!=0))                  
{
//stores odd prime numbers    
arr1[b]=i; 
//stores odd prime numbers
arr2[b]=i;  
//increments the value of b by 1
b++;            
}                 
c=0;             
} 
System.out.println("Odd and Prime Pairs are: ");             
for(i=0;i<b;i++)             
{                 
for(j=i;j<b;j++)                 
{                
//calculates the sum of two odd prime numbers    
sum=arr1[i]+arr2[j]; 
//checks the sum is equal to the given number or not            
if(sum==k)                  
{      
//prints pair of odd prime numbers    
System.out.print(arr1[i]+" , "+arr2[j]); 
System.out.println();                     
}                 
}             
}             
System.out.println(k+" is a Goldbach number.");         
}     
} // end of main method 
} // end of class

Output 1:

Output 2:

Output 3:

Let's see another logic to find the Goldbach number.

GoldbachNumberExample2.java

import java.util.*;
public class GoldbachNumberExample2
{
public static void main(String args[])
{
Scanner sc=new Scanner(System.in);
System.out.println("Enter the number: ");
int n=sc.nextInt();
int po[]=new int[n/2];
int i,j,s=0,c,k=0,r;
if(n%2==0)
{
for(i=1;i<=n;i+=2)
{
c=0;
for(j=1;j<=i;j++)
{
if(i%j==0)
c++;
}
if(c==2)
{
po[k]=i;
k++;
}
}
for(i=0;i<n/2;i++)
{
r=po[i];
for(j=i+1;j<n/2;j++)
{
s=r+po[j];
if(s==n)
{
System.out.println("It is a goldbach number.");
System.exit(0);
}
else
s=r;
}
}
System.out.println("It is not a goldbach number.");
}
else
System.out.println("Invalid input! Please input an even number.");
}
}

Output 1: