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Goldbach Numbers

ISC 2018 Computer Science Practical, Question 1 · Number programs

The question

A Goldbach number is a positive even integer that can be expressed as the sum of two odd primes. Note: All even integer numbers greater than 4 are Goldbach numbers

Example: 6=3+3 10=3+7 10=5+5 Hence, 6 has one odd prime pair 3 and 3. Similarly, 10 has two odd prime pairs, i.e. 3 and 7, 5 and 5.

Write a program to accept an even integer 'N', where N>9 and N<50. Find all the odd prime pairs whose sum is equal to the number 'N'.

Test your program with the following data and some random data:

Example 1:
INPUT: N=14
OUTPUT:
PRIME PAIRS ARE:
3, 11
7, 7

Example 2:
INPUT N=30

OUTPUT:
PRIME PAIRS ARE:
7, 23
11, 19
13, 17

Example 3
INPUT: N=17
OUTPUT:
INVALID INPUT. NUMBER IS ODD

Example 4:
INPUT: N=126
OUTPUT:
INVALID INPUT. NUMBER OUT OF RANGE.

Question: ISC 2018 Computer Science Paper 2 (Practical), Question 1, set by the Council for the Indian School Certificate Examinations (CISCE). Solution and video: Vinay Singh.

Java solution

ISC2018Q1.java Download GitHub

import java.util.*;
class ISC2018Q1{
    private static int primes[]={3,5,7,11,13,17,19,23,29,31,37,41,43,47};
    public static void main(String[] args) {
        Scanner in = new Scanner( System.in );
        System.out.print("INPUT: N = ");
        int N = in.nextInt();
        System.out.println("OUTPUT: ");

        if( N>9 && N<50){
            if(N%2==0){
                System.out.println("PRIME PAIRS ARE:");
                int half=N/2;
                for( int i=0; primes[i]<=half; i++){
                    if( isPrime(N-primes[i])){
                        System.out.println(primes[i]+", "+(N-primes[i]));
                    }
                }
            }else{
                System.out.println("INVALID INPUT. NUMBER IS ODD");
            }
        }else{
            System.out.println("INVALID INPUT. NUMBER OUT OF RANGE.");

        }
        in.close();
    }
    public static boolean isPrime(int number){
        
        // for( int i=0;i<primes.length;i++){
        //     if(number==primes[i]) return true;
        // }
        for(int prime: primes){
            if(number==prime) return true;
        }

        return false;
    }
}

Goldbach Numbers

The question

Java solution

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