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Java Programming Exercies

Java Exercises: Accept a even number from the user and create a combinations that express the given number as a sum of two prime numbers

Java Basic: Exercise-233 with Solution

Write a Java program that accept a even number (n should be greater than or equal to 4 and less than or equal to 50,000, Goldbach number) from the user and create a combinations that express the given number as a sum of two prime numbers. Print the number of combinations.

Goldbach number: A Goldbach number is a positive even integer that can be expressed as the sum of two odd primes.[4] Since four is the only even number greater than two that requires the even prime 2 in order to be written as the sum of two primes, another form of the statement of Goldbach's conjecture is that 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. The following are examples of Goldbach partitions for some even numbers:
6 = 3 + 3
8 = 3 + 5
10 = 3 + 7 = 5 + 5
12 = 7 + 5
...
100 = 3 + 97 = 11 + 89 = 17 + 83 = 29 + 71 = 41 + 59 = 47 + 53

Sample Solution:

Java Code:

 import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
 
public class Main {
 
    public static void main(String[] args) throws NumberFormatException,IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        StringBuilder builder = new StringBuilder();
        int max = 50000;
        System.out.print("Input an even number: "); 
        boolean[] primes = new boolean[max + 1];
        int count = 1;
        for (int i = 3; i <= max; i += 2) {
            if (!primes[i]) {
                count++;
                if (i <= Math.sqrt(max)) {
                    for (int j = i; j <= max / i; j += 2) {
                        primes[(int) (i * j)] = true;
                    }
                }
            }
        }
        int[] prime = new int[count];
        prime[0] = 2;
        int count2 = 1;
        for (int i = 3; i <= max; i += 2) {
            if (!primes[i]) {
                prime[count2] = i;
                count2++;
            }
        }
        int[] g = new int[max + 1];
        for (int i = 0; i <= prime.length; i++) {
            for (int j = i; j < prime.length && prime[i] + prime[j] <= max; j++) {
                g[prime[i] + prime[j]]++;
            }
        }
 
           int n = Integer.parseInt(reader.readLine());
           builder.append(g[n]).append('\n');
		   System.out.print("\nNumber of combinations: "); 
           System.out.print(builder);
 
    }
}

Sample Output:

Input an even number: 100

Number of combinations: 6

Flowchart:

Flowchart: Accept a even number from the user and create a combinations that express the given number as a sum of two prime numbers.

Java Code Editor:

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