Goldbach's conjecture - http://en.wikipedia.org/wiki/Goldbach%27s_conjecture

Goldbach.java

/* Demonstrates the Goldbach's conjecture - Every even integer greater than 2 can be expressed as the sum of two primes
 *
 * author: Igor Hercowitz 
 *
 * usage: java Goldbach <number>  
 * output: the sum of the primes list 
 *
 * ex:
 * > java Goldbach 100
 * 100 can be writen as: [97+3, 89+11, 83+17, 71+29, 59+41, 53+47]
 * 
 *
 */

import java.lang.Math;
import java.util.List;
import java.util.ArrayList;
import java.util.Collections;

public class Goldbach {

    public boolean is_prime(int n) {
        if ( (n % 2) == 0) return false;
        
        double squarert = Math.abs(Math.sqrt(n))+1;
  
        for (int i=3; i < squarert; i+=2) {
            if ( (n % i) == 0) return false;
        }         

        return true;
 
    }


    public static void main(String[] args) {
        int value = Integer.parseInt(args[0]);

        Goldbach g = new Goldbach();
        List<Integer> primes = new ArrayList<Integer>();

        for (int i=3; i < value; i+=2) {
            if (g.is_prime(i)) {
                primes.add(i);
            }
        }

        Collections.reverse(primes);

        List<String> expressions = new ArrayList<String>();

        while (primes.size() > 0) {
            int x = primes.remove(0);
            
            int y = value - x;
            if (primes.indexOf(y) != -1) {    
                primes.remove(primes.indexOf(y));
                expressions.add(x+"+"+y);
            }

        }

        System.out.println(value+" can be writen as: " + expressions);

    }

}