46

package Euler;

import java.util.ArrayList;
package Euler;

import java.util.ArrayList;
public class p046 {
    public static void main(String[] args){
        int compositeList[] = Euler.listOddComposites(10000);
        for(int i:compositeList){
            if(checkGoldbach(i)==false){
                System.out.println(i+" is the smallest counterexample to Goldbach's conjecture.");
                break;
            }
        }

    }
    public static boolean checkGoldbach(int i){
        int primeList[]=Euler.listPrimes(10000);
        ArrayList<Boolean> goldbach=new ArrayList<Boolean>();
        for(int j=0;primeList[j]<i&!goldbach.contains(true);j++){
            if((Math.sqrt((i-primeList[j])/2))%1==0){
                System.out.println(i+"="+j+"+2*"+(int)Math.sqrt((i-primeList[j])/2)+"^2");
                goldbach.add(true);
            }
        }
        if(goldbach.contains(true))
            return true;
        else
            return false;
    }
}


ODD COMPOSITES SIEVE.

public static int[] listOddComposites(int n) {
        boolean[] isprime = listPrimality(n);
        int count = 0;
        for (boolean b : isprime) {
            if (!b)
                count++;
        }
        int[] result = new int[count];
        for (int i = 4, j = 0; i < isprime.length; i++) {
            if (!isprime[i]&&i%2!=0) {
                result[j] = i;
                j++;
            }
        }
        int c=1,i=0;
        for(i=0;c!=0;i++){
            if(result[i]==0){
                c=0;
            }
        }
        int[] finalListTrim = new int[i-1];
        for(int j=0;j<i-1;j++){
            finalListTrim[j]=result[j];
        }
        return finalListTrim;
    }
public static boolean[] listPrimality(int n) {
        boolean[] result = new boolean[n+1];
        if (n >= 2)
            result[2] = true;
        for (int i = 3; i <= n; i += 2)
            result[i] = true;
        for (int i = 3, end = (int)Math.sqrt(n); i <= end; i += 2) {
            if (result[i]) {
                for (int j = i * i; j <= n; j += i << 1)
                    result[j] = false;
            }
        }
        return result;
    }