public class Goldbach					// use recursion to compute prime pairs that sum up to every even number from 6 to 9998
{
	public static void main(String[] args)
	{
		int i;
		boolean temp=true;
		for(i=6;i<10000;i+=2)			// we will search from 6 to 9998 to see if Goldbach's theorem holds for these numbers
		{
			temp=find(3,i-3);			// our prime numbers will all be odd, so we start at i=3 and see if i-3 is also prime, if not, we try the next pair at i+2 and i-3-2
			if(!temp) System.out.println(i + " is not a Goldblatt number");  // if we find such a pair, output it
		}
			
	}
	
	public static boolean find(int x, int y)		// x will start at 3 and increment by 2 each time, y will start at i-3 and decrement by 2 each time until we find two primes
	{
		if(x>y) return false;						// if x > y we haven't found such a pair, we have proven Goldbach's theorem as false!
		else if(isprime(x,2)&&isprime(y,2))			// otherwise if x and y are both primes, output this pair and return true
		{
			System.out.println((x+y) + " = " + x + " + " + y);
			return true;
		}
		else return find(x+2,y-2);					// otherwise recurse
	}
	
	public static boolean isprime(int x,int y)		// recursive prime method - determine if x is prime starting with divisor y
	{
		if(y>x/2) return true;						// if y > x/2 we have tested from 2..x/2 and haven't found a divisor and therefore these is none other than 1 and x, so x is prime
		else if(x%y==0) return false;				// otherwise if y divides into x evenly, then y is a divisor and so x is not prime
		else return isprime(x,y+1);					// otherwise continue to recurse trying y+1 as a divisor
	}
	
}