/*
   Lab : Lab4 
   Day : Tuesday  [ 19 Aug 08 ]

   Problem Number: 01
   Problem Title : Goldbach's Conjecture
   
   Theory : 
        Let we have to test Goldbach's Conjecture for a variable of name num.

 	Then we have to do following
	   Generate every possible pair of positive numbers whose sum is equal to the number num. 
           and for every such pair of numbers (let us call numbers in pair as firstNum and secondNum) test 
           Whether both number are prime or not 

   	Testing prime number
	   As stated in problem if a number n is not devided by any number from  3 to n/2 the it is considered as prime
           Therefore 
                     initially we assume that the number is prime as 
                     	nIsPrime = 1;
                     then we generate all numbers from 3 to n/2 and test whether n is divisible by any one of them 
		     if n is divisible by any one of them then we set 
			nIsPrime = 0;
 */

class sol_lab4_prob01{

   	public static void main(String args[])
	{		
		int num; // The number to be tested for Goldbach's Conjecture
		int i;	 // loop counter	

 		num = 50; // assign some value to num

		System.out.println("Number : "+num + " can be expressed as");
				
                // Loop to generate all possible psitive pairs of numbers (firstNum + secondNum) whose sum is equal to num
		for( i = 2 ; i < num / 2 ; i = i + 1 )
		{
			int firstNum;
			int secondNum;
			int j;

			int firstNumIsPrime;
			int secondNumIsPrime;

			firstNum = i;
			secondNum = num - i;

			firstNumIsPrime = 1;
			secondNumIsPrime = 1;
			
			// Testing whether firstNum is prime
			for( j = 3 ; j <= firstNum/2 ; j++ )
			{
				if( ( firstNum % j ) == 0 )
				{
                                  	firstNumIsPrime = 0;
					break;
				}
			} 

			// Testing whether secondNum is prime
			for( j = 3 ; j <= secondNum/2 ; j++ )
			{
				if( ( secondNum % j ) == 0 )
				{
                                  	secondNumIsPrime = 0;
					break;
				}
			}

			// when both (firstNum & secondNum) are prime then print them
			if( ( firstNumIsPrime == 1 ) && ( secondNumIsPrime == 1) )
			{
				System.out.println(num + " = " + firstNum + " + " + secondNum);				
			}
		}		
	}	
}