Goldbach's Conjecture problem

I just started using C++ no more than a week ago. I have to write a program that solves Goldbach's conjecture (Wikipedia provides a simple overview if you don't know what this is), but since my program will be dealing mostly will smaller values, speed and efficiency aren't of the highest importance. I have found codes that are already written online, but I need to come up with one of my own. So far, this is what I have written:

Code:

`#include <iostream> `

using namespace std;

int main () {

long int x;

int a,b;

cout << "Enter the number: ";

cin >> x;

cout << endl;

if (x<=2) {

cerr << "Goldbach's conjecture only works for even integers greater than 2. ";

cout << endl;

cout << endl;

return 0;

}

if ((x%2)!=0) {

cerr << "Goldbach's conjecture only works for even integers. ";

cout << endl;

cout << endl;

return 0;

}

for (a=2; a<=x; a++)

{

for (b=2; b<=x; b++)

{

if ((x>2) && ((x%2)==0) && (a<=b) && (a+b==x)){

cout << a << " and " << b << endl;

}

}

}

return 0;

}

This program takes the value that is entered and splits it into as many pairs as possible that add up to the original input. Is there a way for me to limit this so that only the pairs containing two primes appear? Or if this is not possible, what else should I do? Remember, this doesn't have to very fast or that efficient.

Thanks for reading.