Here we verify the conjecture for small numbers.

§1.

So, this is a program to see if even numbers from 4 to 100 can all be written as a sum of two primes. Christian Goldbach asked Euler in 1742 if every even number greater than 2 can be written this way. This remains open, though —

Computer verification has been made up to around \(10^{18}\), but by rather better methods. 
    define RANGE 100

    #include <stdio.h>

    int main(int argc, char *argv[]) {
        for (int i=4; i<RANGE; i=i+2)
            <Solve Goldbach's conjecture for i 1.1>;
    }

§1.1. This ought to print: 

        4 = 2+2
        6 = 3+3
        8 = 3+5
        10 = 3+7 = 5+5
        12 = 5+7
        14 = 3+11 = 7+7
        ...

We'll print each different pair of primes adding up to i. We only check in the range \(2 \leq j \leq i/2\) to avoid counting pairs twice over (thus \(8 = 3+5 = 5+3\), but that's hardly two different ways).

<Solve Goldbach's conjecture for i 1.1> = 

        printf("%d", i);
        for (int j=2; j<=i/2; j++)
            if ((isprime(j)) && (isprime(i-j)))
                printf(" = %d+%d", j, i-j);
        printf("\n");

This code is used in §1.