Use Euclid's algorithm to Prove Goldbach's Guess?? Please Help!

My teacher asked me to write a C program to prove Goldbach's Guess using Euclid's algorithm: Any even number greater or equal to 6 can be the sum of two odd prime number. Please use Euclid's algorithm to write the program. For any input that is greater or equal to 6 and that is an even number, print two odd prime number whose sum is equal to the input.

I only know that Euclid's algorithm is used to calculate the greatest common divisor. I have no idea on how to use it to prove the Goldbach's Guess. Could somebody give me some hints? Thanks.