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.

Make a list of primes. Divide a number by one of them. See if the that number is a prime.


Quzah.

Do you actually have it called the "greatest common divisor" when it was taught to you? We always learned the "greatest common factor".

*shrug*

Anyway, from what I understand the modern Goldbach Conjecture has yet to be fully proven by anyone. So I don't know how your teacher expects his students to do it. :)

No, my teacher don't actually expect me to prove this Conjecture. He just want me to write a program which print out two odd prime numbers according to the input. And the program should use Euclid's algorithm.

>> Do you actually have it called the "greatest common divisor" when it was taught to you? We always learned the "greatest common factor".

<< Well...I am not from English speaking country, my English is really not good enough to express everything in English. It's very common that I write out something which is not what I really want to say.