Sieve of Atkin explanation

Question

I am doing a project at the moment and I need an efficient method for calculating prime numbers. I have used the sieve of Eratosthenes but, I have been searching around and

Answer 1

Edit: the only thing that I still do not understand is what the x and y variables are referring to in the pseudo code. Could someone please shed some light on this for me?

For a basic explanation of the common use of the 'x' and 'y' variables in the Wikipedia page pseudo-code (or other better implementations of the Sieve of Atkin), you might find my answer to another related question helpful.