The equation isn't prime...
It's in the form of a^2-b^2
IT CANNOT BE PRIME!
It is the factors of (a-b) x (a+b).
Whatever...
Factoring the equation, we get the following factors:
(2 ^ 1024) - 1=(2^512 - 1) x (2^512 + 1)
Now you may see something that you can do.
Factor.
We can factor this equation for a long time until you get:
(2 - 1) x (2 + 1) .
Yay!