I have to find functions f : $\displaystyle \mathbb{N}$ $\displaystyle \mapsto$ $\displaystyle \mathbb{N}$ such that f(xf(y) + y) = yf(x) + f(y) (for all x, y natural numbers) and f(x) is a prime number for any prime number x.

Well... I don't have many ideas.

x=0: f(0) = 0

x=y: f(x(f(x)+1)) = f(x)(x+1), for any natural x.

I want to prove that f(x) = x.