# Prime ideals in multi-variable polynomial rings over $\mathbb{Z}$

There is a nice classification of prime ideals in the ring $$\mathbb{Z}[x]$$, see this question.

Is there any generalization of this result, on $$\mathbb{Z}[x_1,\cdots,x_n]$$?

Due to this post, I guess there is not a 'theorem' for large $$n$$. However, does anyone know the answer for $$n=2$$?

What are the prime ideals of $$\mathbb{Z}[x,y]$$?