WolframAlpha, Solve for specific values of Z

Question

I have the following command I am entering:

solve[y=prime(x-1)+(z)/prime(x-1)+1, z=28] over the integers

I would like to be able to say:

Solve for z=28,29,30 or 31 .

Is there any way to do that?

I tried the following, but it fails:

solve[y=prime(x-1)+(z)/prime(x-1)+1, z={28,29,30,21}] over the integers

Update

I guess the proper question is how do I tell WA that I want to solve Y, given Z can be 4 specific values.

solve[y=prime(x-1)+(z)/prime(x-1)+1, z> 27, z<32] over the integers