Number of Prime Implicants VS Essential Prime implicants with don't care

Question

So the Prime implicants are those largest square or rectangle made up of bunch of adjacent minterms Essential Prime implicants are those prime implicants which also cover a particular midterm/s. But I can't find much definition about when the function has don't care. This question asks about implicant, but not the essential ones

Let's say we have a function as f(x,y,z)=m(0,1,6,7)

the K-map as:

--------------------------------------------------
| c\ab |      |      |     |     |
--------------------------------------------------
|      |   1  |      |  1  |     |
--------------------------------------------------
|      |   1  |      |  1  |     |
--------------------------------------------------

From the k-map, we can see there are 4 implicants and 2 prime implicants and 2 essential prime implicants, right ?

My questions is: Are don't-cares considered as 1/0 when we counting essential/prime /implicants as well once we mark them as 1/0?

Now we have a similar function as f(x,y,z)=m(0,1,6,7) + d(2,3) so the k map as:

--------------------------------------------------
| c\ab |      |      |     |     |
--------------------------------------------------
|      |   1  | x(1) |  1  |     |
--------------------------------------------------
|      |   1  | x(1) |  1  |     |
--------------------------------------------------

In this k-map, we have 6 implicants for each one: and 2 prime implicants from

1 x(1)
1 x(1)

of the left and

 x(1) 1
 x(1) 1

Of the right.

and 2 essential prime implicants from those prime implicants.

so 6 implicants and 2 prime implicants and 2 essential prime implicants for f(x,y,z)=m(0,1,6,7) + d(2,3).