QUESTION:  Can you explain the difference between the concepts
of "irredundance" and "prime"?  

ANSWER: 
In the following, read x' as x-bar. Consider the following 
cover:

x'z' + x y' + x z

This is a "prime cover" which means all the cubes in it are prime.
Here is what prime means: A cube is prime if when you remove a literal
from it, it is no longer an implicant of the function. Here's an example:

Draw a diagram for the function above. Now let's take a look at why
xz is prime. If we remove the literal x from xz, i.e. if we expand it
to the cube z, we observe that the minterm x'yz (which is in the cube z)
is not in the on-set of the original function. Similarly, when we expand
xz to x, we see that the minterm xyz' (which is in the cube x) is not
in the on-set of the original function. That means xz cannot be expanded
any more, and is therefore a prime. A prime is a cube that cannot
be made bigger and still be contained in the function.

By a similar argument, you can show that xy' is prime. However, in the
cover above, xy' is redundant. If you draw the diagram, you will see 
that the vertices covered by xy' are already covered by the other two
cubes. Thus, we don't need xy' in the cover: it is redundant. 

Now, as an exercise, consider the following function

x'z' + xy' + xyz

Argue that xyz is not prime but is irredundant.

So we've seen examples of cubes that can be only one of prime and redundant.