Here's a homework problem:

Is L_4 Regular?
Let L_4 = L*, where L={0^i1^i | i>=1}.

I know L is non-regular and I know that Kleene Star is a closed operation, so my assumption is that L_4 is non-regular.

However my professor provided an example of the above in which L = {0^p | p is prime}, which he said was regular by proving that L* was equal to L(000* + e) by saying each was a subset of one another (e in this case means the empty word).

So his method involved forming a regex of 0^p, but how I can do that when I essentially have one already?