TOC regular language

Question

L={a^p|p is prime}  is not regular.but kleene closure of L is regular.How?
L* is regular how??

Answer 1

L = {a², a³, a⁵, a⁷, a¹¹, a¹³,....}*

L will generate $\varepsilon$

L will definitely generate all even powers of a because of {a²}*

L will generate a³

Now, take any other power of a, it will definitely be generated by L. Eg a⁶ = a²a²a²

a⁹ = a⁷a² or a³a³a³

So, L generates all powers of a except for a itself.

Language generated by L can be given as {a}* - {a} which is nothing but regular