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TOC regular language

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

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