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$L=\left \{ a^{n}:\text{n is the product of two prime number} \right \}$$L$ is regular or non regular?
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I think using pumping lemma we can say it is non regular
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How to apply pumping lemma for this given language??
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you can understand this way,

since it is infinite language 'n' should be in AP(Arithmetic progression), (ex : in place of 'n', if it were 2p+1 or 5p or 9p+100 where p is any natural number....etc then it would have been in AP) then only loop can be formed, thats what pumpimg lemma says, => if a loop cant be formed in an infinite language, then it is not regular.

in the above language, n is product of two prime numbers, so we cant form a loop.
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daksirp, did you mean

L={a2n+1 : n is a prime number} is REGULAR?

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no, language should be in AP. not n.

ex : (a, aaa, aaaaa, ......), { a2n+1 ​​​​| n >= 0 }, this forms an AP.

in ur que, n is a prime number so it isnt in AP. therefore we cannot form a loop, so not regular..

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I commented, before you edited your own comment
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yaaaa.