Decidability and reducibility

Question

Consider the language given below

$L=\left \{ \left \langle M \right \rangle |M\ is\ TM \ and \ |L(M)|\ is\ prime\right \}$ is it deciable or not ? Explain with fact ?

Answer 1

Not all TM's having language in which length of string is prime. It is non trivial property and also non monotonic property .

Hence, undecidable and not even RE .

Explain with fact ? Do you want reduction ?

Comments

Yes .By reduction.

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but $|L(M)|$ is prime means number of strings in $L$ is prime rt? Not the length of words in $L$.

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yes sir number of strings in $L$ is prime .