Read the following statements carefully.

$[1]$. It is completely impossible to find a non-constant infinite arithmetic progression such that all of the terms are prime numbers.

$[2]$. It isn't possible to find a non-constant polynomial $f(x)$ with integer coefficients such that $f(x)$ is a prime number for all integer values of $x$.

$[3]$. If $f(x)=4x-1$, it is possible to find infinite values of $x$ such that $f(x)$ is a prime.

Which of these are correct?

This problem is from the set "MCQ Is Not As Easy As 1-2-3". You can see the rest of the problems here.

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