Find Primes!

Read the following statements carefully.

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

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

[3][3]. If f(x)=4x1f(x)=4x-1, it is possible to find infinite values of xx such that f(x)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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