Find Primes!

Number Theory Level 3

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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