[Math] Prove or Disprove that there exists an integer $n$ such that $4n^2 -12n +8$ is prime

Question

Prove or Disprove that there exists an integer $n$ such that $4n^2 -12n +8$ is prime.

So we have a strictly positive and even term minus a strictly even term plus an even. Hmm. A counterexample maybe, but I'd rather not guess a number to prove/disprove it. Which I doubt is as easy it sounds.

Since it looks to be strictly even it would mean it can't be prime since integers greater than 2 that are even are not prime?

Answer 1

$4n^2-12n+8=4(n^2-3n+2)$ can't be prime because it is a multiple of $4$