$n^2+n+1$ is not prime if $n$ is a perfect square $>1$ In searching for primes of the form $n^2+n+1$, why should one omit as choices of $n$ those integers that are perfect squares?
I know that the form $Ak+B$ contains infinitely many primes if $\gcd(A,B)=1$, $k=0,1,2...$.
$n^2+n+1 = n(n+1)+1$, so it is in the above form. I know that perfect squares do not give prime in this form when I put each term. Please explain.

$$n^4+n^2+1=(n^2-n+1)(n^2+n+1)$$, so $n^4+n^2+1$ is not prime for $n\ge 2$
