Answer
There are no integers in where $6n^2 + 27$ is prime.
Work Step by Step
$6n^2 + 27$ can be factored as $3(2n^2 + 9)$. It is apparent that $2n^2 + 9$ is an integer and greater than $1$, so it will factor into two integers greater than one, one of which will be $3$
