A pattern?

Consider the sequence of numbers where when n is a positive integer,

$a_n=(2n+1)^2-2$

The sequence goes 7, 23, 47, 79, 119, 167 when n = 1,2,...,6

And surprisingly, all of these are primes! Will $a_n$ always be prime?

*P.S. I know I lied. So if you noticed it, I already know. If you haven't noticed it... look again...