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...

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