TITLE: When are $9^{n} - 2$ and $9^{n} + 2$ both prime?
QUESTION [9 upvotes]: Inspired by the discussion at a since-deleted thread:

Question: For $n > 2$, are  $9^{n} - 2$ and $9^{n} + 2$ ever both prime?"

It seems that many different techniques were tried, ranging from Wilson's Theorem to a generalization of Clement's Theorem, and by looking at a couple of relevant OEIS sequences (A090649; A128455).
Note that $9^{n} + 2$ is prime for $n$ beginning with:
$$0, 1, 2, 4, 5, 7, 12, 13, 18, 49, 55, 63, 193, 247, \ldots$$
Similarly, $9^{n}-2$ is prime for $n$ beginning with:
$$1, 2, 3, 11, 45, 51, 260, 324, 390, 393, 1112, 3092, 4445, 10373 \ldots$$

REPLY [9 votes]: A solution was ultimately published in the Pi Mu Epsilon Journal, 13(7), Fall 2012, pp. 431 (JSTOR).
It was attributed to Paul S. Bruckman (separate PME interview) and reads, in part, as follows.