Superduperfactorial Primes: Primes of the form A055462(k)-1 or A055462(k)+1.

[Jonathan Post]

Superduperfactorial Primes: Primes of the form A055462(k)-1 or A055462(k)+1.

2, 3, 23, 6911, 238878721, 5944066965503999

This is to superduperfactorials as factorial primes are to factorials,
and as subfactorial primes are to subfactorials, and as hyperfactorial
primes are to hyperfactorials.

I know that njas and other dislike generic sequences named "primes of
the form xxx...", but in this case, the analogues to sub-, super-,
hyper-, and ultrafactorial primes gibes this a context.

Would anyone like to Mathematica-ize or extend this before vacation
ends and we submit?