et . ..
" A prime p is called primorial or prime-factorial if it has the form p = Pi(n) +- 1 for some number n, where Pi(n) stands for the product 2, 3, 5, 7 11 . .. of all the primes < = n. A prime is called factorial if it is of the form n! +- 1. The first factorial primes are:
n! - 1 is prime for n = 3, 4, 6, 7, 12, 14, 30, 32, 33, 38, 94, 166,...
n! + 1 is prime for n = 1, 2, 3, 11, 13, 27, 37, 41, 73, 77, 116, 154...
The largest known primorial prime is Pi(24029) + 1, found by Caldwell in 1993. The largest known factorial prime is 3610! - 1 [Caldwell, 1993]. It is not known if there are infinitely many primorial or factorial primes.
Primes of the form 22n+1 are known as Fermat primes. "