7823

This number is a prime.

Let f(n) = n!!! + 3^5, where n!!! is the triple factorial (n x (n-3) x (n-6)...). For which primes p is f(p) also prime? The first eight answers are 7, 11, 23, 47, 53, 89, 4999, and 7823, with f(7823) being a 9023-digit prime. This curio is related to certain formulas that produce numbers with a high density of pseudoprimes. [Keith]