factorial prime

The only factorial that is prime is 2!, so if "factorial primes" are to be worth mentioning, the term must mean something other than a factorial that is prime. In fact, as usually defined, factorial primes come in two flavors: factorials plus one (n!+1) and factorials minus one (n!-1). It is conjectured that there are infinitely many of each of these.

n!+1 is prime for n=1, 2, 3, 11, 27, 37, 41, 73, 77, 116, 154, 320, 340, 399, 427, 872, 1477, 6380, and 26951 (107707 digits).
n!-1 is prime for n=3, 4, 6, 7, 12, 14, 30, 32, 33, 38, 94, 166, 324, 379, 469, 546, 974, 1963, 3507, 3610, 6917, 21480, and 34790 (142891 digits).

Both forms have been tested to n=37000 [CG2000].

Related pages (outside of this work)

Organized searches for factorial primes (check status or perhaps join in!)
Primorial Primes The top twenty
Factorial Primes The top twenty
Deficient factorials by Rene Dohmen

References:

BCP82
J. P. Buhler, R. E. Crandall and M. A. Penk, "Primes of the form n! ± 1 and 2 · 3 · 5 ^... p ± 1," Math. Comp., 38:158 (1982) 639--643. Corrigendum in Math. Comp. 40 (1983), 727. MR 83c:10006
Borning72
A. Borning, "Some results for k! ± 1 and 2 · 3 · 5 ^... p ± 1," Math. Comp., 26 (1972) 567--570. MR 46:7133
Caldwell95
C. Caldwell, "On the primality of n! ± 1 and 2 · 3 · 5 ^... p ± 1," Math. Comp., 64:2 (1995) 889--890. MR 95g:11003
CG2000
C. Caldwell and Y. Gallot, "On the primality of n! ± 1 and 2 × 3 × 5 × ^... × p ± 1," Math. Comp., 71:237 (2002) 441--448. MR 2002g:11011 (Abstract available) (Annotation available)
Templer80
M. Templer, "On the primality of k! + 1 and 2 * 3 * 5 * ^... * p + 1," Math. Comp., 34 (1980) 303-304. MR 80j:10010