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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].
See Also: Factorial, PrimorialPrime, MultifactorialPrime Related pages (outside of this work) 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) 639643. 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) 567570. MR 46:7133
 Caldwell95
 C. Caldwell, "On the primality of n! ± 1 and 2 · 3 · 5 ^{...} p ± 1," Math. Comp., 64:2 (1995) 889890. 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) 441448. 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) 303304. MR 80j:10010
