primorial prime

Clearly the primorial numbers themselves, n#, are rarely prime (in fact just for n = 2 where 2# = 2). So when defining primorial primes authors considered two different flavors--primorials plus one: p#+1 and primorials minus one: p#-1.  We call primes of both of these forms primorial primes. Both forms have been tested for all primes p less than 100000 [CG00].

The study of these numbers may have originated with Euclid's proof that there are infinitely many primes which uses p#.

See Also: FactorialPrime, 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) 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)
Dubner87
H. Dubner, "Factorial and primorial primes," J. Recreational Math., 19:3 (1987) 197--203.
Dubner89a
H. Dubner, "A new primorial prime," J. Recreational Math., 21:4 (1989) 276.
Templer80
M. Templer, "On the primality of k! + 1 and 2 * 3 * 5 * ... * p + 1," Math. Comp., 34 (1980) 303-304.  MR 80j:10010
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