A088054 Factorial primes: primes which are within 1 of a factorial number.

2, 3, 5, 7, 23, 719, 5039, 39916801, 479001599, 87178291199, 10888869450418352160768000001, 265252859812191058636308479999999, 263130836933693530167218012159999999, 8683317618811886495518194401279999999

Offset

1,1

Comments

Conjecture: 3 is the intersection of A002981 and A002982.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..29

C. Caldwell's The Top Twenty, Factorial Primes.

R. Mestrovic, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof, arXiv preprint arXiv:1202.3670 [math.HO], 2012-2018. - From N. J. A. Sloane, Jun 13 2012

Wikipedia, Factorial prime.

Example

3! + 1 = 7; 7! - 1 = 5039.
39916801 is a term because 11! + 1 is prime.

Mathematica

t = {}; Do[ If[PrimeQ[n! - 1], AppendTo[t, n! - 1]]; If[PrimeQ[n! + 1], AppendTo[t, n! + 1]], {n, 50}]; t (* Robert G. Wilson v *)
Union[Select[Range[50]!-1, PrimeQ], Select[Range[50]!+1, PrimeQ]] (Noe)
fp[n_] := Module[{nf=n!}, Select[{nf-1, nf+1}, PrimeQ]]; Flatten[ Table[ fp[i], {i, 50}]] (* Harvey P. Dale, Dec 18 2010 *)
Select[Flatten[#+{-1, 1}&/@(Range[50]!)], PrimeQ] (* Harvey P. Dale, Apr 08 2019 *)

Prog

(Python)
from itertools import count, islice
from sympy import isprime
def A088054_gen(): # generator of terms
    f = 1
    for k in count(1):
        f *= k
        if isprime(f-1):
            yield f-1
        if isprime(f+1):
            yield f+1
A088054_list = list(islice(A088054_gen(), 10)) # Chai Wah Wu, Feb 18 2022

Crossrefs

Cf. A000142, A002981, A002982.

Union of A055490 and A088332.

Sequence in context: A368805 A262339 A110094 * A249509 A085907 A024777

Adjacent sequences: A088051 A088052 A088053 * A088055 A088056 A088057

Keyword

easy,nice,nonn

Author

Christopher M. Tomaszewski (cmt1288(AT)comcast.net), Nov 02 2003

Extensions

Corrected by Paul Muljadi, Oct 11 2005

More terms from Robert G. Wilson v and T. D. Noe, Oct 12 2005

Status

approved