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 A088054 Factorial primes: primes which are within 1 of a factorial number. 5
 2, 3, 5, 7, 23, 719, 5039, 39916801, 479001599, 87178291199, 10888869450418352160768000001, 265252859812191058636308479999999, 263130836933693530167218012159999999, 8683317618811886495518194401279999999 (list; graph; refs; listen; history; text; internal format)
 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: A070029 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

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Last modified August 14 17:36 EDT 2022. Contains 356122 sequences. (Running on oeis4.)