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A088054 Factorial primes: primes which are within 1 of a factorial number. 3

%I

%S 2,3,5,7,23,719,5039,39916801,479001599,87178291199,

%T 10888869450418352160768000001,265252859812191058636308479999999,

%U 263130836933693530167218012159999999,8683317618811886495518194401279999999

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

%C Conjecture: 3 is the intersection of A002981 and A002982.

%H R. Mestrovic, <a href="http://arxiv.org/abs/1202.3670">Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof</a>, arXiv preprint arXiv:1202.3670, 2012 - From N. J. A. Sloane, Jun 13 2012

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Factorial_prime">Factorial prime</a>.

%H C. Caldwell's The Top Twenty, <a href="http://primes.utm.edu/top20/page.php?id=30">Factorial Primes</a>.

%e 3!+1=7; 7!-1=5039

%e 39916801 is a term because 11!+1 is prime.

%t 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_ *)

%t Union[Select[Range[50]!-1, PrimeQ], Select[Range[50]!+1, PrimeQ]] (Noe)

%t fp[n_] := Module[{nf=n!}, Select[{nf-1,nf+1},PrimeQ]]; Flatten[ Table[ fp[i],{i,50}]] [From Harvey P. Dale, Dec. 18, 2010]

%t Select[Flatten[#+{-1,1}&/@(Range[50]!)],PrimeQ] (* _Harvey P. Dale_, Apr 08 2019 *)

%Y Cf. A000142, A002981, A002982.

%Y Union of A055490 and A088332.

%K easy,nice,nonn

%O 1,1

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

%E Corrected by _Paul Muljadi_, Oct 11 2005

%E More terms from _Robert G. Wilson v_ and _T. D. Noe_, Oct 12 2005

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Last modified August 6 15:19 EDT 2020. Contains 336248 sequences. (Running on oeis4.)