

A002982


Numbers n such that n!  1 is prime.
(Formerly M2321)


66



3, 4, 6, 7, 12, 14, 30, 32, 33, 38, 94, 166, 324, 379, 469, 546, 974, 1963, 3507, 3610, 6917, 21480, 34790, 94550, 103040, 147855, 208003
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OFFSET

1,1


COMMENTS

The corresponding primes n!1 are often called factorial primes.


REFERENCES

J.M. De Koninck, Ces nombres qui nous fascinent, Entry 166, p. 53, Ellipses, Paris 2008.
R. K. Guy, Unsolved Problems in Number Theory, Section A2.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

Table of n, a(n) for n=1..27.
A. Borning, Some results for k!+1 and 2.3.5...p+1, Math. Comp., 26:118 (1972), pp. 567570.
J. P. Buhler et al., Primes of the form n!+1 and 2.3.5....p+1, Math. Comp., 38:158 (1982), pp. 639643.
Chris K. Caldwell, Factorial Primes
C. K. Caldwell and Y. Gallot, On the primality of n!+1 and 2*3*5*...*p+1, Math. Comp., 71:237 (2002), pp. 441448.
P. Carmody, Factorial Prime Search Progress Pages
R. K. Guy & N. J. A. Sloane, Correspondence, 1985
H. Dubner, Factorial and primorial primes, J. Rec. Math., 19 (No. 3, 1987), 197203. (Annotated scanned copy)
Des MacHale and Joseph Manning, Maximal runs of strictly composite integers, The Mathematical Gazette, 99 (2015), pp 213219. doi:10.1017/mag.2015.28.
R. Mestrovic, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC2012) and another new proof, arXiv preprint arXiv:1202.3670 [math.HO], 2012.
R. Ondrejka, The Top Ten: a Catalogue of Primal Configurations
PrimeGrid, World Record Factorial Prime!!!
PrimeGrid, Announcement of 94550, (2010)  Felix Fröhlich, Jul 11 2014
PrimeGrid, Announcement of 103040, (2010)  Felix Fröhlich, Jul 11 2014
PrimeGrid, Announcement of 147855, (2013)  Felix Fröhlich, Jul 11 2014
Maxie D. Schmidt, New Congruences and Finite Difference Equations for Generalized Factorial Functions, arXiv:1701.04741 [math.CO], 2017.
Eric Weisstein's World of Mathematics, Factorial
Eric Weisstein's World of Mathematics, Factorial Prime
Eric Weisstein's World of Mathematics, Integer Sequence Primes
R. G. Wilson, V, Letter to N. J. A. Sloane, Jan. 1989
Index entries for sequences related to factorial numbers


MATHEMATICA

Select[Range[10^3], PrimeQ[ #!1] &] (* Vladimir Joseph Stephan Orlovsky, May 01 2008 *)


PROG

(PARI) is(n)=ispseudoprime(n!1) \\ Charles R Greathouse IV, Mar 21 2013
(MAGMA) [n: n in [0..500]  IsPrime(Factorial(n)1)]; // Vincenzo Librandi, Sep 07 2017


CROSSREFS

Cf. A002981 (numbers n such that n!+1 is prime).
Cf. A055490 (primes of form n!1).
Cf. A088332 (primes of form n!+1).
Sequence in context: A105133 A211384 A281828 * A290432 A276783 A288731
Adjacent sequences: A002979 A002980 A002981 * A002983 A002984 A002985


KEYWORD

hard,more,nonn,nice


AUTHOR

N. J. A. Sloane


EXTENSIONS

21480 sent in by Ken Davis (ken.davis(AT)softwareag.com), Oct 29 2001
Updated Feb 26 2007 by Max Alekseyev, based on progress reported in the Carmody web site.
Inserted missing 21480 and 34790 (see Caldwell). Added 94550, discovered Oct 05 2010. Eric W. Weisstein, Oct 06 2010
103040 was discovered by James Winskill, Dec 14 2010. It has 471794 digits. Corrected by Jens Kruse Andersen, Mar 22 2011
a(26) = 147855 from Felix Fröhlich, Sep 02 2013
a(27) = 208003 from Sou Fukui, Jul 27 2016


STATUS

approved



