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A002982 Numbers n such that n! - 1 is prime.
(Formerly M2321)
37
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 (list; graph; refs; listen; history; text; internal format)
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..26.

A. Borning, Some results for k!+-1 and 2.3.5...p+-1, Math. Comp., 26:118 (1972), pp. 567-570.

J. P. Buhler et al., Primes of the form n!+-1 and 2.3.5....p+-1, Math. Comp., 38:158 (1982), pp. 639-643.

C. K. Caldwell, Primorial factorial numbers

C. K. Caldwell and Y. Gallot, On the primality of n!+-1 and 2*3*5*...*p+-1, Math. Comp., 71:237 (2002), pp. 441-448.

P. Carmody, Factorial Prime Search Progress Pages

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, 2012

R. Ondrejka, The Top Ten: a Catalogue of Primal Configurations

PrimeGrid, World Record Factorial Prime!!! [From Eric W. Weisstein, Oct 06 2010]

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

Eric Weisstein's World of Mathematics, Factorial.

Eric Weisstein's World of Mathematics, Factorial Prime

Eric Weisstein's World of Mathematics, Integer Sequence Primes

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

CROSSREFS

Cf. A002981 (primes of form n!+1).

Sequence in context: A033162 A105133 A211384 * A093707 A058639 A161001

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

Term 147855 added, Felix Fröhlich, Sep 02 2013

STATUS

approved

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Last modified September 1 19:34 EDT 2014. Contains 246317 sequences.