|
| |
|
|
A002982
|
|
Numbers n such that n! - 1 is prime.
(Formerly M2321)
|
|
34
| |
|
|
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
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| The corresponding primes n!-1 are often called factorial primes.
|
|
|
REFERENCES
| A. Borning, Some results for k!+-1 and 2.3.5...p+-1, Math. Comp., 26 (1972), 567-570.
J. P. Buhler et al., Primes of the form n!+-1 and 2.3.5....p+-1, Math. Comp., 38 (1982), 639-643.
C. K. Caldwell and Y. Gallot, On the primality of n!+-1 and 2*3*5*...*p+-1, Math. Comp., 71 (2001), 441-448.
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
| Author?, Title?
C. K. Caldwell, The Prime Pages
C. K. Caldwell, Primorial factorial numbers
P. Carmody, Factorial Prime Search Progress Pages
R. Ondrejka, The Top Ten: a Catalogue of Primal Configurations
PrimeGrid, World Record Factorial Prime!!! [From Eric W. Weisstein (eric(AT)weisstein.com), Oct 06 2010]
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics (1).
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics (2).
Eric Weisstein's World of Mathematics, Integer Sequence Primes
Index entries for sequences related to factorial numbers
The prime 34790!-1 was discovered by Leon Marchal on May 16, 2002. - Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jul 18 2002
|
|
|
MATHEMATICA
| Select[Range[10^3], PrimeQ[ #!-1] &] (from Vladimir Orlovsky (4vladimir(AT)gmail.com), May 01 2008)
|
|
|
CROSSREFS
| Cf. A002981 (primes of form n!+1).
Sequence in context: A153883 A033162 A105133 * A093707 A058639 A161001
Adjacent sequences: A002979 A002980 A002981 * A002983 A002984 A002985
|
|
|
KEYWORD
| hard,nonn,nice
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
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. 5, 2010. Eric W. Weisstein (eric(AT)weisstein.com), Oct 06 2010
103040 was discovered by James Winskill, Dec 14 2010. It has 471794 digits. Corrected by Jens Kruse Andersen (jens.k.a(AT)get2net.dk), Mar 22 2011
|
| |
|
|
