1,3

If n+1 is prime then (by Wilson's theorem) n+1 divides n!+1. Thus for n > 2 if n+1 is prime n is not in the sequence. - Farideh Firoozbakht (f.firoozbakht(AT)sci.ui.ac.ir), Aug 22 2003

For n>2, n!+1 is prime <==> nextprime((n+1)!)>(n+1)nextprime(n!) and we can conjecture that for n>2 if n!+1 is prime then (n+1)!+1 is not prime. - Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 03 2004

The prime members are in A093804 (numbers n such that Sum_{d|n} d! is prime) since Sum_{d|n} d! = n! + 1 if n is prime. - Jonathan Sondow (jsondow(AT)alumni.princeton.edu)

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 116, p. 40, Ellipses, Paris 2008.

H. Dubner, Factorial and primorial primes, J. Rec. Math., 19 (No. 3, 1987), 197-203.

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).

C. K. Caldwell, The Prime Pages

C. K. Caldwell, Primorial and Factorial Primes

N. Kuosa, Source for 6380.

H. Mishima, Factors of N!+1

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

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

3!+1 = 7 is prime, so 3 is in the sequence.

v={0, 1, 2}; Do[If[ !PrimeQ[n+1]&&PrimeQ[n!+1], v=Append[v, n]; Print[v]], {n, 3, 29651}]

Cf. A002982 (n!-1 is prime), A064295. A088332 gives the primes.

Equals A090660 - 1.

See also A002982 (n!-1 is prime).

Cf. A093804.

Sequence in context: A041811 A056851 A048412 this_sequence A075641 A104081 A003455

Adjacent sequences: A002978 A002979 A002980 this_sequence A002982 A002983 A002984

hard,nonn,nice

N. J. A. Sloane (njas(AT)research.att.com).

6380 sent in by Jud McCranie (j.mccranie(AT)comcast.net), May 08 2000.

26951 from Ken Davis (kraden(AT)ozemail.com.au), May 24 2002