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.

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.

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

njas

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