%I A002981 M0908
%S A002981 0,1,2,3,11,27,37,41,73,77,116,154,320,340,399,427,872,1477,6380,26951
%N A002981 Numbers n such that n! + 1 is prime.
%C A002981 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
%C A002981 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
%C A002981 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)
%D A002981 C. K. Caldwell and Y. Gallot, On the primality of n!+-1 and 2*3*5*...*p+-1, 
               Math. Comp., 71 (2001), 441-448.
%D A002981 J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 116, p. 40, Ellipses, 
               Paris 2008.
%D A002981 H. Dubner, Factorial and primorial primes, J. Rec. Math., 19 (No. 3, 
               1987), 197-203.
%D A002981 R. K. Guy, Unsolved Problems in Number Theory, Section A2.
%D A002981 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A002981 C. K. Caldwell, <a href="http://primes.utm.edu/">The Prime Pages</a>
%H A002981 C. K. Caldwell, <a href="http://www.utm.edu/research/primes/lists/top20/
               PrimorialFactorial.html">Primorial and Factorial Primes</a>
%H A002981 N. Kuosa, <a href="http://www.hut.fi/~nkuosa/primeform/">Source for 6380.</
               a>
%H A002981 H. Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/
               matha104.htm">Factors of N!+1</a>
%H A002981 R. Ondrejka, <a href="http://www.utm.edu/research/primes/lists/top_ten/
               ">The Top Ten: a Catalogue of Primal Configurations</a>
%H A002981 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Factorial.html">Link to a section of The World of Mathematics (1).</
               a>
%H A002981 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               FactorialPrime.html">Link to a section of The World of Mathematics 
               (2).</a>
%H A002981 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               IntegerSequencePrimes.html">Integer Sequence Primes</a>
%H A002981 <a href="Sindx_Fa.html#factorial">Index entries for sequences related 
               to factorial numbers</a>
%e A002981 3!+1 = 7 is prime, so 3 is in the sequence.
%t A002981 v={0, 1, 2}; Do[If[ !PrimeQ[n+1]&&PrimeQ[n!+1], v=Append[v, n]; Print[v]], 
               {n, 3, 29651}]
%Y A002981 Cf. A002982 (n!-1 is prime), A064295. A088332 gives the primes.
%Y A002981 Equals A090660 - 1.
%Y A002981 See also A002982 (n!-1 is prime).
%Y A002981 Cf. A093804.
%Y A002981 Sequence in context: A041811 A056851 A048412 this_sequence A075641 A104081 
               A003455
%Y A002981 Adjacent sequences: A002978 A002979 A002980 this_sequence A002982 A002983 
               A002984
%K A002981 hard,nonn,nice
%O A002981 1,3
%A A002981 N. J. A. Sloane (njas(AT)research.att.com).
%E A002981 6380 sent in by Jud McCranie (j.mccranie(AT)comcast.net), May 08 2000.
%E A002981 26951 from Ken Davis (kraden(AT)ozemail.com.au), May 24 2002