A051856 Numbers k such that (k!)^2 + k! + 1 is prime.

0, 1, 2, 3, 4, 6, 76, 2837, 6001, 7076

Offset: 1

Author

Andrew Walker (ajw01(AT)uow.edu.au), Dec 13 1999

Keywords

• nonn
• hard
• more

Examples

			6 is in the sequence because (6!)^2+6!+1=519121 is prime.
		

References

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

Links

• C. K. Caldwell, The Prime Pages
• C. Nash, Prime Form [broken link]
• M. Oakes, Re: Gaussian primorial and factorial primes, Primeform, Dec 21 2010 [broken link]
• Mike Oakes, Andrew Walker, David Broadhurst, Gaussian primorial and factorial primes, digest of 7 messages in primeform Yahoo group, Dec 20 - Dec 21, 2010.

Crossrefs

Cf. A002981, A002982, A046029.

Programs

Mathematica

Do[If[PrimeQ[n!^2+n!+1], Print[n]], {n, 600}] (* Farideh Firoozbakht, Jul 12 2003 *)

Extensions

Edited by R. J. Mathar, Aug 08 2008

a(8)-a(10) from Serge Batalov, Nov 24 2011