A046029 Numbers k such that (k!)^2 + 1 is prime.

0, 1, 2, 3, 4, 5, 9, 10, 11, 13, 24, 65, 76, 127162

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• more
• hard

Comments

a(14) > 780. - Ralf Stephan, Oct 21 2002

a(14) > 2500. - Gabriel Cunningham (gcasey(AT)mit.edu), Feb 23 2004

a(14) > 10000. - Charles R Greathouse IV, Nov 16 2006

a(14) > 16000. - Robert Price, Aug 13 2011

a(15) > 150000. - Ryan Propper, Jun 25 2025

Examples

			9 is a term because (9!)^2 + 1 is prime.
		

References

• H. Ibstedt, A Few Smarandache Sequences, Smarandache Notions Journal, Vol. 8, No. 1-2-3, 1997, 170-183.

Links

• Mike Oakes, Re: Gaussian primorial and factorial primes, Primeform, Dec 21 2010.
• Mike Oakes, Andrew Walker, David Broadhurst, Gaussian primorial and factorial primes, digest of 7 messages in primeform Yahoo group, Dec 20 - Dec 21, 2010.
• Eric Weisstein's World of Mathematics, Factorial

Crossrefs

Cf. A020549, A051739.

Programs

Magma

[n: n in [0..90] |IsPrime(Factorial(n)^2+1)]; // Vincenzo Librandi, May 28 2015

Mathematica

Do[ If[ PrimeQ[n!^2 + 1], Print[n]], {n, 500}] (* Robert G. Wilson v, Apr 14 2004 *)
Select[Range[1000], PrimeQ[(#!^2 + 1)] &] (* Vincenzo Librandi, May 28 2015 *)

Extensions

a(14) from Ryan Propper, Jun 25 2025