A100288 Primes of the form (1!)^2 + (2!)^2 + (3!)^2 +...+ (k!)^2.

5, 41, 617, 15017, 25935017, 1651637417, 13301522971817, 41117342095090841723228045851817, 2616218222822143606864564493635469851817

Offset: 1

Author

T. D. Noe, Nov 11 2004

Keywords

• nonn
• fini

Comments

Jonathan Vos Post contributed these numbers to Prime Curios.

Examples

			41 = (1!)^2 + (2!)^2 + (3!)^2 is prime.
		

Links

• G. L. Honaker, Jr. and C. Caldwell, Prime Curios!

Crossrefs

Cf. A100289 (k such that (1!)^2 + (2!)^2 + (3!)^2 + ... + (k!)^2 is prime).

See also A061062, A104344.

Programs

Mathematica

Select[Accumulate[Table[(n!)^2,{n,30}]],PrimeQ] (* Harvey P. Dale, May 09 2025 *)

PARI

lista(nn) = {my(s=1); for(k=2, nn, s+=(k!)^2; if(ispseudoprime(s), print1(s, ", "))); } \\ Jinyuan Wang, Mar 08 2020