A142959 Numbers k such that both (k!)^2 + k! + 1 and (k!)^2 + 1 are prime.

1, 2, 3, 4, 76

Offset: 1

Author

Lekraj Beedassy, Jul 13 2008

Keywords

• nonn
• more

Comments

For the numbers of digits of the associated primes, see A142960.

a(6) > 150000, because A46029(15) > 150000 and A46029(14) = 127162 is not a term here since (127162!)^2 + 127162! + 1 is divisible by 2049703. - Giovanni Resta, Aug 12 2025

References

• J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 76, pp 26, Ellipses, Paris 2008.

Crossrefs

Cf. A142960, A046029, A051856.

Programs

Mathematica

Select[Range[80],With[{c=#!},AllTrue[c^2+{c+1,1},PrimeQ]]&] (* Harvey P. Dale, Aug 11 2025 *)

Formula

A046029 INTERSECT A051856. - R. J. Mathar, Aug 08 2008