A085147 Numbers k such that k!!!! - 1 is prime.

3, 4, 6, 8, 12, 16, 22, 24, 54, 56, 98, 152, 156, 176, 256, 454, 460, 720, 750, 770, 800, 1442, 2846, 5920, 7066, 12778, 19978, 22726, 25938, 27780, 36072, 39746, 48244

Offset: 1

Author

Hugo Pfoertner, Jun 25 2003

Keywords

• hard
• nonn

Comments

The search for multifactorial primes started by Ray Ballinger is now continued by a team of volunteers on the website of Ken Davis (see link).

Links

• Ken Davis, Status of Search for Multifactorial Primes.
• Ken Davis, Results for n!4-1.

Crossrefs

Cf. A007662 (quadruple factorials), A085146.

Programs

Mathematica

MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[0, 1000], PrimeQ[MultiFactorial[#, 4] - 1] & ] (* Robert Price, Apr 19 2019 *)
Select[Range[48300],PrimeQ[Times@@Range[#,1,-4]-1]&] (* Harvey P. Dale, Aug 11 2020 *)

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008