A329176 Numbers k such that k![4] - 128 is prime, where k![4] = A007662(k) = quadruple factorial.

11, 13, 17, 19, 25, 27, 29, 41, 47, 61, 75, 113, 181, 251, 287, 339, 521, 533, 573, 687, 739, 1015, 1243, 1811, 2073, 2851, 2939, 3421, 4055, 4211, 4477, 5219, 6151, 8851, 9251, 14219, 17123, 21703, 24313, 25053, 28811, 33065, 49305, 50775, 52693, 69805, 82077, 87771

Offset: 1

Author

Robert Price, Nov 07 2019

Keywords

• nonn

Comments

a(49) > 10^5.

The first 5 primes associated with this sequence are: 103, 457, 9817, 65707, 5220997.

Links

• C. K. Caldwell, The Prime Glossary, multifactorial prime
• C. Caldwell and H. Dubner (Eds): The top ten prime numbers: from the unpublished collections of R. Ondrejka (May 2001), Table 21 F, p. 75.
• Ken Davis, Status of Search for Multifactorial Primes.
• Joe McLean, Interesting Sources of Probable Primes

Crossrefs

Cf. A007662, A283553.

Programs

Mathematica

MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[1000], (x = MultiFactorial[#, 4] - 128; x > 0 && PrimeQ[x]) &]
Select[Range[10,90000],PrimeQ[Times@@Range[#,1,-4]-128]&] (* Harvey P. Dale, May 13 2022 *)