A329177 Numbers k such that k![4] - 256 is prime, where k![4] = A007662(k) = quadruple factorial.

15, 17, 19, 21, 23, 25, 33, 39, 41, 43, 53, 63, 67, 73, 157, 167, 181, 195, 221, 327, 363, 419, 849, 861, 1233, 1265, 1599, 2413, 2515, 4009, 8291, 8475, 10685, 13957, 17453, 18409, 19117, 22739, 33313, 37861, 59703, 64983, 80697

Offset: 1

Author

Robert Price, Nov 07 2019

Keywords

• nonn

Comments

a(44) > 10^5.

The first 5 primes associated with this sequence are: 3209, 9689, 65579, 208589, 1513949.

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• C. Caldwell and H. Dubner (Eds): The top ten prime numbers: from the unpublished collections of R. Ondrejka (May 2001), Table 21 F, p. 75.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] - 256; x > 0 && PrimeQ[x]) &]
Select[Range[10,1600],PrimeQ[Times@@Range[#,1,-4]-256]&] (* The program generates the first 27 terms of the sequence. To generate more, increase the second Range constant but the program may take a long time to run. *) (* Harvey P. Dale, Aug 01 2022 *)