A291343 Numbers k such that k!4 + 2^3 is prime, where k!4 = k!!!! is the quadruple factorial number (A007662).

3, 5, 7, 9, 11, 13, 19, 23, 25, 33, 39, 41, 63, 67, 71, 85, 87, 91, 133, 171, 243, 291, 1239, 1543, 1879, 2169, 2421, 3149, 3323, 3377, 3501, 3529, 5433, 5599, 7299, 11227, 11275, 13939, 27147, 32435, 86455, 92105

Offset: 1

Author

Robert Price, Aug 22 2017

Keywords

• nonn
• more

Comments

Corresponding primes are: 11, 13, 29, 53, 239, 593, 65843, 1514213, 5221133, ...

a(43) > 10^5.

Terms > 33 correspond to probable primes.

Examples

			13!4 + 2^3 = 13*9*5*1 + 8 = 593 is prime, so 13 is in the sequence.
		

Links

• Henri & Renaud Lifchitz, PRP Records. Search for n!4+8.
• Joe McLean, Interesting Sources of Probable Primes
• OpenPFGW Project, Primality Tester

Crossrefs

Cf. A007662, A037082, A084438, A123910, A242994.

Programs

Mathematica

MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 4] + 2^3] &]
Select[Range[100000],PrimeQ[Times@@Range[#,1,-4]+8]&] (* Harvey P. Dale, Oct 29 2022 *)

Extensions

a(41)-a(42) from Robert Price, Sep 25 2019