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Numbers k such that k!!!! - 1 is prime.
2

%I #17 May 31 2024 19:57:08

%S 3,4,6,8,12,16,22,24,54,56,98,152,156,176,256,454,460,720,750,770,800,

%T 1442,2846,5920,7066,12778,19978,22726,25938,27780,36072,39746,48244

%N Numbers k such that k!!!! - 1 is prime.

%C 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).

%H Ken Davis, <a href="http://mfprimes.free-dc.org">Status of Search for Multifactorial Primes</a>.

%H Ken Davis, <a href="http://mfprimes.free-dc.org/mfdata/f04m.html">Results for n!4-1</a>.

%t MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];

%t Select[Range[0, 1000], PrimeQ[MultiFactorial[#, 4] - 1] & ] (* _Robert Price_, Apr 19 2019 *)

%t Select[Range[48300],PrimeQ[Times@@Range[#,1,-4]-1]&] (* _Harvey P. Dale_, Aug 11 2020 *)

%Y Cf. A007662 (quadruple factorials), A085146.

%K hard,nonn

%O 1,1

%A _Hugo Pfoertner_, Jun 25 2003

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