A204664 Numbers n such that n!8-2 is prime.

4, 5, 7, 9, 11, 15, 17, 25, 27, 33, 47, 59, 63, 77, 87, 89, 93, 95, 107, 119, 127, 133, 139, 193, 201, 217, 269, 291, 369, 373, 435, 445, 669, 803, 831, 859, 907, 1271, 1705, 1743, 1849, 3087, 3189, 3497, 4221, 4475, 5119, 6013, 8023, 9237, 12755, 16501, 16747, 17021, 17309, 20671, 21539, 28377, 33625, 35645, 36831, 54663, 56223, 65299, 66159, 68121, 69339, 70579, 73511, 77745, 94601

Offset: 1

Author

M. F. Hasler, Jan 17 2012

Keywords

• nonn
• hard

Comments

n!8 = A114800(n).

See also links in A156165.

For odd k, n!k +- 2 is even for all n > k and thus cannot be prime.

a(62) > 50000. - Robert Price, Aug 27 2012

The first 10 associated primes: 2, 3, 5, 7, 31, 103, 151, 3823, 16927, 126223. - Robert Price, Mar 10 2017

a(72) > 10^5. - Robert Price, Apr 24 2017

Links

• C. Caldwell and H. Dubner (Eds): The top ten prime numbers: from the unpublished collections of R. Ondrejka (May 2001), Table 21 F, p. 75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.

Crossrefs

Cf. A204657, A204658, A204659, A204660, A204661, A204662, A204663, A156165, A156167, A085150, A085148, A085146, A037083, A080778, A002981.

Programs

Mathematica

MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[4, 50000], PrimeQ[MultiFactorial[#, 8] - 2] &] (* Robert Price, Mar 10 2017 *)

PARI

for(n=0,9999,isprime(prod(i=0,(n-2)\8,n-8*i)-2)& print1(n","))

Extensions

a(46)-a(61) from Robert Price, Aug 27 2012

a(62)-a(71) from Robert Price, Apr 24 2017