A204663 Numbers n such that n!8 + 2 is prime.

0, 1, 3, 5, 9, 13, 15, 21, 23, 27, 33, 35, 45, 53, 55, 57, 75, 79, 109, 197, 221, 227, 267, 333, 413, 545, 695, 703, 801, 967, 1029, 1329, 1351, 1475, 1549, 1757, 2173, 2861, 3161, 3167, 3885, 4681, 4965, 6277, 6655, 8477, 9821, 9959, 10269, 17999, 23349, 29347, 29477, 30181, 34133, 36687, 40985, 43395, 47499

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(60) > 50000. - Robert Price, Aug 19 2012

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• C. Caldwell and H. Dubner (Eds): The top ten prime numbers: from the unpublished collections of R. Ondrejka (May 2001), Table 21 F, p. 75.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, A204664, A156165, A156167, A085150, A085148, A085146, A037083, A080778, A002981.

Programs

Mathematica

Select[Range[0,9999], PrimeQ[Product[# - 8i,{i, 0, Floor[(# - 2)/8]}] + 2] &] (* Indranil Ghosh, Mar 13 2017 *)

PARI

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

Extensions

a(39)-a(59) from Robert Price, Aug 19 2012