A204657 Numbers n such that n!10 + 2 is prime.

0, 1, 3, 5, 9, 11, 13, 19, 21, 25, 41, 57, 79, 127, 135, 149, 165, 177, 193, 209, 223, 255, 273, 287, 297, 375, 433, 459, 481, 565, 1079, 1435, 1543, 1771, 1913, 1983, 2063, 2305, 2653, 6789, 8757, 11149, 13671, 15433, 16369, 17261, 18129, 22129, 22785, 22875, 25235, 25247, 26329, 27675, 33391, 39075, 41195, 47435, 47621, 48409, 59235, 59715, 61571, 65433, 78761, 83033

Offset: 1

Author

M. F. Hasler, Jan 17 2012

Keywords

• nonn
• hard

Comments

n!10 = Product_{k=0..floor((n-1)/10)}(n - 10k).

a(61) > 50000. - Robert Price, Jun 10 2012

The first 11 primes associated with this sequence: 3, 3, 5, 7, 11, 13, 41, 173, 233, 1877, 293603. - Robert Price, Mar 10 2017

a(67) > 10^5. - Robert Price, Mar 31 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• C. Caldwell and H. Dubner (Eds): The top ten prime numbers: from the unpublished collections of R. Ondrejka (May 2001), Table 21 F, p. 75.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.
• Nathan Russell, n!10+2 results, primenumbers group, Jan 2012.
• Nathan Russell, n!10+2 results, message 23995 in primenumbers Yahoo group, Jan 17, 2012.

Crossrefs

Cf. A204658, A204659, A204660, A204661, A204662, A204663, A204664, A156165, A156167, A085150, A085148, A085146, A037083, A080778, A002981.

Programs

Mathematica

MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 10] + 2] &]

PARI

for(n=0,9999,isprime(prod(i=0,(n-2)\10,n-10*i)+2)& print1(n","))

Extensions

a(40)-a(59) from Robert Price, Jun 10 2012

Inserted missing term of 6789 by Robert Price, Mar 10 2017

a(61)-a(66) from Robert Price, Mar 31 2017