A204656 -id:A204656 - cp's OEIS frontend

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

M. F. Hasler, Jan 17 2012

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

C. Caldwell and H. Dubner (Eds): The top ten prime numbers: from the unpublished collections of R. Ondrejka (May 2001), Table 21 F, p. 75.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

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

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

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

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

A288369 Primes of the form k!10 + 1, where k!10 is the decuple factorial number (A288327).

Original entry on oeis.org

2, 3, 5, 7, 11, 97, 45697, 4133377, 4060162871525377, 294880677941535796547813377, 46001385758879584261458886657, 7636230035974010987402175184897, 35568742809600000000000000000001, 18067746635539299564851337380417765377

Offset: 1

Robert Price, Jun 08 2017

nonn

Robert Price, Table of n, a(n) for n = 1..21
Joe McLean, Interesting Sources of Probable Primes.

Cf. A204656, A288327.

MultiFactorial[n_, k_] := If[n<1, 1, n*MultiFactorial[n-k, k]];
Select[Table[MultiFactorial[i, 10] + 1, {i, 0, 100}], PrimeQ[#]&]

a(n) = 1 + A288327(A204656(n+1)). - Elmo R. Oliveira, Feb 26 2025

cp's OEIS Frontend

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

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