A288370 Primes of the form k!10 + 2, where k!10 is the decuple factorial number (A288327).

3, 5, 7, 11, 13, 41, 173, 233, 1877, 293603, 318482201, 3047775608243, 22045250515087152640289, 1302844523174285888671877, 930620100318118916029523201, 4831436058626442432403564453127, 2060356301148292483532951454058361, 9936127455089061347552058319626135203

Offset: 1

Author

Robert Price, Jun 08 2017

Keywords

• nonn

Links

• Robert Price, Table of n, a(n) for n = 1..29
• Henri and Renaud Lifchitz, PRP Records.Search for n!10+2.
• Joe McLean, Interesting Sources of Probable Primes.
• OpenPFGW Project, Primality Tester.

Crossrefs

Cf. A204657, A288327.

Programs

Mathematica

MultiFactorial[n_, k_] := If[n<1, 1, n*MultiFactorial[n-k, k]];
Select[Table[MultiFactorial[i, 10] + 2, {i, 0, 100}], PrimeQ[#]&]
Select[Table[Times@@Range[n,1,-10]+2,{n,200}],PrimeQ] (* Harvey P. Dale, May 26 2025 *)

Formula

a(n) = 2 + A288327(A204657(n+1)). - Elmo R. Oliveira, Feb 26 2025