A035094 Smallest prime of form (n!)*k + 1.

2, 3, 7, 73, 241, 2161, 15121, 161281, 1088641, 10886401, 39916801, 958003201, 18681062401, 1133317785601, 9153720576001, 83691159552001, 1778437140480001, 12804747411456001, 851515702861824001, 41359334139002880001, 766364132575641600001, 20232013099996938240001

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Comments

This is one possible generalization of "the least prime problem in special arithmetic progressions" when n in nk+1 is replaced by n!.

a(n) is the smallest prime p such that the multiplicative group modulo p has a subgroup of order n!. - Joerg Arndt, Oct 18 2020

Examples

			a(5)=241 because in arithmetic progression 120k+1=5!k+1 the second term is prime, 241.
		

Links

• Index entries for sequences related to primes in arithmetic progressions

Crossrefs

Analogous case is A034694. Special case for k=1 is A002981.

Cf. A035093 (values of k).

Programs

Mathematica

sp[n_]:=Module[{nf=n!,k=1},While[!PrimeQ[nf*k+1],k++];nf*k+1]; Array[sp,20] (* Harvey P. Dale, Jan 27 2013 *)

PARI

a(n) = for(k=1, oo, if(isprime(k*n! + 1), return(k*n! + 1))); \\ Daniel Suteu, Oct 18 2020