A037151 Smallest prime > n!.

2, 3, 7, 29, 127, 727, 5051, 40343, 362897, 3628811, 39916801, 479001629, 6227020867, 87178291219, 1307674368043, 20922789888023, 355687428096031, 6402373705728037, 121645100408832089, 2432902008176640029, 51090942171709440031, 1124000727777607680031

Offset: 1

Author

Jud McCranie

Keywords

• nonn

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..450
• Antonín Čejchan, Michal Křížek, and Lawrence Somer, On Remarkable Properties of Primes Near Factorials and Primorials, Journal of Integer Sequences, Vol. 25 (2022), Article 22.1.4.

Crossrefs

Cf. A000142, A033932, A087421, A151800.

Programs

Mathematica

PrimeNext[n_]:=Module[{k},k=n+1;While[ !PrimeQ[k],k++ ];k]; Table[PrimeNext[n! ],{n,40}] (* Vladimir Joseph Stephan Orlovsky, May 30 2010 *)
Table[NextPrime[n!],{n,25}] (* Harvey P. Dale, Dec 12 2010 *)

Python

from sympy import factorial, nextprime
def a(n): return nextprime(factorial(n))
print([a(n) for n in range(1, 23)]) # Michael S. Branicky, May 22 2022

Formula

a(n) = A151800(A000142(n)) = A000142(n) + A033932(n).

Extensions

Extended by Ray Chandler, Mar 07 2010