A087421 -id:A087421 - cp's OEIS frontend

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

Jud McCranie

nonn

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.

Cf. A000142, A033932, A087421, A151800.

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 *)

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

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

Extended by Ray Chandler, Mar 07 2010

A187874 Second smallest prime after n!.

Original entry on oeis.org

3, 3, 5, 11, 31, 131, 733, 5059, 40351, 362903, 3628819, 39916817, 479001643, 6227020873, 87178291241, 1307674368149, 20922789888041, 355687428096053, 6402373705728061, 121645100408832109, 2432902008176640037, 51090942171709440037

Offset: 0

Vladimir Joseph Stephan Orlovsky, Mar 14 2011

nonn

			2!=2, second smallest prime=5;
3!=6, second smallest prime=11; ..

Cf. A037151, A037152, A087421.

Mathematica
```
NextPrime[Range[0, 30]!, 2]
```

cp's OEIS Frontend

A037151 Smallest prime > n!.

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