A151894 Numbers k such that k! + second prime after k! is prime.

2, 3, 5, 6, 7, 8, 11, 17, 42, 66, 76, 93, 139, 157, 226, 290, 415, 522, 774, 794, 1947

Offset: 1

Author

Artur Jasinski, Apr 12 2008

Keywords

• nonn
• more
• hard

Comments

Because numbers of the form (k! + prime) are divisible by all primes <= k that means that the first prime number can have the form k! + next prime after k! and no primes of the form k! + m for m > 1 and m < next prime after k!.

Crossrefs

Cf. A002981, A151892, A151893, A151903.

Programs

Mathematica

a = {}; Do[If[PrimeQ[n! + NextPrime[n!,2]], AppendTo[a, n]], {n, 200}]; a

PARI

is(k) = {my(f = k!); isprime(f + nextprime(nextprime(f + 1) + 1));} \\ Amiram Eldar, Oct 23 2024

Extensions

a(15)-a(20) from Amiram Eldar, Oct 23 2024

a(21) from Michael S. Branicky, Oct 24 2024