A096177 Primes p such that primorial(p)/2 + 2 is prime.

2, 3, 5, 7, 13, 29, 31, 37, 47, 59, 109, 223, 307, 389, 457, 1117, 1151, 2273, 9137, 10753, 15727, 25219, 26459, 29251, 30259, 52901, 194471

Offset

1,1

Comments

a(27) > 172000. - Robert Price, May 10 2019

Some of the results were computed using the PrimeFormGW (PFGW) primality-testing program. - Hugo Pfoertner, Nov 16 2019

Links

Table of n, a(n) for n=1..27.

Example

a(3)=7 because primorial(7)/2 + 2 = A070826(4) + 2 = 2*3*5*7/2 + 2 = 107 is prime.

Mathematica

k = 1; Do[If[PrimeQ[n], k = k*n; If[PrimeQ[k/2 + 2], Print[n]]], {n, 2, 100000}] (* Ryan Propper, Jul 03 2005 *)

Prog

(PARI) P=1/2; forprime(p=2, 1e4, if(isprime((P*=p)+2), print1(p", "))) \\ Charles R Greathouse IV, Mar 14 2011

Crossrefs

Cf. A070826, A096178 primes of the form primorial(p)/2+2, A096547 primes p such that primorial(p)/2-2 is prime, A067024 smallest p+2 that has n distinct prime factors, A014545 primorial primes, A087398.

Sequence in context: A037021 A359505 A114741 * A075238 A346408 A158281

Adjacent sequences: A096174 A096175 A096176 * A096178 A096179 A096180

Keyword

more,nonn

Author

Hugo Pfoertner, Jun 27 2004

Extensions

7 additional terms, corresponding to probable primes, from Ryan Propper, Jul 03 2005

Edited by T. D. Noe, Oct 30 2008

a(26) from Robert Price, May 10 2019

a(27) from Tyler Busby, Mar 17 2024

Status

approved