A096547 Primes p such that primorial(p)/2 - 2 is prime.

5, 7, 11, 13, 17, 19, 23, 31, 41, 53, 71, 103, 167, 431, 563, 673, 727, 829, 1801, 2699, 4481, 6121, 7283, 9413, 10321, 12491, 17807, 30307, 31891, 71917, 172517

Offset

1,1

Comments

Some of the results were computed using the PrimeFormGW (PFGW) primality-testing program. - Hugo Pfoertner, Nov 14 2019

a(32) > 180000. - Tyler Busby, Mar 29 2024

Links

Table of n, a(n) for n=1..31.

Example

Prime 7 is a term because primorial(7)/2 - 2 = A034386(7)/2 - 2 = 2*3*5*7/2 - 2 = 103 is prime.

Maple

b:= proc(n) b(n):= `if`(n=0, 1, `if`(isprime(n), n, 1)*b(n-1)) end:
q:= p-> isprime(p) and isprime(b(p)/2-2):
select(q, [$1..500])[];

Mathematica

k = 1; Do[k *= Prime[n]; If[PrimeQ[k - 2], Print[Prime[n]]], {n, 2, 3276}] (* Ryan Propper, Oct 25 2005 *&)
Prime[#]&/@Flatten[Position[FoldList[Times, Prime[Range[1000]]]/2-2, _?PrimeQ]] (* Harvey P. Dale, Jun 09 2023 *)

Crossrefs

Cf. A070826, A096177 primes p such that primorial(p)/2+2 is prime, A096178 primes of the form primorial(p)/2+2, A014545 primorial primes, A087398.

Cf. A034386.

Sequence in context: A230227 A101635 A118941 * A216524 A128824 A098420

Adjacent sequences: A096544 A096545 A096546 * A096548 A096549 A096550

Keyword

nonn,more,hard

Author

Hugo Pfoertner, Jun 27 2004

Extensions

5 more terms from Ryan Propper, Oct 25 2005

a(29)-a(31) from Tyler Busby, Mar 16 2024

Status

approved