A057706 Smaller of twin primes whose average is a primorial number.

5, 29, 2309

Offset: 1

Author

Labos Elemer, Oct 24 2000

Keywords

• nonn
• bref

Comments

According to Caldwell, the next term, if it exists, has more than 100000 digits. - T. D. Noe, May 08 2012

Examples

			(5+7)/2 = 6 = 2*3, (29+31)/2 = 30 = 2*3*5, (2309+2311)/2 = 2310 = 2*3*5*7*11.
		

Links

• Chris K. Caldwell, Primorial prime.
• Rudolf Ondrejka, The Top Ten: a Catalogue of Primal Configurations, 2001, tables 20A, 20B.
• Eric Weisstein's World of Mathematics, Primorial Prime.
• Index entries for sequences related to primorial numbers.

Crossrefs

Cf. A000040 (primes), A002110 (primorials, p#).

Cf. A006862 (Euclid, p#+1), A005234 (prime p#+1), A014545 (index prime p#+1).

Cf. A057588 (Kummer, p#-1), A006794 (prime p#-1), A057704 (index prime p#-1).

Programs

Mathematica

Select[FoldList[Times, Prime@ Range@ 40], AllTrue[# + {-1, 1}, PrimeQ] &] - 1 (* Michael De Vlieger, Jul 15 2017 *)

Python

from sympy import isprime, prime, primerange
def auptoprimorial(limit):
  phash, alst = 1, []
  for p in primerange(1, prime(limit)+1):
    phash *= p
    if isprime(phash-1) and isprime(phash+1): alst.append(phash-1)
  return alst
print(auptoprimorial(5)) # Michael S. Branicky, May 29 2021

Extensions

Offset corrected by Arkadiusz Wesolowski, May 08 2012