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%I #25 Apr 03 2023 10:36:09
%S 5,29,2309
%N Smaller of twin primes whose average is a primorial number.
%C According to Caldwell, the next term, if it exists, has more than 100000 digits. - _T. D. Noe_, May 08 2012
%H Chris K. Caldwell, <a href="https://t5k.org/glossary/page.php?sort=PrimorialPrime">Primorial prime</a>.
%H Rudolf Ondrejka, <a href="https://primes.utm.edu/lists/top_ten/topten.pdf">The Top Ten: a Catalogue of Primal Configurations</a>, 2001, tables 20A, 20B.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimorialPrime.html">Primorial Prime</a>.
%H <a href="https://oeis.org/wiki/Index_to_OEIS:_Section_Pri#primorial_numbers.2C_sequences_related_to_:">Index entries for sequences related to primorial numbers</a>.
%e (5+7)/2 = 6 = 2*3, (29+31)/2 = 30 = 2*3*5, (2309+2311)/2 = 2310 = 2*3*5*7*11.
%t Select[FoldList[Times, Prime@ Range@ 40], AllTrue[# + {-1, 1}, PrimeQ] &] - 1 (* _Michael De Vlieger_, Jul 15 2017 *)
%o (Python)
%o from sympy import isprime, prime, primerange
%o def auptoprimorial(limit):
%o phash, alst = 1, []
%o for p in primerange(1, prime(limit)+1):
%o phash *= p
%o if isprime(phash-1) and isprime(phash+1): alst.append(phash-1)
%o return alst
%o print(auptoprimorial(5)) # _Michael S. Branicky_, May 29 2021
%Y Cf. A000040 (primes), A002110 (primorials, p#).
%Y Cf. A006862 (Euclid, p#+1), A005234 (prime p#+1), A014545 (index prime p#+1).
%Y Cf. A057588 (Kummer, p#-1), A006794 (prime p#-1), A057704 (index prime p#-1).
%K nonn,bref
%O 1,1
%A _Labos Elemer_, Oct 24 2000
%E Offset corrected by _Arkadiusz Wesolowski_, May 08 2012
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