A178642 -id:A178642 - cp's OEIS frontend

A178641 Primes p such that primorial(p)/2 + 2 is composite.

11, 17, 19, 23, 41, 43, 53, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 311, 313, 317, 331, 337

Offset: 1

Vladimir Joseph Stephan Orlovsky, May 31 2010

nonn

			3*5*7*11 + 2 = 13*89 is composite.

Cf. A002110, A096177, A178642, A178648.

pp=1;lst={};Do[p=Prime[n];pp*=p;If[ !PrimeQ[pp+2],AppendTo[lst,p]],{n,2,2*5!}];lst

A178648 Primes p such that primorial(p)/2 +- 2 are primes.

Original entry on oeis.org

5, 7, 13, 31

Offset: 1

Vladimir Joseph Stephan Orlovsky, May 31 2010

No further terms up to the 500th prime, i.e., 3571. - Harvey P. Dale, May 09 2023

			3*5 = 15; 15-2 and 15+2 are primes.

Carlos Rivera, Puzzle 974. More twins like these..., The Prime Puzzles & Problems Connection.

Cf. A070826, A178641, A178642.

Intersection of A096177 and A096547.

pp=1;lst={};Do[p=Prime[n];pp*=p;If[PrimeQ[pp-2]&&PrimeQ[pp+2],Print[Date[],p];AppendTo[lst,p]],{n,2,4!}];lst
Module[{nn=15,pr,pm},pr=Prime[Range[nn]];pm=FoldList[Times,pr];Select[Thread[ {pr,pm}],AllTrue[ #[[2]]/2+{2,-2},PrimeQ]&]][[;;,1]] (* Harvey P. Dale, May 09 2023 *)

cp's OEIS Frontend

A178641 Primes p such that primorial(p)/2 + 2 is composite.

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