A178641 -id:A178641 - cp's OEIS frontend

A178642 Primes p such that primorial(p)/2 - 2 is not prime.

3, 29, 37, 43, 47, 59, 61, 67, 73, 79, 83, 89, 97, 101, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347

Offset: 1

Vladimir Joseph Stephan Orlovsky, May 31 2010

nonn

			3*5*7*11*13*17*19*23*29 - 2 = 43*167*450473 is composite.

Cf. A002110, A096177, A096547, A178641.

pp=1;lst={};Do[p=Prime[n];pp*=p;If[ !PrimeQ[pp-2],AppendTo[lst,p]],{n,2,2*5!}];lst
Transpose[Select[With[{pros=Rest[FoldList[Times,1,Prime[Range[100]]]]}, Table[ {Prime[n], pros[[n]]},{n,100}]],!PrimeQ[Last[#]/2-2]&]][[1]] (* Harvey P. Dale, Mar 02 2012 *)

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

A178642 Primes p such that primorial(p)/2 - 2 is not prime.

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