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%I #11 Jan 09 2021 02:47:56
%S 3,29,37,43,47,59,61,67,73,79,83,89,97,101,107,109,113,127,131,137,
%T 139,149,151,157,163,173,179,181,191,193,197,199,211,223,227,229,233,
%U 239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347
%N Primes p such that primorial(p)/2 - 2 is not prime.
%e 3*5*7*11*13*17*19*23*29 - 2 = 43*167*450473 is composite.
%t pp=1;lst={};Do[p=Prime[n];pp*=p;If[ !PrimeQ[pp-2],AppendTo[lst,p]],{n,2,2*5!}];lst
%t 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 *)
%Y Cf. A002110, A096177, A096547, A178641.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, May 31 2010