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%I #8 Jan 09 2021 02:47:41
%S 11,17,19,23,41,43,53,61,67,71,73,79,83,89,97,101,103,107,113,127,131,
%T 137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,227,229,
%U 233,239,241,251,257,263,269,271,277,281,283,293,311,313,317,331,337
%N Primes p such that primorial(p)/2 + 2 is composite.
%e 3*5*7*11 + 2 = 13*89 is composite.
%t pp=1;lst={};Do[p=Prime[n];pp*=p;If[ !PrimeQ[pp+2],AppendTo[lst,p]],{n,2,2*5!}];lst
%Y Cf. A002110, A096177, A178642, A178648.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, May 31 2010