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%I #8 Nov 21 2019 13:57:14
%S 83,97,113,227,229,251,269,271,277,283,313,317,331,353,389,397,419,
%T 433,457,463,491,503,509,523,557,563,593,599,601,617,641,653,683,691,
%U 733,743,751,757,761,773,797,823,829,857,863,937,941,971,977,1013,1031,1049
%N Primes p such that p1 = floor(p/2)+p is not prime and p2 = ceiling(p/2)+p is not prime, p3 = floor(p1/2)+p1 is not prime and p5 = ceiling(p1/2)+p1 is not prime, p4 = floor(p2/2)+p2 is not prime and p6 = ceiling(p2/2)+p2 is not prime.
%t lst={};Do[p=Prime[n];If[ !PrimeQ[p1=Floor[p/2]+p]&&!PrimeQ[p2=Ceiling[p/2]+p],If[ !PrimeQ[p3=Floor[p1/2]+p1]&&!PrimeQ[p5=Ceiling[p1/2]+p1],If[ !PrimeQ[p4=Floor[p2/2]+p2]&&!PrimeQ[p6=Ceiling[p2/2]+p2],AppendTo[lst,Prime[n]]]]],{n,6!}];lst
%t nonpQ[p_]:=Module[{p1=Floor[p/2]+p,p2=Ceiling[p/2]+p},NoneTrue[ {p1,p2,Floor[ p1/2]+p1,Ceiling[p1/2]+p1,Floor[p2/2]+p2,Ceiling[p2/2]+ p2},PrimeQ]]; Select[Prime[Range[200]],nonpQ] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Nov 21 2019 *)
%Y Cf. A158708, A158709, A158710, A158711, A158712, A158713, A158714.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Mar 24 2009