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%I #4 Jun 21 2012 17:15:00
%S 3,5,29,71,113,263,1103,2339,3203,3413,3593,3659,3719,4421,5939,6269,
%T 7841,9011,9029,13121,13841,14423,15671,17033,19073,22079,22811,26783,
%U 27851,28949,29303,30839,31973,32063,32141,34301,38543,38873,39119
%N Primes p such that (p-1)*p*(p+1)-p-2 and (p-1)*p*(p+1)+p+2 are primes.
%C 2*3*4=24-3-2=19, 2*3*4=24+3+2=29, ...
%t lst={};Do[p=Prime[n];If[PrimeQ[(p-1)*p*(p+1)-p-2]&&PrimeQ[(p-1)*p*(p+1)+p+2],AppendTo[lst,p]],{n,8!}];lst
%t prQ[n_]:=Module[{x=n^3-n,y=n+2},And@@PrimeQ[{x+y,x-y}]]; Select[Prime[ Range[4200]],prQ] (* _Harvey P. Dale_, Jun 21 2012 *)
%Y Cf. A053184, A038872, A141158, A038615, A098058, A038936, A089270, A140559, A154939
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jan 17 2009