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%I #6 May 02 2023 15:20:38
%S 5,11,1031,2711,3851,4421,5867,8837,10067,12041,12251,12611,17957,
%T 21491,21521,22037,22481,23537,32141,32411,42641,48311,48731,49367,
%U 50261,53231,60167,72167,77417,80147,80447,81047,87641,88337,90527,95231
%N Lesser of twin primes p1 such that p1*p2-4 and p1*p2-6 are twin prime numbers.
%C 5*7=35; 35-4=31; 35-6=29; 29,31 twin primes
%H Harvey P. Dale, <a href="/A174957/b174957.txt">Table of n, a(n) for n = 1..1000</a>
%t lst={};Do[p1=Prime[n];p2=p1+2;If[PrimeQ[p2]&&PrimeQ[p1*p2-4]&&PrimeQ[p1*p2-6],(*Print[p1];*)AppendTo[lst,p1]],{n,8!}];lst
%t ltp[{a_,b_}]:=b-a==2&&AllTrue[a*b-{4,6},PrimeQ]; Select[Partition[Prime[ Range[ 10000]],2,1],ltp][[All,1]] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Dec 07 2017 *)
%Y Cf. A001359, A174913, A174915, A174916, A174917, A174920, A174922, A174955.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Apr 02 2010