%I #6 Dec 20 2022 19:19:16
%S 67,17317,80317,97117,398467,1333417,1423717,1876267,2317267,3332167,
%T 4890367,5456317,5911417,6151867,6622867,9151717,9522367,11013967,
%U 13372717,15381967,17080267,21663067,22439017,22552417,24262267
%N Primes of form: sum of prime 5-tuples (A022007).
%F 7+11+13+17+19=67
%t lst={};Do[p=Prime[n];If[PrimeQ[p+4]&&PrimeQ[p+6]&&PrimeQ[p+10]&&PrimeQ[p+12],s=p+p+4+p+6+p+10+p+12;If[PrimeQ[s],AppendTo[lst,s]]],{n,10!}];lst
%t Select[Total/@Select[Partition[Prime[Range[350000]],5,1],Differences[#]=={4,2,4,2}&],PrimeQ] (* _Harvey P. Dale_, Dec 20 2022 *)
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Sep 25 2008