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Primes of form: sum of prime 5-tuples (A022007).
0

%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