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%I #5 Apr 11 2022 22:04:42
%S 53,83,7433,978683,1238033,2325833,3168983,3305483,4148633,4289783,
%T 5112533,5456333,5867933,6231833,6842333,12093383,12499733,13820633,
%U 14201333,15516383,18107333,19189283,19470233,21121883,24887183
%N Primes that are the sum of prime 5-tuples (A022006).
%F 5+7+11+13+17=53
%t lst={};Do[p=Prime[n];If[PrimeQ[p+2]&&PrimeQ[p+6]&&PrimeQ[p+8]&&PrimeQ[p+12],s=p+p+2+p+6+p+8+p+12;If[PrimeQ[s],AppendTo[lst,s]]],{n,10!}];lst
%t Select[Total/@Select[Partition[Prime[Range[16*10^5]],5,1],Differences[#] == {2,4,2,4}&],PrimeQ] (* _Harvey P. Dale_, Dec 08 2014 *)
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Sep 25 2008
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