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%I #4 Aug 24 2016 12:11:54
%S 4253,626617,1841681,2169007,2484931,9198577,9600571,16738861,
%T 21240283,21836767,23121403,23405593,27437131,31189801,33615229,
%U 36035029,44275331,57940061,65499923,79780271,81630529,83169227,108246967,111928343
%N Ennea-Primes. Prime Numbers n (single prime number in-between 8 twin primes) such that Sum of 9 prime numbers (8 twin primes and single prime number in-between) are primes.
%C {5 penta-} {9 ennea-} Table of non-technical numeric prefixes -- http://en.wikipedia.org/wiki/Numerical_prefix
%e {4229,4231} {4241,4243} {4253} {4259,4261} {4271,4273} Sum = 38261.
%t a={};Do[p0=Prime[n];a1=Prime[n-4];a2=Prime[n-3];b1=Prime[n-2];b2=Prime[n-1];c1=Prime[n+1];c2=Prime[n+2];d1=Prime[n+3];d2=Prime[n+4];sp=a1+a2+b1+b2+p0+c1+c2+d1+d2;If[PrimeQ[sp]&&a2-a1==2&&b2-b1==2&&c2-c1==2&&d2-d1==2,AppendTo[a,p0]],{n,5,10^6}];a
%t spn8Q[m_]:=Module[{d=Differences[m]},PrimeQ[Total[m]]&&d[[1]] == d[[3]] == d[[6]] == d[[8]]==2]; Select[Partition[Prime[Range[650000]],9,1],spn8Q][[All,5]] (* _Harvey P. Dale_, Aug 24 2016 *)
%K nonn,uned
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, May 08 2008
%E More terms from _Harvey P. Dale_, Aug 24 2016
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