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A137869 Primes p with property that (p - previous prime) >= 6 and (next prime - p) >= 6.

%I A137869 #23 Oct 29 2023 17:55:47
%S A137869 53,89,157,173,211,251,257,263,293,331,337,359,367,373,389,409,449,
%T A137869 479,509,541,547,557,563,577,587,593,607,631,653,683,691,701,709,719,
%U A137869 727,733,751,787,797,839,919,929,947,953,977,983,991,997,1039,1069,1103,1109,1117
%N A137869 Primes p with property that (p - previous prime) >= 6 and (next prime - p) >= 6.
%H A137869 Robert Israel, <a href="/A137869/b137869.txt">Table of n, a(n) for n = 1..10000</a>
%p A137869 M:=1000; t1:=[];
%p A137869 for i from 2 to M do
%p A137869 p:=ithprime(i); o:=prevprime(p); q:=nextprime(p);
%p A137869 if p-o >= 6 and q-p >= 6 then t1:=[op(t1),p]; fi; od:
%p A137869 t1; # _N. J. A. Sloane_
%t A137869 lst={};Do[p=Prime[n];If[ !PrimeQ[p-2]&&!PrimeQ[p+2]&&!PrimeQ[p-4]&&!PrimeQ[p+4],AppendTo[lst,p]],{n,6!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Jul 20 2009 *)
%t A137869 Select[Partition[Prime[Range[200]],3,1],Min[Differences[#]]>5&][[;;,2]] (* _Harvey P. Dale_, Oct 29 2023 *)
%o A137869 (PARI) p=q=2;forprime(r=2,999,r-q>4 & q-p>4 & print1(q","); p=q; q=r) \\ _M. F. Hasler_, May 02 2009
%o A137869 (Magma) [p:p in PrimesInInterval(3,1200)|p-PreviousPrime(p) ge 6 and NextPrime(p)-p ge 6]; // _Marius A. Burtea_, Aug 11 2019
%Y A137869 These are the primes not in A167773.
%Y A137869 Cf. A053070.
%K A137869 nonn
%O A137869 1,1
%A A137869 _Vladimir Joseph Stephan Orlovsky_, Apr 29 2008
%E A137869 Edits and more terms from _N. J. A. Sloane_, May 02 2009