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A124582 Primes p such that q-p >= 6, where q is the next prime after p.

%I A124582 #23 Mar 29 2016 16:41:12
%S A124582 23,31,47,53,61,73,83,89,113,131,139,151,157,167,173,181,199,211,233,
%T A124582 241,251,257,263,271,283,293,317,331,337,353,359,367,373,383,389,401,
%U A124582 409,421,433,443,449,467,479,491,503,509,523,541,547,557,563,571,577
%N A124582 Primes p such that q-p >= 6, where q is the next prime after p.
%H A124582 R. Zumkeller, <a href="/A124582/b124582.txt">Table of n, a(n) for n = 1..1000</a>
%H A124582 K. Soundararajan, <a href="http://dx.doi.org/10.1090/S0273-0979-06-01142-6">Small gaps between prime numbers: the work of Goldston-Pintz-Yildirim</a>, Bull. Amer. Math. Soc., 44 (2007), 1-18.
%H A124582 <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>
%F A124582 a(n) ~ n log n. - _Charles R Greathouse IV_, Jun 04 2015
%p A124582 d:=6; M:=1000; t0:=[]; for n from 1 to M do p:=ithprime(n); if nextprime(p) - p >= d then t0:=[op(t0),p]; fi; od: t0;
%t A124582 t={};q=6;Do[If[Prime[n+6]-Prime[n+5]>=q,AppendTo[t,Prime[n+5]]],{n,1,200}];t (* _Vladimir Joseph Stephan Orlovsky_, Feb 02 2012 *)
%t A124582 Transpose[Select[Partition[Prime[Range[200]],2,1],#[[2]]-#[[1]] >= 6&]] [[1]] (* _Harvey P. Dale_, May 15 2013 *)
%o A124582 (PARI) is(n)=!isprime(n+2) && !isprime(n+4) && n>2 && isprime(n) \\ _Charles R Greathouse IV_, Jun 04 2015
%Y A124582 Complement of A124589.
%Y A124582 Cf. A134099, A134100, A134101.
%K A124582 nonn
%O A124582 1,1
%A A124582 _N. J. A. Sloane_, Dec 19 2006