cp's OEIS Frontend

A124590 Primes p such that q-p <= 6, where q is the next prime after p.

%I A124590 #23 Jan 25 2022 13:00:18
%S A124590 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,97,
%T A124590 101,103,107,109,127,131,137,149,151,157,163,167,173,179,191,193,197,
%U A124590 223,227,229,233,239,251,257,263,269,271,277,281,307,311,313,331,347,349,353,367
%N A124590 Primes p such that q-p <= 6, where q is the next prime after p.
%C A124590 Goldston, Graham, Pintz, & Yilidirm give a conditional proof that this sequence is infinite; see their Theorem 4. - _Charles R Greathouse IV_, Jul 31 2013
%H A124590 Charles R Greathouse IV, <a href="/A124590/b124590.txt">Table of n, a(n) for n = 1..10000</a>
%H A124590 D. A. Goldston, S. W. Graham, J. Pintz, C. Y. Yilidirm, <a href="http://arxiv.org/abs/math.NT/0506067">Small gaps between primes or almost primes</a> (2005)
%H A124590 K. Soundararajan, <a href="http://arxiv.org/abs/math/0605696">Small gaps between prime numbers: the work of Goldston-Pintz-Yildirim</a>, Bull. Amer. Math. Soc. 44 (2007), pp. 1-18.
%H A124590 <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>
%F A124590 A000040 MINUS A083371. - _R. J. Mathar_, Jun 15 2008
%F A124590 A124589 UNION A031924. - _R. J. Mathar_, Jan 23 2022
%F A124590 a(n) >> n log^2 n. - _Charles R Greathouse IV_, Jan 31 2017
%o A124590 (PARI) v=List([2]);p=3;forprime(q=5,1e3,if(q-p<=6,listput(v,p));p=q);Vec(v) \\ _Charles R Greathouse IV_, Jul 31 2013
%o A124590 (PARI) list(lim)=my(v=List(),p=2); forprime(q=3,nextprime(lim\1+1), if(q-p<7, listput(v,p)); p=q); Vec(v) \\ _Charles R Greathouse IV_, Jan 31 2017
%Y A124590 Cf. A083371, A124589, A031924.
%K A124590 nonn,easy
%O A124590 1,1
%A A124590 _N. J. A. Sloane_, Dec 19 2006