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%I A046133 #33 Apr 29 2023 13:59:54
%S A046133 5,7,11,17,19,29,31,41,47,59,61,67,71,89,97,101,127,137,139,151,167,
%T A046133 179,181,199,211,227,229,239,251,257,269,271,281,337,347,367,389,397,
%U A046133 409,419,421,431,449,467,479,487,491,509,557,587,601,607,619,631,641
%N A046133 Primes p such that p + 12 is also prime.
%C A046133 Using the Elliott-Halberstam conjecture, Maynard proves that there are an infinite number of primes here. - _T. D. Noe_, Nov 26 2013
%D A046133 P. D. T. A. Elliott and H. Halberstam, A conjecture in prime number theory, Symposia Mathematica, Vol. IV (INDAM, Rome, 1968/69), pages 59-72, Academic Press, London, 1970.
%H A046133 T. D. Noe, <a href="/A046133/b046133.txt">Table of n, a(n) for n = 1..1000</a>
%H A046133 James Maynard, <a href="https://arxiv.org/abs/1311.4600">Small gaps between primes</a>, arXiv:1311.4600 [math.NT], 2013-2019.
%H A046133 Maxie D. Schmidt, <a href="https://arxiv.org/abs/1701.04741">New Congruences and Finite Difference Equations for Generalized Factorial Functions</a>, arXiv:1701.04741 [math.CO], 2017.
%H A046133 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TwinPrimes.html">Twin Primes</a>.
%H A046133 Wikipedia, <a href="http://en.wikipedia.org/wiki/Elliott-Halberstam_conjecture">Elliott-Halberstam conjecture</a>.
%F A046133 a(n) >> n log^2 n. \\ _Charles R Greathouse IV_, Apr 28 2015
%t A046133 Select[Range[1000], PrimeQ[#] && PrimeQ[#+12]&] (* _Vladimir Joseph Stephan Orlovsky_, Aug 29 2008 *)
%t A046133 Select[Prime[Range[200]],PrimeQ[#+12]&] (* _Harvey P. Dale_, Jan 16 2016 *)
%o A046133 (PARI) select(p->isprime(p+12), primes(100)) \\ _Charles R Greathouse IV_, Apr 28 2015
%Y A046133 Different from A015917.
%K A046133 nonn
%O A046133 1,1
%A A046133 _Eric W. Weisstein_

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