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A046133 p and p+12 are both prime. 25


%S 5,7,11,17,19,29,31,41,47,59,61,67,71,89,97,101,127,137,139,151,167,

%T 179,181,199,211,227,229,239,251,257,269,271,281,337,347,367,389,397,

%U 409,419,421,431,449,467,479,487,491,509,557,587,601,607,619,631,641

%N p and p+12 are both prime.

%C Using the Elliott-Halberstam conjecture, Maynard proves that there are an infinite number of primes here. - _T. D. Noe_, Nov 26 2013

%D 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 T. D. Noe, <a href="/A046133/b046133.txt">Table of n, a(n) for n = 1..1000</a>

%H James Maynard, <a href="https://arxiv.org/abs/1311.4600">Small gaps between primes</a>, arxiv 1311.4600 [math.NT], 2013-2019.

%H 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TwinPrimes.html">Twin Primes</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Elliott-Halberstam_conjecture">Elliott-Halberstam conjecture</a>

%F a(n) >> n log^2 n. \\ _Charles R Greathouse IV_, Apr 28 2015

%t Select[Range[1000], PrimeQ[#] && PrimeQ[#+12]&] (* _Vladimir Joseph Stephan Orlovsky_, Aug 29 2008 *)

%t Select[Prime[Range[200]],PrimeQ[#+12]&] (* _Harvey P. Dale_, Jan 16 2016 *)

%o (PARI) select(p->isprime(p+12), primes(100)) \\ _Charles R Greathouse IV_, Apr 28 2015

%Y Different from A015917.

%K nonn

%O 1,1

%A _Eric W. Weisstein_

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Last modified February 25 19:39 EST 2021. Contains 341618 sequences. (Running on oeis4.)