|
%I #33 Apr 29 2023 13:59:54
%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 Primes p such that p + 12 is also 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_
|
