A046133 - OEIS

A046133

Primes p such that p + 12 is also prime.

5, 7, 11, 17, 19, 29, 31, 41, 47, 59, 61, 67, 71, 89, 97, 101, 127, 137, 139, 151, 167, 179, 181, 199, 211, 227, 229, 239, 251, 257, 269, 271, 281, 337, 347, 367, 389, 397, 409, 419, 421, 431, 449, 467, 479, 487, 491, 509, 557, 587, 601, 607, 619, 631, 641

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OFFSET

1,1

COMMENTS

Using the Elliott-Halberstam conjecture, Maynard proves that there are an infinite number of primes here. - T. D. Noe, Nov 26 2013

REFERENCES

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.

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

James Maynard, Small gaps between primes, arXiv:1311.4600 [math.NT], 2013-2019.

Maxie D. Schmidt, New Congruences and Finite Difference Equations for Generalized Factorial Functions, arXiv:1701.04741 [math.CO], 2017.

Eric Weisstein's World of Mathematics, Twin Primes.

Wikipedia, Elliott-Halberstam conjecture.

FORMULA

a(n) >> n log^2 n. \\ Charles R Greathouse IV, Apr 28 2015

MATHEMATICA

Select[Range[1000], PrimeQ[#] && PrimeQ[#+12]&] (* Vladimir Joseph Stephan Orlovsky, Aug 29 2008 *)

Select[Prime[Range[200]], PrimeQ[#+12]&] (* Harvey P. Dale, Jan 16 2016 *)

PROG