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

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

(PARI) select(p->isprime(p+12), primes(100)) \\ Charles R Greathouse IV, Apr 28 2015

Crossrefs

Different from A015917.

Sequence in context: A254672 A056775 A015917 * A086136 A136052 A301913

Adjacent sequences: A046130 A046131 A046132 * A046134 A046135 A046136

Keyword

nonn

Author

Eric W. Weisstein

Status

approved