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
Keywords
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.
Crossrefs
Different from A015917.
Programs
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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 *)
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PARI
select(p->isprime(p+12), primes(100)) \\ Charles R Greathouse IV, Apr 28 2015
Formula
a(n) >> n log^2 n. \\ Charles R Greathouse IV, Apr 28 2015
Comments