

A046133


p and p+12 are both prime.


25



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 ElliottHalberstam 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 5972, 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], 20132019.
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, ElliottHalberstam 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



