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
KEYWORD
nonn
AUTHOR
STATUS
approved