Search: id:A065421
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%I A065421
%S A065421 1,9,0,2,1,6,0,5,8,3,1,0,4
%N A065421 Decimal expansion of Viggo Brun's constant B, also known as the twin 
               primes Brun's constant B_2: Sum (1/p + 1/q) as (p,q) runs through 
               the twin primes.
%C A065421 Another constant related to the twin primes is the twin primes constant 
               C_2 (sometimes also denoted PI_2) A005597 defined in connection with 
               the Hardy-Littlewood conjecture concerning the distribution pi_2(x) 
               of the twin primes.
%D A065421 V. Brun, La serie 1/5 + 1/7 + 1/11 + 1/13 + 1/17 + 1/19 + 1/29 + 1/31 
               + 1/41 + 1/43 + 1/59 + 1/61 + ... ou les denominateurs sont "nombres 
               premiers jumeaux" est convergente ou finie, Bull Sci. Math. 43 (1919) 
               100-104 and 124-128.
%D A065421 R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, 
               Springer, NY, 2001; see p. 14.
%D A065421 S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 133-135.
%D A065421 D. Shanks and J. W. Wrench, Brun's constant, Math. Comp. 28 (1974) 293-299; 
               28 (1974) 1183; Math. Rev. 50 #4510.
%H A065421 C. K. Caldwell, The Prime Glossary, <a href="http://primes.utm.edu/glossary/
               page.php?sort=BrunsConstant">Brun's constant</a>
%H A065421 S. R. Finch, <a href="http://algo.inria.fr/bsolve/constant/brun/brun.html">
               Brun's Constant</a>
%H A065421 P. Sebah, <a href="http://numbers.computation.free.fr/Constants/Primes/
               twin.html">Numbers, constants and computation</a>
%H A065421 T. R. Nicely, <a href="http://www.trnicely.net/twins/twins.html">Enumeration 
               to 10^14 of the twin primes and Brun's constant</a>.
%H A065421 T. R. Nicely, <a href="http://www.trnicely.net/counts.html">Prime Constellations 
               Research Project</a>
%H A065421 Wikipedia, <a href="http://en.wikipedia.org/wiki/Brun%27s_constant">Brun's 
               constant</a>
%F A065421 (1/3+1/5) + (1/5+1/7) + (1/11+1/13) + ...
%e A065421 1.902160583190 +- 0.000000001175 [Nicely]
%Y A065421 Cf. A005597 Decimal expansion of twin prime constant C_2 = Product_{ 
               p prime >= 3 } (1-1/(p-1)^2).
%Y A065421 Sequence in context: A013570 A065471 A089481 this_sequence A093767 A107091 
               A153790
%Y A065421 Adjacent sequences: A065418 A065419 A065420 this_sequence A065422 A065423 
               A065424
%K A065421 hard,nonn,cons,nice
%O A065421 1,2
%A A065421 Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 08 2000
%E A065421 Corrected by N. J. A. Sloane (njas(AT)research.att.com), Nov 16, 2001
%E A065421 More terms computed by Pascal Sebah (pascal_sebah(AT)ds-fr.com), Jul 
               15, 2001
%E A065421 Further terms computed by Pascal Sebah (psebah(AT)yahoo.fr), Aug 22 2002
%E A065421 Commented and edited by Daniel Forgues (squid(AT)zensearch.com), Jul 
               28 2009

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