Difference between revisions of "Brun's constant"

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Brun's constant $B_2$ is the sum of the reciprocals of the pairs of [[twin prime|twin primes]], i.e.
 
Brun's constant $B_2$ is the sum of the reciprocals of the pairs of [[twin prime|twin primes]], i.e.
$$B_2 = \displaystyle\sum_{p,p+2 \mathrm{\hspace{2pt} prime}} \dfrac{1}{p} + \dfrac{1}{p+2}.$$
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$$B_2 = \displaystyle\sum_{p,p+2 \mathrm{\hspace{2pt} prime}} \dfrac{1}{p} + \dfrac{1}{p+2}=1.9021605831\ldots.$$
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=References=
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[http://www.ams.org/journals/mcom/1974-28-125/S0025-5718-1974-0352022-X/S0025-5718-1974-0352022-X.pdf Brun's constant]<br />
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[http://gallica.bnf.fr/ark:/12148/bpt6k486270d La série 1/5+1/7+1/11+1/13+1/17+1/19+1/29+1/31+1/41+1/43+1/59+1/61+..., où les dénominateurs sont nombres premiers jumeaux est convergente ou finie]
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[[Category:SpecialFunction]]

Latest revision as of 18:58, 24 May 2016

Brun's constant $B_2$ is the sum of the reciprocals of the pairs of twin primes, i.e. $$B_2 = \displaystyle\sum_{p,p+2 \mathrm{\hspace{2pt} prime}} \dfrac{1}{p} + \dfrac{1}{p+2}=1.9021605831\ldots.$$

References

Brun's constant
La série 1/5+1/7+1/11+1/13+1/17+1/19+1/29+1/31+1/41+1/43+1/59+1/61+..., où les dénominateurs sont nombres premiers jumeaux est convergente ou finie