Difference between revisions of "Brun's constant"
From specialfunctionswiki
| (2 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
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. | ||
$$B_2 = \displaystyle\sum_{p,p+2 \mathrm{\hspace{2pt} prime}} \dfrac{1}{p} + \dfrac{1}{p+2}=1.9021605831\ldots.$$ | $$B_2 = \displaystyle\sum_{p,p+2 \mathrm{\hspace{2pt} prime}} \dfrac{1}{p} + \dfrac{1}{p+2}=1.9021605831\ldots.$$ | ||
| + | |||
| + | =References= | ||
| + | [http://www.ams.org/journals/mcom/1974-28-125/S0025-5718-1974-0352022-X/S0025-5718-1974-0352022-X.pdf Brun's constant]<br /> | ||
| + | [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] | ||
| + | |||
| + | [[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
