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Brun's constant
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(Definition)
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Brun's constant is the sum of the reciprocals of all twin primes \begin{equation*} B=\sum_{\substack{p\\p+2 \text{ is prime}}} \left(\frac{1}{p}+\frac{1}{p+2}\right)\approx 1.9216058. \end{equation*}Viggo Brun proved that the constant exists by using a new sieving method, which later became known as Brun's sieve.
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"Brun's constant" is owned by bbukh.
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Cross-references: twin primes, reciprocals, sum
There is 1 reference to this entry.
This is version 5 of Brun's constant, born on 2002-12-27, modified 2006-11-03.
Object id is 3847, canonical name is BrunsConstant.
Accessed 5455 times total.
Classification:
| AMS MSC: | 11N05 (Number theory :: Multiplicative number theory :: Distribution of primes) | | | 11N36 (Number theory :: Multiplicative number theory :: Applications of sieve methods) |
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Pending Errata and Addenda
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