PlanetMath: Brun's constant

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Brun's constant

(Definition)

Brun's constant is the sum of the reciprocals of all twin primes

$\displaystyle B=\sum_{\substack{p\\ p+2 \text{ is prime}}} \left(\frac{1}{p}+\frac{1}{p+2}\right)\approx 1.9216058.$

Viggo Brun proved that the constant exists by using a new sieving method, which later became known as Brun's sieve.

"Brun's constant" is owned by bbukh.

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Keywords:

Brun's sieve, twin primes

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Cross-references: twin primes, reciprocals, sum
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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 4732 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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