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# Brun’s constant

*Brun’s constant* is the sum of the reciprocals of all twin primes

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

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

Keywords:

Brun's sieve, twin primes

Related:

BrunsPureSieve

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

11N36*no label found*11N05

*no label found*

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