# Definition:Brun's Constant

## Definition

Brun's constant is the sum of the series consisting of the reciprocals of the twin primes:

$B_2 := \paren {\dfrac 1 3 + \dfrac 1 5} + \paren {\dfrac 1 5 + \dfrac 1 7} + \paren {\dfrac 1 {11} + \dfrac 1 {13} } + \paren {\dfrac 1 {17} + \dfrac 1 {19} } + \paren {\dfrac 1 {29} + \dfrac 1 {31} } + \cdots$

Its approxmiate decimal expansion is:

$B_2 \approx 1 \cdotp 90216 \, 05831 \, 04 \ldots$

Estimates of its value are occasionally refined as further work is done to establish its nature.

## Also defined as

Some sources do not include one of the instances of $\dfrac 1 5$.

## Source of Name

This entry was named for Viggo Brun.