\begin{definition}[Definition:Brun's Constant]
'''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:
:$B_2 \approx 1 \cdotp 90216 \, 05831 \, 04 \ldots$
{{OEIS|A065421}}
Estimates of its value are occasionally refined as further work is done to establish its nature.
\end{definition}