Sum of Reciprocals of Twin Primes

Theorem
The sum of the reciprocals of all the twin primes:
 * $\dfrac 1 3 + \dfrac 1 5 + \dfrac 1 7 + \dfrac 1 {11} + \dfrac 1 {13} + \dfrac 1 {17} + \dfrac 1 {19} + \dfrac 1 {29} + \dfrac 1 {31} + \cdots$

is either finite or convergent.