Alternating sum of the reciprocals of the twin primes $\sum(\frac1p-\frac1{p+2})$

Question

I ask if the limit of the alternating sum of the reciprocals of the twin primes $$\sum_{p,\,p+2\,\in\,P}\Big(\frac1p-\frac1{p+2}\Big)=\frac13-\frac15+\frac15-\frac17+\frac1{11}-\frac1{13}\;+\;...=0.2159679498...$$ has been ever named in any way, similarly to Brun's constant.

Many thanks.