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Sum of reciprocals of maximal prime gaps and primes

Let $G_r =$ http://oeis.org/A005250, and $P_r =$ http://oeis.org/A002386. $\sum_{n=1}^{\infty}{\frac{1}{G_r}} = c_1$ $\sum_{n=1}^{\infty}{\frac{1}{P_r}} = c_2$ Do the constants c_1 and c_2 exist? The …