In a recent work Friedlander studied the problem of how large consecutive prime gaps should be in order that the sum of the reciprocals should be divergent. Supposing a very deep Hypothesis, a generalization of the Hardy--Littlewood prime k-tuple conjecture, he gave an almost precise answer for it. In the present work we give an unconditional answer for a much weaker form of the same problem.
Magyar et al. (Mon,) studied this question.