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The analysis reveals unconditional insights on prime gaps, suggesting implications for divergence in sums of reciprocals.
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.
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Magyar et al. (2025) studied this question.
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