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In particular we propose an analytical formula for the sum of reciprocals of gaps between consecutive primes $<x : ~ M_{-1}(x)\\sim \\frac{\\pi^2(x)}{x-2\\pi(x)}\\log\\Big(\\frac{x}{2\\pi(x)}\\Big) \\sim x \\log \\log(x)/\\log^2(x)$. 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