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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 863.11058

**Autor: ** Erdös, Paul; Nathanson, Melvyn B.

**Title: ** On the sum of the reciprocals of the differences between consecutive primes. (In English)

**Source: ** Chudnovsky, D. V. (ed.) et al., Number theory: New York seminar, 1991-1995. New York, NY: Springer, 97-101 (1996).

**Review: ** This paper asks, for which values of c does the sum **sum**^{oo}_{n = 2} {1\over {n(log log n)^{c}(p_{n+1}-p_{n})}}, where p_{n} is the nth prime, converge? It is shown that the sum converges for c > 2, and a heuristic argument, suggesting divergence for c = 2, is presented. The proofs are elementary.

**Reviewer: ** D.R.Heath-Brown (Oxford)

**Classif.: ** * 11N05 Distribution of primes

**Keywords: ** sum of reciprocals of the differences between consecutive primes

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