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

sumoon = 2 {1\over {n(log log n)c(pn+1-pn)}},

where pn 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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