Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  107.26601
Autor:  Erdös, Pál; Prachar, K.
Title:  Sätze und Probleme über pk/k. (Theorems and problems on pk/k.) (In German)
Source:  Abh. Math. Semin. Univ. Hamb. 25, 251-256 (1962).
Review:  The main result is the following: if pk stands for the kth prime, then c1 log2x \leq sumpk \leq x | {pk+1 \over k+1} - {pk \over k} | \leq c2 log2 x with some positive constants c1,c2. The proof is elementary and appeals only once to an estimate obtainable by Brun's method.
Reviewer:  S.Knapowski
Classif.:  * 11N05 Distribution of primes
                   00A07 Problem books
Index Words:  number theory

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