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**Zentralblatt MATH**

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

**Zbl.No: ** 245.10032

**Autor: ** Erdös, Paul

**Title: ** Some problems on consecutive prime numbers. (In English)

**Source: ** Mathematika, Lond. 19, 91-95 (1972).

**Review: ** Continuing his work on consecutive primes, it is proved here that the number of (k-1)-tuples **{**d_{n+1}, ... ,d_{n+k-1} **}**, **max** **{**d_{n+1}: 1 \leq i \leq k-1 **}** < 10 k log x, 1 \leq n \leq x, is greater than c(log x)^{k-1}, where d_{j} = p_{j+1}-p_{j}. Some related results and conjectures are included.

**Reviewer: ** R.G.Buschmann

**Classif.: ** * 11N13 Primes in progressions

11N35 Sieves

11N05 Distribution of primes

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