## Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  296.10021
Autor:  Erdös, Paul; Shorey, T.N.
Title:  On the greatest prime factor of 2p-1 for a prime p and other expressions. (In English)
Source:  Acta Arith. 30, 257-265 (1976).
Review:  It is proved that for almost all primes p, the greatest prime factor of (2p-1) exceeds cp ({log p \over log log p})2 where c > 0 is an absolute constant. The proof depends on Brun's Sieve method and Baker's theory on linear forms in the logarithms of algebraic numbers. Some results relating to the greatest prime factor of other arithmetic expressions are also proved.
Classif.:  * 11N05 Distribution of primes
11B99 Sequences and sets
11B39 Special numbers, etc.

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