This article is cited in 2 papers

Properties of large prime divisors of numbers of the form $p-1$

M. A. Cherepnev

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The main result of this paper is the fact that the fraction of primes $p\le x$ satisfying the condition that $p-1$ has a prime divisor $q>\exp(\ln x/\ln\ln x)$ and the number of prime divisors of $q-1$ essentially differ from $\ln\ln(x/n)$, where $n=(p-1)/q$, tends to zero as $x$ increases.

UDC: 511

Received: 29.03.2004
Revised: 04.05.2006

DOI: 10.4213/mzm3367

 English version: Mathematical Notes, 2006, 80:6, 863–867

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