On the largest prime factor of shifted primes

Authors
Chen, Feng Juan Chen, Yong Gao
Citation
Chen, Feng Juan et Chen, Yong Gao, On the largest prime factor of shifted primes, Acta mathematica Sinica. English series (Print) , 33(3), 2017, pp. 377-382
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
33
Issue
3
Year of publication
2017
Pages
377 - 382
Database
ACNP
SICI code
Abstract
For any integer n . 2, let P(n) be the largest prime factor of n. In this paper, we prove that the number of primes p . x with P(p.1) . p c is more than (1.c+o(1)).(x) for 0 < c < 1/2. This extends a recent result of Luca, Menares and Madariaga for 1/4 . c . 1/2. We also pose two conjectures for further research.