On a conjecture on shifted primes with large prime factors

被引：2
|
作者：
Ding, Yuchen [1 ]
机构：
[1] Yangzhou Univ, Sch Math Sci, Yangzhou 225002, Peoples R China
来源：
ARCHIV DER MATHEMATIK | 2023年 / 120卷 / 03期
基金：
中国国家自然科学基金; 中国博士后科学基金;
关键词：
Shifted prime; The Bombieri-Vinogradov theorem; Dichotomy; Exceptional set; VALUES;
D O I：
10.1007/s00013-022-01820-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let P be the set of all primes and pi(x) be the number of primes up to x. For any n >= 2, let P+(n) be the largest prime factor of n. For 0 < c < 1, let T-c(x) = # {p <= x : p is an element of P , P+(p - 1) >= p(C)}. In this note, we prove that there exists some c < 1 such that lim sup (x ->infinity) T-c(x)/pi(x) < 1/2, which disproves a conjecture of Chen and Chen.
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页码：245 / 252
页数：8
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