On the largest prime factor of shifted primes

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• 作者：Feng Juan Chen ; Yong Gao Chen
• 关键词：Prime factor ; shifted prime
• 刊名：Acta Mathematica Sinica, English Series
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：33
• 期：3
• 页码：377-382
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
• ISSN：1439-7617
• 卷排序：33

文摘

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) ≥ pc is more than (1−c+o(1))π(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.