摘要
For any integer n ≥ 2, let P（n） be the largest prime factor of n. In this paper, we prove 1 This 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 extends a recent result of Luca, Menares and Madariaga for1/4≤c≤1/2. We also pose two conjectures for further research.
For any integer n ≥ 2, let P（n） be the largest prime factor of n. In this paper, we prove 1 This 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 extends a recent result of Luca, Menares and Madariaga for1/4≤c≤1/2. We also pose two conjectures for further research.
基金
Supported by National Natural Science Foundation of China(Grant Nos.11571174,11401411 and 11371195)
