On shifted primes with large prime factors and their products
Number Theory
2017-04-13 v1
Abstract
We estimate from below the lower density of the set of prime numbers p such that p-1 has a prime factor of size at least p^c, where c lies in between 1/4 and 1/2. We also establish upper and lower bounds on the counting function of the set of positive integers n up to x with exactly k prime factors, counted with or without multiplicity, such that the largest prime factor of gcd(p-1 : p | n) exceeds n^{1/2k}.
Keywords
Cite
@article{arxiv.1311.2527,
title = {On shifted primes with large prime factors and their products},
author = {Florian Luca and Ricardo Menares and Amalia Pizarro-Madariaga},
journal= {arXiv preprint arXiv:1311.2527},
year = {2017}
}
Comments
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