PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

How strong can primes be

Volume 179 / 2017

Ping Xi Acta Arithmetica 179 (2017), 363-373 MSC: 11Y05, 11N05, 11N13. DOI: 10.4064/aa8578-5-2017 Published online: 14 June 2017

Abstract

We prove that there are a positive proportion of primes $p$ such that $p+1$ has a prime factor at least $\sqrt{p}$, $p-1$ has a prime factor $q$ at least $\sqrt{p}$, and $q-1$ has a prime factor at least $p^{0.0705}$. Moreover, there are a positive proportion of primes $p$ such that both $p+1$ and $p-1$ have prime factors at least $p^\theta$ with $\theta={1}/{2}+{1}/{36}.$ These are related to strong primes appearing in RSA schemes.

Authors

  • Ping XiDepartment of Mathematics
    Xi’an Jiaotong University
    Xi’an 710049, P.R. China
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image