A+ CATEGORY SCIENTIFIC UNIT

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