Geodesic
How strong can primes be
Ping Xi1
1 Department of Mathematics Xi’an Jiaotong University Xi’an 710049, P.R. China
Acta Arithmetica, Tome 179 (2017) no. 4, pp. 363-373

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/aa8578-5-2017
Keywords: prove there positive proportion primes has prime factor least sqrt p has prime factor least sqrt q has prime factor least moreover there positive proportion primes p have prime factors least theta theta these related strong primes appearing rsa schemes

Ping Xi 1

1 Department of Mathematics Xi’an Jiaotong University Xi’an 710049, P.R. China 
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Ping Xi. How strong can primes be. Acta Arithmetica, Tome 179 (2017) no. 4, pp. 363-373. doi: 10.4064/aa8578-5-2017

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