On the proximity of large primes

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F18%3AA1901XZR" target="_blank" >RIV/61988987:17310/18:A1901XZR - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1515/ms-2017-0160" target="_blank" >http://dx.doi.org/10.1515/ms-2017-0160</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1515/ms-2017-0160" target="_blank" >10.1515/ms-2017-0160</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On the proximity of large primes

Popis výsledku v původním jazyce

By a sphere-packing argument, we show that there are infinitely many pairs of primes that are close to each other for some metrics on the integers. In particular, for any numeration basis q, we show that there are infinitely many pairs of primes the base q expansion of which differ in at most two digits. Likewise, for any fixed integer t; there are infinitely many pairs of primes, the first t digits of which are the same. In another direction, we show that, there is a constant c depending on q such that for infinitely many integers m there are at least c log log m primes which differ from m by at most one base q digit. (C) 2018 Mathematical Institute Slovak Academy of Sciences.

Název v anglickém jazyce

On the proximity of large primes

Popis výsledku anglicky

By a sphere-packing argument, we show that there are infinitely many pairs of primes that are close to each other for some metrics on the integers. In particular, for any numeration basis q, we show that there are infinitely many pairs of primes the base q expansion of which differ in at most two digits. Likewise, for any fixed integer t; there are infinitely many pairs of primes, the first t digits of which are the same. In another direction, we show that, there is a constant c depending on q such that for infinitely many integers m there are at least c log log m primes which differ from m by at most one base q digit. (C) 2018 Mathematical Institute Slovak Academy of Sciences.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

MATHEMATICA SLOVACA

ISSN

0139-9918

e-ISSN

1337-2211

Svazek periodika

68

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

6

Strana od-do

981-986

Kód UT WoS článku

000448428200004

EID výsledku v databázi Scopus

2-s2.0-85056144572