On the proximity of large primes

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
On the proximity of large primes
Original language description
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.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)