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Uspekhi Mat. Nauk, 2011, Volume 66, Issue 2(398), Pages 3–14 (Mi umn9419)  

This article is cited in 6 scientific papers (total in 7 papers)

A property of the set of prime numbers

A. A. Karatsuba

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: A phenomenon of interdependency between the structure of positive integers and the form of their prime factors is discovered. This paper was prepared for publication by E. A. Karatsuba and M. E. Changa, based on A. A. Karatsuba's drafts and notes from 2007–2008. Details of calculations are due to Changa.
Bibliography: 10 titles.

Keywords: prime factors, arithmetic progressions.

DOI: https://doi.org/10.4213/rm9419

Full text: PDF file (501 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2011, 66:2, 209–220

Bibliographic databases:

Document Type: Article
UDC: 511
MSC: 11N25
Received: 06.01.2011

Citation: A. A. Karatsuba, “A property of the set of prime numbers”, Uspekhi Mat. Nauk, 66:2(398) (2011), 3–14; Russian Math. Surveys, 66:2 (2011), 209–220

Citation in format AMSBIB
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\transl
\jour Russian Math. Surveys
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\pages 209--220
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  • https://doi.org/10.4213/rm9419
  • http://mi.mathnet.ru/eng/umn/v66/i2/p3

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. A. Gritsenko, E. A. Karatsuba, M. A. Korolev, I. S. Rezvyakova, D. I. Tolev, M. E. Changa, “Scientific Achievements of Anatolii Alekseevich Karatsuba”, Proc. Steklov Inst. Math., 280, suppl. 2 (2013), S1–S22  mathnet  crossref  crossref  zmath  isi  elib
    2. M. E. Changa, “On the Quantity of Numbers of Special Form Depending on the Parity of the Number of Their Different Prime Divisors”, Math. Notes, 97:6 (2015), 941–945  mathnet  crossref  crossref  mathscinet  isi  elib
    3. M. E. Changa, “A problem involving integers all of whose prime divisors belong to given arithmetic progressions”, Russian Math. Surveys, 71:4 (2016), 790–792  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    4. A. V. Shubin, “Fractional Parts of the Function $x/n$”, Math. Notes, 100:5 (2016), 731–742  mathnet  crossref  crossref  mathscinet  isi  elib
    5. M. A. Korolev, “On Anatolii Alekseevich Karatsuba's works written in the 1990s and 2000s”, Proc. Steklov Inst. Math., 299 (2017), 1–43  mathnet  crossref  crossref  isi  elib  elib
    6. M. E. Changa, “On a sum of Legendre symbols”, Russian Math. Surveys, 73:5 (2018), 919–921  mathnet  crossref  crossref  adsnasa  isi  elib
    7. M. E. Changa, “On integers whose number of prime divisors belongs to a given residue class”, Izv. Math., 83:1 (2019), 173–183  mathnet  crossref  crossref  adsnasa  isi  elib
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