Skip to main content

Computation of some number-theoretic coverings

Expository Papers

Part of the Lecture Notes in Mathematics book series (LNM,volume 884)

Abstract

In this expository lecture, we give a survey of the Polignac problem concerning the primality of k-2n and the Sierpinski problem concerning the primality of 1+k.2n. Various numerical results are given related to the problem of determining the smallest k for which 1+k.2n is always composite.

Keywords

  • Chinese Remainder Theorem
  • Historical Survey
  • Congruence Class
  • Negative Solution
  • Fermat Number

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. Baillie, G. V. Cormack, H. C. Williams, Some Results Concerning a Problem of Sierpinski, submitted, Math. Comp.

    Google Scholar 

  2. G. V. Cormack and H. C. Williams, Some Very Large Primes of the Form k.2n+1, Math. Comp. 35 (1980), 1419–1421.

    MathSciNet  MATH  Google Scholar 

  3. P. Erdös, On Integers of the Form 2n+p and Some Related Problems, Summa Brasiliense Mathematicae II-8 (1950), p.119.

    Google Scholar 

  4. O. Ore, cf. Solution to Problem 4995, Amer. Math. Monthly 70 (1963), p. 101.

    CrossRef  MathSciNet  Google Scholar 

  5. R. M. Robinson, A Report on Primes and on Factors of Fermat Numbers, Proc. Amer. Math. Soc. 9 (1958), pp. 673–681.

    MathSciNet  MATH  Google Scholar 

  6. W. Sierpinski, 250 Problems in Elementary Number Theory, Elsevier, New York, (1970), p. 10 and p. 64.

    MATH  Google Scholar 

  7. W. Sierpinski, Sur un problème concernant les nombres K.2n+1, Elemente der Mathematik 15 (1960), pp. 73–74 (cf. also p. 85).

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1981 Springer-Verlag

About this paper

Cite this paper

Stanton, R.G., Williams, H.C. (1981). Computation of some number-theoretic coverings. In: McAvaney, K.L. (eds) Combinatorial Mathematics VIII. Lecture Notes in Mathematics, vol 884. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0091803

Download citation

  • DOI: https://doi.org/10.1007/BFb0091803

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10883-2

  • Online ISBN: 978-3-540-38792-3

  • eBook Packages: Springer Book Archive