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Computation of some number-theoretic coverings

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Combinatorial Mathematics VIII

Part of the book series: Lecture Notes in Mathematics ((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.

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References

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

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

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

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

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

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

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

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Author information

Authors and Affiliations

  1. Department of Computer Science, The University of Manitoba, R3T 2N2, Winnipeg, Canada

    R. G. Stanton & H. C. Williams

Authors
  1. R. G. Stanton
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  2. H. C. Williams
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Editor information

Kevin L. McAvaney

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© 1981 Springer-Verlag

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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

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

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10883-2

  • Online ISBN: 978-3-540-38792-3

  • eBook Packages: Springer Book Archive

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