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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
R. Baillie, G. V. Cormack, H. C. Williams, Some Results Concerning a Problem of Sierpinski, submitted, Math. Comp.
G. V. Cormack and H. C. Williams, Some Very Large Primes of the Form k.2n+1, Math. Comp. 35 (1980), 1419–1421.
P. Erdös, On Integers of the Form 2n+p and Some Related Problems, Summa Brasiliense Mathematicae II-8 (1950), p.119.
O. Ore, cf. Solution to Problem 4995, Amer. Math. Monthly 70 (1963), p. 101.
R. M. Robinson, A Report on Primes and on Factors of Fermat Numbers, Proc. Amer. Math. Soc. 9 (1958), pp. 673–681.
W. Sierpinski, 250 Problems in Elementary Number Theory, Elsevier, New York, (1970), p. 10 and p. 64.
W. Sierpinski, Sur un problème concernant les nombres K.2n+1, Elemente der Mathematik 15 (1960), pp. 73–74 (cf. also p. 85).
Author information
Authors and Affiliations
Editor information
Rights 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