Dissecting a Sieve to Cut Its Need for Space

  • William F. Galway
Conference paper

DOI: 10.1007/10722028_17

Part of the Lecture Notes in Computer Science book series (LNCS, volume 1838)
Cite this paper as:
Galway W.F. (2000) Dissecting a Sieve to Cut Its Need for Space. In: Bosma W. (eds) Algorithmic Number Theory. ANTS 2000. Lecture Notes in Computer Science, vol 1838. Springer, Berlin, Heidelberg

Abstract

We describe a “dissected” sieving algorithm which enumerates primes in the interval [x1, x2], using \(O(x_{2}^{1/3})\) bits of memory and using \(O(x_{2} -- x_{1} + x^{1/3}_{2}\) arithmetic operations on numbers of \(O(\rm ln \it x_{2})\) bits. This algorithm is based on a recent algorithm of Atkin and Bernstein [1], modified using ideas developed by Voronoï for analyzing the Dirichlet divisor problem [20]. We give timing results which show our algorithm has roughly the expected running time.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • William F. Galway
    • 1
  1. 1.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA

Personalised recommendations