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Dissecting a Sieve to Cut Its Need for Space

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Algorithmic Number Theory (ANTS 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1838))

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Abstract

We describe a “dissected” sieving algorithm which enumerates primes in the interval [x 1, x 2], 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.

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Authors and Affiliations

  1. Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, IL, 61801, USA

    William F. Galway

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  1. William F. Galway
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Editor information

Editors and Affiliations

  1. Mathematisch Instituut, Universiteit Nijmegen, Postbus 9010, 6500 GL, Nijmegen, The Netherlands

    Wieb Bosma

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© 2000 Springer-Verlag Berlin Heidelberg

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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. https://doi.org/10.1007/10722028_17

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  • DOI: https://doi.org/10.1007/10722028_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67695-9

  • Online ISBN: 978-3-540-44994-2

  • eBook Packages: Springer Book Archive

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