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Trading time for space in prime number sieves

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Algorithmic Number Theory (ANTS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1423))

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Abstract

A prime number sieve is an algorithm that finds the primes up to a bound n. We present four new prime number sieves. Each of these sieves gives new space complexity bounds for certain ranges of running times. In particular, we give a linear time sieve that uses only O(√n/(log log n)2) bits of space, an O l(n/ log log n) time sieve that uses O(n/((log n)l log log n)) bits of space, where l>1 is constant, and two super-linear time sieves that use very little space.

Supported by NSF Grant CCR-9626877

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Butler University, 4600 Sunset Avenue, 46208, Indianapolis, Indiana, USA

    Jonathan P. Sorenson

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  1. Jonathan P. Sorenson
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Joe P. Buhler

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© 1998 Springer-Verlag Berlin Heidelberg

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Sorenson, J.P. (1998). Trading time for space in prime number sieves. In: Buhler, J.P. (eds) Algorithmic Number Theory. ANTS 1998. Lecture Notes in Computer Science, vol 1423. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054861

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  • DOI: https://doi.org/10.1007/BFb0054861

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64657-0

  • Online ISBN: 978-3-540-69113-6

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