Dissecting a Sieve to Cut Its Need for Space

  • William F. Galway
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1838)


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.


Quadratic Form Lattice Point Cache Memory Congruence Class Operation Count 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

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

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