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Abstract: . We introduce an algorithm that computes the prime numbers up to N using O(N=log log N) additions and N 1=2+o(1) bits of memory. The algorithm enumerates representations of integers by certain binary quadratic forms. We present implementation results for this algorithm and one of the best previous algorithms. 1. (Update)
Context of citations to this paper: More
...sum over p m serves as a correction term, allowing larger h for a given error bound. To e#ciently sieve for primes near x, I modify a method due to Atkin and Bernstein [AB99], using a technique similar to that used by Vorono to treat the Dirichlet divisor problem [Vor03]...
Cited by: More
Research Statement - Galway (Correct)
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BibTeX entry: (Update)
A. O. L. Atkin and D. J. Bernstein, Prime sieves using binary quadratic forms, Dept. of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 60607-7045. Preprint available at http://pobox.com/#djb/papers/primesieves.dvi, 1999. http://citeseer.ist.psu.edu/atkin99prime.html More
@misc{ atkin99prime,
author = "A. Atkin and D. Bernstein",
title = "Prime sieves using binary quadratic forms",
text = "A. O. L. Atkin and D. J. Bernstein, Prime sieves using binary quadratic
forms, Dept. of Mathematics, Statistics, and Computer Science, University
of Illinois at Chicago, 60607-7045. Preprint available at http://pobox.com/#djb/papers/primesieves.dvi,
1999.",
year = "1999",
url = "citeseer.ist.psu.edu/atkin99prime.html" }
Citations (may not include all citations):439 An introduction to the theory of numbers (context) - Hardy, Wright - 1979
9 A linear algorithm for incremental digital display of circul.. (context) - Bresenham - 1977
9 Algebraic number theory (context) - Fr, Martin et al. - 1991
7 Fast compact prime number sieves (context) - Pritchard - 1983
5 The segmented sieve of Eratosthenes and primes in arithmetic.. (context) - Bays, Hudson - 1977
4 Explaining the wheel sieve (context) - Pritchard - 1982
3 Zen of graphics programming (context) - Abrash - 1995
2 The rst occurrence of large gaps between successive primes (context) - Brent - 1973
2 Experiments on the lattice problem of Gauss (context) - Keller, Swenson - 1963
1 Algorithm 356: a prime number generator using the treesort p.. (context) - Singleton - 1969
1 A space-ecient fast prime number sieve (context) - Dunten, Jones et al. - 1996
1 A sublinear additive sieve for nding prime numbers (context) - Pritchard - 1981
1 Algorithm 357: an ecient prime number generator (context) - Singleton - 1969
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