Prime sieves using binary quadratic forms
Authors:
A. O. L. Atkin and D. J. Bernstein
Translated by:
Journal:
Math. Comp. 73 (2004), 1023-1030
MSC (2000):
Primary 11Y11; Secondary 11E25
DOI:
https://doi.org/10.1090/S0025-5718-03-01501-1
Published electronically:
December 19, 2003
MathSciNet review:
2031423
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We introduce an algorithm that computes the prime numbers up to using
additions and
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.
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Additional Information
A. O. L. Atkin
Affiliation:
Department of Mathematics, Statistics, and Computer Science (M/C 249), The University of Illinois at Chicago, Chicago, Illinois 60607–7045
Email:
aolatkin@uic.edu
D. J. Bernstein
Affiliation:
Department of Mathematics, Statistics, and Computer Science (M/C 249), The University of Illinois at Chicago, Chicago, Illinois 60607–7045
Email:
djb@pobox.com
DOI:
https://doi.org/10.1090/S0025-5718-03-01501-1
Received by editor(s):
September 7, 1999
Received by editor(s) in revised form:
March 30, 2002
Published electronically:
December 19, 2003
Additional Notes:
The second author was supported by the National Science Foundation under grant DMS–9600083.
Article copyright:
© Copyright 2003
A. O. L. Atkin and D. J. Bernstein