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Abstract
This paper offers numerical evidence for a conjecture that primality proving may be done in (logN)3 + o(1) operations by examining the growth rate of quantities known as pseudosquares and pseudocubes. In the process, a novel method of solving simultaneous congruences—doubly-focused enumeration— is examined. This technique, first described by D. J. Bernstein, allowed us to obtain record-setting sieve computations in software on general purpose computers.
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Authors and Affiliations
Centre for Information Security and Cryptography, University of Calgary, 2500 University Dr. NW, Calgary, Alberta, T2N 1N4, Canada
Kjell Wooding & Hugh C. Williams
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- Hugh C. Williams
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Editors and Affiliations
Technische Universität Berlin, Germany
Florian Hess
Institut für Mathematik, MA 8–1, Technische Universität Berlin, Straße des 17. Juni 136, 10623, Berlin, Germany
Sebastian Pauli
Institut für Mathematik, Technische Universität Berlin, Fakultät II, MA 8-1, Strasse des 17. Juni 136, 10623, Berlin, Germany
Michael Pohst
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Wooding, K., Williams, H.C. (2006). Doubly-Focused Enumeration of Pseudosquares and Pseudocubes. In: Hess, F., Pauli, S., Pohst, M. (eds) Algorithmic Number Theory. ANTS 2006. Lecture Notes in Computer Science, vol 4076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11792086_16
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