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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Some results on pseudosquares
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by R. F. Lukes, C. D. Patterson and H. C. Williams PDF
Math. Comp. 65 (1996), 361-372 Request permission

Abstract:

If $p$ is an odd prime, the pseudosquare $L_p$ is defined to be the least positive nonsquare integer such that $L_p\equiv 1\pmod {8}$ and the Legendre symbol $(L_p/q)=1$ for all odd primes $q\le p$. In this paper we first discuss the connection between pseudosquares and primality testing. We then describe a new numerical sieving device which was used to extend the table of known pseudosquares up to $L_{271}$. We also present several numerical results concerning the growth rate of the pseudosquares, results which so far confirm that $L_p> e^{\sqrt {p/2}}$, an inequality that must hold under the extended Riemann Hypothesis.
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Additional Information
  • R. F. Lukes
  • Affiliation: Department of Computer Science, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2
  • Email: rflukes@cs.umanitoba.ca
  • C. D. Patterson
  • Affiliation: Xilinx Development Corporation, 52 Mortonhall Gate, Edinburgh EH16 6TJ, Scotland
  • H. C. Williams
  • Affiliation: Department of Computer Science, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2
  • Email: hugh_williams@csmail.cs.umanitoba.ca
  • Received by editor(s): August 23, 1993
  • Received by editor(s) in revised form: April 8, 1994
  • Additional Notes: Research of the third author supported by NSERC of Canada grant #A7649
  • © Copyright 1996 American Mathematical Society
  • Journal: Math. Comp. 65 (1996), 361-372
  • MSC (1991): Primary 11A51, 11Y11, 11-04, 11Y55
  • DOI: https://doi.org/10.1090/S0025-5718-96-00678-3
  • MathSciNet review: 1322892