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Journal of Systems Science and Complexity

, Volume 32, Issue 5, pp 1473–1478 | Cite as

Primality Testing for Numbers of the Form h · 2n ± 1

  • Dandan HuangEmail author
  • Yunling KangEmail author
Article
  • 42 Downloads

Abstract

This paper studies the problem of primality testing for numbers of the form h · 2n ± 1, where h < 2n is odd, and n is a positive integer. The authors describe a Lucasian primality test for these numbers in certain cases, which runs in deterministic quasi-quadratic time. In particular, the authors construct a Lucasian primality test for numbers of the form 3 · 5 · 17 · 2n ± 1, where n is a positive integer, in half of the cases among the congruences of n modulo 12, by means of a Lucasian sequence with a suitable seed not depending on n. The methods of Bosma (1993), Berrizbeitia and Berry (2004), Deng and Huang (2016) can not test the primality of these numbers.

Keywords

Lucasian primality test Lucasian sequence primality testing reciprocity law 

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Copyright information

© The Editorial Office of JSSC & Springer-Verlag GmbH Germany 2019

Authors and Affiliations

  1. 1.School of Software Engineering and School of CybersecurityJinling Institute of TechnologyNanjingChina
  2. 2.School of Statistics and MathematicsNanjing Audit UniversityNanjingChina

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