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A primality test for \(4Kp^n-1\) numbers

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Abstract

We present a Lucasian type primality test, not explicitly based on Lucas sequences, for numbers written in the form \(N=4Kp^n-1\). This test is a generalization of the classical Lucas–Lehmer test for Mersenne numbers using as underlying group \(\mathcal {G}_N:=\{z \in (\mathbb {Z}/N\mathbb {Z})[i]: z\overline{z} \equiv 1 \pmod N\}\).

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Acknowledgements

The authors wish to thank the anonymous referees for their many insightful comments and suggestions that helped to improve the paper.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de Oviedo, Avda. Calvo Sotelo, s/n, 33007, Oviedo, Spain

    J. M. Grau

  2. Centro Universitario de la Defensa, Ctra. de Huesca, s/n, 50090, Zaragoza, Spain

    A. M. Oller-Marcén

  3. Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, Avda de los Castros s/n, 39005, Santander, Spain

    D. Sadornil

Authors
  1. J. M. Grau
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  2. A. M. Oller-Marcén
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  3. D. Sadornil
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Correspondence to A. M. Oller-Marcén.

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Communicated by Ilse Fischer.

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Daniel Sadornil is partially supported by the Spanish Government under projects MTM2014-55421-P and MTM2017-83271-R.

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Grau, J.M., Oller-Marcén, A.M. & Sadornil, D. A primality test for \(4Kp^n-1\) numbers. Monatsh Math 191, 93–101 (2020). https://doi.org/10.1007/s00605-019-01354-x

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