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

  • J. M. Grau
  • A. M. Oller-MarcénEmail author
  • D. Sadornil


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 \(\mathcal {G}_N:=\{z \in (\mathbb {Z}/N\mathbb {Z})[i]: z\overline{z} \equiv 1 \pmod N\}\).


Proth numbers Primality test Lucas sequences Lucasian primality test 

Mathematics Subject Classification

11A51 11Y11 11Y40 



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. 1.Departamento de MatemáticasUniversidad de OviedoOviedoSpain
  2. 2.Centro Universitario de la DefensaZaragozaSpain
  3. 3.Departamento de Matemáticas, Estadística y ComputaciónUniversidad de CantabriaSantanderSpain

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