Primality testing through algebraic groups

Alexander Gurevich*, Boris Kunyavskiĭ

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We propose a deterministic primality test based on a section of a group scheme. Pépin's test and the tests of Lucas-Lehmer type are special cases of our construction, provided the group scheme is taken to be the multiplicative group and the Waterhouse-Weisfeiler group scheme, respectively. Besides, we suggest a test involving formal completions of these schemes.

Original languageAmerican English
Pages (from-to)555-564
Number of pages10
JournalArchiv der Mathematik
Issue number6
StatePublished - Dec 2009
Externally publishedYes

Bibliographical note

Funding Information:
Acknowledgements. The authors’ research was supported in part by the Ministry of Absorption (Israel), the Minerva Foundation through the Emmy Noether Research Institute of Mathematics, and a grant from the Ministry of Science, Culture and Sport (Israel) and the Russian Foundation for Basic Research (the Russian Federation). A part of the work was done during the visit of the second named author to ENS (Paris) in April–May 2008. The support of these institutions is highly appreciated. We thank the referee for helpful suggestions.


  • Formal group law
  • Group scheme
  • Primality testing


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