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.
Bibliographical noteFunding 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