BIT Numerical Mathematics

, Volume 32, Issue 3, pp 529–534

Effective primality tests for integers of the formsN=k3n+1 andN=k2m3n+1

  • Andreas Guthmann
Scientific Notes

DOI: 10.1007/BF02074886

Cite this article as:
Guthmann, A. BIT (1992) 32: 529. doi:10.1007/BF02074886


Using third roots of unity Proth's theorem for primality testing is generalized to integers of the formN=k3n+1, avoiding the use of Lucas sequences which are more suitable ifN+1 is factored instead ofN−1. This approach has the advantage of being easily combined with Proth's test and gives polynomial time algorithms for testing integers of the formN=k2m3n+1.

Copyright information

© BIT Foundations 1992

Authors and Affiliations

  • Andreas Guthmann
    • 1
  1. 1.Fachbereich MathematikUniversität KaiserslauternKaiserslauternGermany

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