Kummer surfaces for primality testing

19 May 2020 Duarte Eduardo Ruíz Noordman Marc Paul

We use the arithmetic of the Kummer surface associated to the Jacobian of a hyperelliptic curve to study the primality of integers of the form $4m^2 5^n-1$. We provide an algorithm capable of proving the primality or compositeness of most of the integers in these families and discuss in detail the necessary steps to implement this algorithm in a computer... (read more)

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Categories


  • ALGEBRAIC GEOMETRY
  • NUMBER THEORY