Probabilistic Primality Testing


Title: Probabilistic Primality Testing
Authors: Daniel Stüwe and Manuel Eberl
Submission date: 2019-02-11

The most efficient known primality tests are probabilistic in the sense that they use randomness and may, with some probability, mistakenly classify a composite number as prime – but never a prime number as composite. Examples of this are the Miller–Rabin test, the Solovay–Strassen test, and (in most cases) Fermat's test.

This entry defines these three tests and proves their correctness. It also develops some of the number-theoretic foundations, such as Carmichael numbers and the Jacobi symbol with an efficient executable algorithm to compute it.

  author  = {Daniel Stüwe and Manuel Eberl},
  title   = {Probabilistic Primality Testing},
  journal = {Archive of Formal Proofs},
  month   = feb,
  year    = 2019,
  note    = {\url{},
            Formal proof development},
  ISSN    = {2150-914x},
License: BSD License
Used by: Mersenne_Primes
Status: [ok] This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.