`fmpz_is_prime_pocklington, fmpz_is_prime_morrison`

Synopsis#include <flint/fmpz.h>

int fmpz_is_prime_pocklington(fmpz_t F, fmpz_t R, const fmpz_t n, nn_ptr pm1, slong num_pm1)source

int fmpz_is_prime_morrison(fmpz_t F, fmpz_t R, const fmpz_t n, nn_ptr pp1, slong num_pp1)source

The $n - 1$ test of Pocklington and the $n + 1$ test of Morrison for odd $n$ (non-square for Morrison), given the num_pm1 (num_pp1) primes pm1 (pp1) dividing $n - 1$ ( $n + 1$ ). Return 0 if $n$ is composite. Otherwise they set $F$ to the factored part of $n \mp 1$ and $R$ to $(n \mp 1)/F$ and return 1, which proves that every prime factor of $n$ is $\equiv 1 \pmod F$ (respectively $\equiv \pm 1$ ). This proves $n$ prime if $F \ge \sqrt n$ (respectively $F > \sqrt n + 1$ ).

Cite this page

The FLINT team, “fmpz_is_prime_pocklington, fmpz_is_prime_morrison (fmpz.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/fmpz/fmpz_is_prime_pocklington.html (generated 2026-11-02).

@misc{flint-doc-fmpz-fmpz-is-prime-pocklington,
  author       = {{The FLINT team}},
  title        = {{fmpz\_is\_prime\_pocklington, fmpz\_is\_prime\_morrison (fmpz.h)}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/fmpz/fmpz_is_prime_pocklington.html},
  note         = {Generated 2026-11-02}
}

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