`_aprcl_is_prime_jacobi_additional_test`

Synopsis#include <flint/aprcl.h>

int _aprcl_is_prime_jacobi_additional_test(const fmpz_t n, ulong p)source

The additional test of step 5 for a prime $p \mid R$ for which $(\mathcal L_p)$ was not established: looks for a prime $q \equiv 1 \pmod{2p}$ (with $4 \| q - 1$ if $p = 2$ ) such that $n^{(q-1)/p} \not\equiv 1 \pmod q$ and checks that the corresponding $h$ is a primitive root of unity (and for $p = 2$ that $q^{(n-1)/2} \equiv -1 \pmod n$ ). Returns 2 if $n$ is proved composite, 1 if the condition holds, and 0 if no suitable $q$ was found.

Cite this page

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

@misc{flint-doc-aprcl-aprcl-is-prime-jacobi-additional-test,
  author       = {{The FLINT team}},
  title        = {{\_aprcl\_is\_prime\_jacobi\_additional\_test (aprcl.h)}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/aprcl/_aprcl_is_prime_jacobi_additional_test.html},
  note         = {Generated 2026-11-02}
}

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