_aprcl_is_prime_jacobi
#include <flint/aprcl.h>primality_test_status _aprcl_is_prime_jacobi(const fmpz_t n, const aprcl_config config)sourceThe Jacobi sum test for n with the given configuration. Returns PRIME, COMPOSITE or UNKNOWN, the latter also when the configuration does not satisfy s^2 > n.
The steps are those of Cohen's Algorithm 9.1.28: a check that n is coprime to Rs; for every prime q \mid s and every prime power p^k \,\|\, q - 1, the test that J_0^u J_v is a root of unity in \mathbb{Z}[\zeta_{p^k}]/(n) (the pairs (p, q) are independent tasks, distributed over the available threads in decreasing order of cost); the conditions (\mathcal L_p), completed by additional tests with an extra prime q where needed; and the final division (aprcl_is_prime_final_division). Moduli of 2 to 16 limbs use the unity_zp_mpn arithmetic, larger ones the unity_zp arithmetic.
The FLINT team, “_aprcl_is_prime_jacobi (aprcl.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/aprcl/_aprcl_is_prime_jacobi.html (generated 2026-10-20).
@misc{flint-doc-aprcl-aprcl-is-prime-jacobi,
author = {{The FLINT team}},
title = {{\_aprcl\_is\_prime\_jacobi (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.html},
note = {Generated 2026-10-20}
}