FLINT3.7.0-dev
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_aprcl_is_prime_jacobi_check_pk, _aprcl_is_prime_jacobi_check_21, _aprcl_is_prime_jacobi_check_22, _aprcl_is_prime_jacobi_check_2k

Synopsis#include <flint/aprcl.h>
slong _aprcl_is_prime_jacobi_check_pk(const unity_zp j, const fmpz_t u, ulong v)source
slong _aprcl_is_prime_jacobi_check_21(ulong q, const fmpz_t n)source
slong _aprcl_is_prime_jacobi_check_22(const unity_zp j, const fmpz_t u, ulong v, ulong q)source
slong _aprcl_is_prime_jacobi_check_2k(const unity_zp j, const unity_zp j2_1, const unity_zp j2_2, const fmpz_t u, ulong v)source

The check for odd pp (with j=J(p,q)j = J(p, q)), for pk=2p^k = 2 (which reduces to (−q)(n−1)/2≡±1(modn)(-q)^{(n-1)/2} \equiv \pm 1 \pmod n, returning 0 for +1+1, 1 for −1-1 and −1-1 otherwise), for pk=4p^k = 4 (with j=J(2,q)j = J(2, q); hh gives ζ4h∈{1,i,−1,−i}\zeta_4^h \in \{1, i, -1, -i\}), and for p=2p = 2, k≥3k \ge 3 (with j=J(2,q)j = J(2, q), j2,1=J3(q)j_{2,1} = J_3(q) and j2,2=J2(q)j_{2,2} = J_2(q)).

Cite this page

The FLINT team, “_aprcl_is_prime_jacobi_check_pk, _aprcl_is_prime_jacobi_check_21, _aprcl_is_prime_jacobi_check_22, _aprcl_is_prime_jacobi_check_2k (aprcl.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/aprcl/_aprcl_is_prime_jacobi_check_pk.html (generated 2026-11-02).