qsieve_knuth_schroeppel
Synopsis
#include <flint/qsieve.h>Chooses the Knuth–Schroeppel multiplier k for n, among the 29 squarefree numbers from 1 to 47, maximising the expected contribution of the small primes to the sieve: kn \bmod 8 and the primes p (up to ks_primes of them) for which kn is a square modulo p, minus \frac12 \log k [Sil1987]. Stores it in qs_inf->k and returns 0, or returns a small prime factor of n if one is found (2 if n is even).
References#
- [Sil1987] R. D. Silverman. The multiple polynomial quadratic sieve. Mathematics of Computation 48 (1987), 329–339.
Cite this page
The FLINT team, “qsieve_knuth_schroeppel (qsieve.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/qsieve/qsieve_knuth_schroeppel.html (generated 2026-10-20).
@misc{flint-doc-qsieve-qsieve-knuth-schroeppel,
author = {{The FLINT team}},
title = {{qsieve\_knuth\_schroeppel (qsieve.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/qsieve/qsieve_knuth_schroeppel.html},
note = {Generated 2026-10-20}
}