In this talk I will explain the way sieving algorithms are implemented in the Generalized Sieve Kernel(G6K) -- an open-source implementation of the currently fastest sieve in practice. I will talk about the Nguen-Vidick sieve algorithm, tuple sieve, and the way these algorithms can be sped up with locality-sensitive hashing, as well about several tricks that allowed to improve the performance of the implementation.

Based on joint work with Martin R. Albrecht, Leo Ducas, Gottfried Herold, Eamonn W. Postlethwaite, Marc Stevens