Conventional sieve approaches in computational number theory generally adopt global exhaustive screening coupled with integral estimation, which inevitably produces redundant candidate intervals; as a result, conventional sieve frameworks have reached a bottleneck in further optimization. This work develops a discrete pre-sieving algorithm leveraging the symmetric decomposition characteristic of even integers. Unlike traditional bidirectional traversal sieves, our algorithm fixes a single prime as the unilateral benchmark and performs hierarchical remainder pre-filtering to eliminate composite numbers at the preprocessing stage. Combined with classical sieve theory, the proposed method achieves continuous contraction of candidate intervals and improves the upper bound estimate of the exceptional set under constrained computational capacity. The architecture possesses outstanding implementability and lays a foundation for follow-up research including numerical quantification, cluster partitioning and boundary refinement.
Mingguang Liu (Thu,) studied this question.