A new Combined Sieve algorithm is presented with cost proportional to the number of enumerated factors over a series of intervals. This algorithm achieves a significant speedup, over a traditional sieve, when handling many ([10^4, 10^7]) intervals concurrently. The speedup comes from a space-time tradeoff and a novel solution to a modular equation. In real world tests, this new algorithm regularly runs 10,000x faster. This faster sieve paired with higher sieving limits eliminates more composites and accelerates the search for large prime gaps by 30-70%. During the development and testing of this new algorithm, two top-10 record merit prime gaps were discovered.

中文翻译：

---

组合筛算法用于主间隙

提出了一种新的组合筛算法，其成本与一系列间隔中枚举因子的数量成正比。当同时处理许多（[10 ^ 4，10 ^ 7]）间隔时，该算法比传统的筛网实现了显着的加速。加速来自于时空权衡和模块化方程的新颖解决方案。在实际测试中，这种新算法的运行速度通常要快10,000倍。这种更快的筛子与更高的筛分极限相结合，消除了更多的复合材料，并加快了30-70％的较大主间隙的搜索速度。在开发和测试此新算法的过程中，发现了两个前10个记录优点优缺点。