We present a revisit of the seeds algorithm to explore the semigroup tree. First, an equivalent definition of seed is presented, which seems easier to manage. Second, we determine the seeds of semigroups with at most three left elements. And third, we find the great-grandchildren of any numerical semigroup in terms of its seeds. The RGD algorithm is the fastest known algorithm at the moment. But if one compares the originary seeds algorithm with the RGD algorithm, one observes that the seeds algorithm uses more elaborated mathematical tools while the RGD algorithm uses data structures that are better adapted to the final C implementations. For genera up to around one half of the maximum size of native integers, the newly defined seeds algorithm performs significantly better than the RGD algorithm. For future compilators allowing larger native sized integers this may constitute a powerful tool to explore the semigroup tree up to genera never explored before. The new seeds algorithm uses bitwise integer operations, the knowledge of the seeds of semigroups with at most three left elements and of the great-grandchildren of any numerical semigroup, apart from techniques such as parallelization and depth first search as wisely introduced in this context by Fromentin and Hivert. The algorithm has been used to prove that there are no Eliahou semigroups of genus $66$, hence proving the Wilf conjecture for genus up to $66$. We also found three Eliahou semigroups of genus $67$. One of these semigroups is neither of Eliahou-Fromentin type, nor of Delgado's type. However, it is a member of a new family suggested by Shalom Eliahou.

翻译：我们重新审视了用于探索半群树的种子算法。首先，提出了一种更易处理的种子等价定义；其次，确定了最多包含三个左元素的半群的种子；最后，以种子为媒介，给出了任意数值半群曾孙的求解方法。RGD算法是目前已知最快的算法。但若将原始种子算法与RGD算法比较，可观察到种子算法运用了更精密的数学工具，而RGD算法则采用了更适配最终C语言实现的数据结构。对于不超过原生整数最大尺寸约一半的亏格数，新定义的种子算法性能显著优于RGD算法。对于未来支持更大原生整型的编译器而言，这将成为探索前所未有高亏格半群树的强力工具。新种子算法采用位整数运算，基于最多含三个左元素的半群种子知识及任意数值半群的曾孙求解方法，同时融合了Fromentin与Hivert在该领域开创性引入的并行化和深度优先搜索技术。该算法已用于证明亏格66范围内不存在Eliahou半群，从而验证了亏格至66的Wilf猜想。我们还发现了三个亏格67的Eliahou半群，其中既非Eliahou-Fromentin型也非Delgado型，但属于Shalom Eliahou提出的新家族成员。