arXiv:2507.06127v1 Announce Type: cross Abstract: Prefix adders are fundamental arithmetic circuits, but their design space grows exponentially with bit-width, posing significant optimization challenges. Previous works face limitations in performance, generalization, and scalability. To address these challenges, we propose PrefixAgent, a large language model (LLM)-powered framework that enables efficient prefix adder optimization. Specifically, PrefixAgent reformulates the problem into subtasks including backbone synthesis and structure refinement, which effectively reduces the search space. More importantly, this new design perspective enables us to efficiently collect enormous high-quality data and reasoning traces with E-graph, which further results in an effective fine-tuning of LLM. Experimental results show that PrefixAgent synthesizes prefix adders with consistently smaller areas compared to baseline methods, while maintaining scalability and generalization in commercial EDA flows.