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Unsupervised domain adaptive hashing is a highly promising research direction within the field of retrieval. It aims to transfer valuable insights from the source domain to the target domain while maintaining high storage and retrieval efficiency. Despite its potential, this field remains relatively unexplored. Previous methods usually lead to unsatisfactory retrieval performance, as they frequently directly apply slightly modified domain adaptation algorithms to hash learning framework, or pursue domain alignment within the Hamming space characterized by limited semantic information. In this paper, we propose a simple yet effective approach named Comparative Prototype Hashing (CPH) for unsupervised domain adaptive image retrieval. We establish a domain-shared unit hypersphere space through prototype contrastive learning and then obtain the Hamming hypersphere space via mapping from the shared hypersphere. This strategy achieves a cohesive synergy between learning uniformly distributed and category conflict-averse feature representations, eliminating domain discrepancies, and facilitating hash code learning. Moreover, by leveraging dual-domain information to supervise the entire hashing model training process, we can generate hash codes that retain inter-sample similarity relationships within both domains. Experimental results validate that our CPH significantly outperforms the state-of-the-art counterparts across multiple cross-domain and single-domain retrieval tasks. Notably, on Office-Home and Office-31 datasets, CPH achieves an average performance improvement of 19.29% and 13.85% on cross-domain retrieval tasks compared to the second-best results, respectively. The source codes of our method are available at: https://github.com/christinecui/CPH.