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The exponential growth of streaming multi-modal data presents critical challenges for cross-modal retrieval: distribution shifts, modality gap, and scarce labels. Semi-supervised online cross-modal hashing has gained increasing interest due to its ability to encode complex streaming data and update hash functions simultaneously. Nevertheless, existing methods can hardly generate high-quality unsupervised hash codes, which fundamentally limits diversity and flexibility during the retrieval process. To this end, we propose a novel method named Prototype Evolution Online Cross-modal Hashing (PEOCH). With semi-supervised streaming data driving prototype evolution, precise and stable hash codes can be generated for both labeled and unlabeled data. Specifically, two simultaneous prototype updates are performed: labeled samples push semantic knowledge into the prototypes, while unlabeled samples pull prototypes to guide hash code generation. A co-optimization mechanism is designed to ensure the prototypes continuously evolve based on the entire streaming data. Besides, an elasticity regularizer integrates discriminability and smoothness constraints, improving the reliability of prototypes. We provide rigorous theoretical guarantees that ensure prototype stability. Extensive experiments on three benchmark datasets demonstrate that PEOCH outperforms state-of-the-art methods, achieving an average improvement of 6.7\% in mAP@all across various retrieval tasks.