Continual Test-Time Adaptation (TTA) seeks to adapt a source pre-trained model to continually changing, unlabeled target domains. Existing TTA methods are typically designed for environments where domain changes occur gradually and can struggle in more dynamic scenarios. Inspired by the principles of online K-Means, this paper introduces a novel approach to continual TTA through visual prompting. We propose a Dynamic Prompt Coreset that not only preserves knowledge from previously visited domains but also accommodates learning from new potential domains. This is complemented by a distance-based weight updating mechanism that ensures the coreset remains current and relevant. Our approach employs a fixed model architecture alongside the coreset and an innovative updating system to effectively mitigate challenges such as catastrophic forgetting and error accumulation. Extensive testing across various benchmarks-including ImageNet-C, CIFAR100-C, and CIFAR10-C-demonstrates that our method consistently outperforms state-of-the-art (SOTA) alternatives, particularly excelling in dynamically changing environments.