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In this paper, we study the problem of mining for frequent trajectories, which is crucial in many application scenarios, such as vehicle traffic management, hand-off in cellular networks, supply chain management. We approach this problem as that of mining for frequent sequential patterns. Our approach consists of a partitioning strategy for incoming streams of trajectories in order to reduce the trajectory size and represent trajectories as strings. We mine frequent trajectories using a sliding windows approach combined with a counting algorithm that allows us to promptly update the frequency of patterns. In order to make counting really efficient, we represent frequent trajectories by prime numbers, whereby the Chinese reminder theorem can then be used to expedite the computation.