Prime-set-based neighbour discovery algorithm for low duty-cycle dynamic WSNs A novel probabilistic algorithm for low duty-cycle dynamic (mobile sensors) wireless sensor networks(WSNs) is proposed. The rapid development of smart phones and mobile sensors had fostered a demand for opportunistic encounter-based networking to support mobile social networking and proximity-based gaming. However, the performance of such applications was restricted by a lack of specialised neighbour discovery algorithms. For existing algorithms, even though the probabilistic algorithms have good performance in average discovery latency, when working with a low duty-cycle, the performance is not so encouraging. Deterministic algorithms can provide bound time for the worst discovery latency, but they sacrificed the average discovery latency. In response, a novel prime-set-based neighbour discovery algorithm (PSBA) is proposed. The PSBA is a probabilistic algorithm tailored to low duty-cycle dynamic WSNs. Leveraging on the certainty of the deterministic algorithm and the randomness of the probabilistic algorithm, the inherent long tail of the probabilistic algorithm can be improved. Also, the average discovery latency of the PSBA can be drastically reduced compared to existing algorithms, which precisely meets the requirements in low duty-cycle dynamic WSNs.