Unexpected failures in rotating machinery may lead to large economic losses and even safety problems. Accurately predictingremaining useful life (RUL) plays an important role in equipment maintenance. Because of the strong non-linearity and noisesensitivity of data-driven models, however, their interpretation is often limited, and it is challenging to incorporate physicaldegradation mechanisms and achieve generalization. This article proposes a Prior-Information and Physics-Informed NeuralNetwork framework for intelligent RUL prediction of rotating machinery. The framework follows a cloud-edge collaborativeparadigm, where vibration signals are firstly processed by an improved particle filter based on a Damage DiscrepancyAccumulation Hypothesis at the edge to extract degradation features, and then Prior-Weighted Self-Attention is applied in thecloud to capture richer features of the degradation process by introducing the perturbation-based prior information. Finally, aFast-Slow Coupling Physics-Informed Neural Network is adopted to fully utilize the physical degradation knowledge for makingthe model more interpretable. The experimental results on a public data set and a self-built rotating-machinery test rig show theeffectiveness of the proposed paradigm in achieving higher accuracy than existing approaches. Moreover, the framework achievesgood performance even under noisy conditions. The work demonstrates the value of using prior information, vibrationdegradation features, and physical knowledge to enable rotating-machinery prognostics with high accuracy and interpretation.