Prognosis and Health Management (PHM), critical for ensuring task completion by complex systems and preventing unexpected failures, is widely adopted in aerospace, manufacturing, maritime, rail, energy, etc. However, PHM's development is constrained by bottlenecks like generalization, interpretation and verification abilities. Presently, generative artificial intelligence (AI), represented by Large Model, heralds a technological revolution with the potential to fundamentally reshape traditional technological fields and human production methods. Its capabilities, including strong generalization, reasoning, and generative attributes, present opportunities to address PHM's bottlenecks. To this end, based on a systematic analysis of the current challenges and bottlenecks in PHM, as well as the research status and advantages of Large Model, we propose a novel concept and three progressive paradigms of Prognosis and Health Management Large Model (PHM-LM) through the integration of the Large Model with PHM. Subsequently, we provide feasible technical approaches for PHM-LM to bolster PHM's core capabilities within the framework of the three paradigms. Moreover, to address core issues confronting PHM, we discuss a series of technical challenges of PHM-LM throughout the entire process of construction and application. This comprehensive effort offers a holistic PHM-LM technical framework, and provides avenues for new PHM technologies, methodologies, tools, platforms and applications, which also potentially innovates design, research & development, verification and application mode of PHM. And furthermore, a new generation of PHM with AI will also capably be realized, i.e., from custom to generalized, from discriminative to generative, and from theoretical conditions to practical applications.