Nuclear Prosperity and Security Act This bill directs the Department of Energy (DOE) to establish and operate a uranium reserve to ensure the availability of uranium mined in the United States in the event of a market disruption and support strategic fuel cycle capabilities in the United States. Uranium that is mined in the United States by an entity that is owned or controlled by the Russian Federation or the People's Republic of China or is incorporated in either country must be excluded from the reserve. DOE must publish a request for information to evaluate (1) how to operate and manage the reserve, (2) how to acquire uranium for the reserve, and (3) the quantity and form of uranium to acquire for the reserve. DOE must also include in its budget materials (1) a request for amounts for the acquisition, transportation, or storage of uranium in the reserve; or (2) an explanation for why such amounts are not requested.