PRIME focuses on three main general research goals: (1) study the interaction of intense particle/radiation and matter under nonequilibrium conditions and (2) study these interactions across a spectrum of time scales (femtoseconds to milliseconds) and spatial scales (nano, micro, macro, and meso) while (3) coupling these studies with state-of-the-art modeling already developed (HEIGHTS, MDCASK, KMC, WBC/REDEP, and ITMC), and under development (MMD, MDCASK+, upgraded KMC, and DYN-ITMC). The vision is that these goals encompass a wide range of applications. The strategic plan for PRIME has three main experiments: a high-intensity laser experiment, a high-intensity plasma gun experiment, and a high-intensity charged-particle experiment. All three experiments are summarized next. PRIME has an integrated facility concept. The laser experiment will provide several functions, including high-intensity laser-matter interactions, laser-produced plasmas, and laser-based diagnostics (e.g., ultrafast laser spectroscopy and laser-induced fluorescence spectroscopy) that will be coupled to the plasma-based and charged-particle-based experiments.