The Astro2020 Decadal Survey recommended a new line of astrophysics observatories intermediate in scale between MIDEXs and Flagship-class observatories. In response, NASA created the Astrophysics Probe Explorer class and solicited proposals for the first generation of Probes. With a larger cost cap, Probes can achieve more ambitious science than SMEXs or MIDEXs and be implemented faster than Flagships—as frequently as one per decade. The PRobe far-Infrared Mission for Astrophysics (PRIMA) is one of two Probe concepts selected by NASA for a concept study in 2024/2025, potentially leading to implementation and launch as early as 2031. PRIMA was designed for a broad range of astrophysics, from how planets assemble their atmospheres, to the coevolution of galaxies and black holes, to the evolving properties of dust and galactic metallicity over cosmic time. Seventy-five percent of PRIMA’s observing time will be allocated to guest observer observations and 25% allocated to principal investigator science; however, the principal investigator science data will be available promptly for guest investigator usage. The observatory features a 1.8-m diameter telescope cooled to 4.5 K with two science instruments: the Far-InfraRed Enhanced Survey Spectrometer (FIRESS) and the PRIMA imager (PRIMAger). FIRESS provides continuous spectral coverage from 24 to 235 μm, in two spectral resolution modes (R ≥ 85 and R ¼ 4400ð112 μm∕λÞ), with spectral mapping capability and order-of-magnitude sensitivity improvement over previous observatories. PRIMAger delivers similar sensitivity advances and first-of-its-kind far-infrared hyperspectral imaging for astrophysics with R ∼ 8 from 25 to 84 μm, and polarimetry in four broadband filters from 80 to 261 μm. PRIMA’s science and technical motivation is outlined, its overall architecture is described, and its cryogenic payload and instruments, including the kinetic inductance detector arrays, and operations and observing modes, are summarized.