  We present a detailed overview of the science goals and predictions for the
Prime-Cam direct detection camera/spectrometer being constructed by the
CCAT-prime collaboration for dedicated use on the Fred Young Submillimeter
Telescope (FYST). The FYST is a wide-field, 6-m aperture submillimeter
telescope being built (first light in mid-2024) by an international consortium
of institutions led by Cornell University and sited at more than 5600 meters on
Cerro Chajnantor in northern Chile. Prime-Cam is one of two instruments planned
for FYST and will provide unprecedented spectroscopic and broadband measurement
capabilities to address important astrophysical questions ranging from Big Bang
cosmology through reionization and the formation of the first galaxies to star
formation within our own Milky Way galaxy. Prime-Cam on the FYST will have a
mapping speed that is over ten times greater than existing and near-term
facilities for high-redshift science and broadband polarimetric imaging at
frequencies above 300 GHz. We describe details of the science program enabled
by this system and our preliminary survey strategies.
