We have developed a two-step " R-transfer" method that efficiently produces translationally ultracold potassium molecules in the X (1)Sigma(+)(g) electronic ground state. Laser-cooled atoms are initially photoassociated at large internuclear separation R to form molecules in high vibrational levels of the 1 (1)Pi(g) state, which are in turn excited by an additional laser to shorter-range Rydberg states such as 5 (1)Pi(u) and 6 (1)Pi(u). Subsequent radiative decay produces ground-state molecules at rates up to 10(5) molecules/second per vibrational level.