First recorded (as “The Prime of Your Life”) by Billy Joel (1982).
Hit version by Billy Joel (US #14/UK #25/AUS #18 1984).
From the wiki: “‘The Longest Time’ was written by Billy Joel and first recorded as the demo ‘The Prime of Your Life’ in 1982. The song would evolve into a tribute of the 1950s Doo-wop sounds that Joel loved. The released single, in 1984, would be recorded quasi-a capella: Only one musical instrument, a bass guitar, is present in the arrangement. All other sounds in the song are Joel’s vocals (14 different background tracks), along with the percussive sounds of finger-snaps and hand-claps.”
Billy Joel, “The Longest Time” (1984):