The Green Bay Packers have 274 passes picked off since 2000.

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packers interceptions thrown since 2000
TEAMGPINTCMPATTPCTYDSAVGYDS/GTDTD%INT%SCKSCKYRATE
Green Bay PackersGreen Bay Packers3482747,84212,35463.591,2217.4262.16805.52.27425,01794.9
StatMuse has team, season-level data for intercepted passes going back to the 1932 season.