Drew Brees had the most games with 400+ passing yards and 3+ passing touchdowns, with 12 games.

who has the most games with 400 passing yard and 3 passing td
Interpreted as:
Who has the most regular-season games with 400 or more passing yard and 3 or more passing td?
BreesManningMarinoBradyPrescottManningMontanaMahomesCousinsFitzpatrickRodgersRoethlisbergerStaffordKriegFoutsJurgensenRiversRyanRomoPalmerBledsoeKramerCarr12111196665555555554444443
NAMEGPYDSTDCMPATTPCTAVGYDS/GTD%INTINT%SCKSCKYRATE
Drew BreesDrew Brees125,2454539955172.49.5437.18.240.716113126.3
Peyton ManningPeyton Manning114,7494630745467.610.5431.710.1102.21158126.6
Dan MarinoDan Marino114,8144433654561.78.8437.68.1203.714116101.9
Tom BradyTom Brady93,9183227639270.410.0435.38.230.81893126.4
Dak PrescottDak Prescott62,6812021630570.88.8446.86.662.01075111.4
Eli ManningEli Manning62,6581919228966.49.2443.06.6134.585898.9
Joe MontanaJoe Montana62,6102517526167.010.0435.09.662.319142122.0
Patrick MahomesPatrick Mahomes52,2452116723172.39.7449.09.131.3956127.7
Kirk CousinsKirk Cousins52,1281617023971.18.9425.66.720.8965117.3
Ryan FitzpatrickRyan Fitzpatrick52,0511914522165.69.3410.28.673.21049110.9
Aaron RodgersAaron Rodgers52,1632014520072.510.8432.610.010.51386138.8
Ben RoethlisbergerBen Roethlisberger52,2851917324969.59.2457.07.620.81278120.3
Matthew StaffordMatthew Stafford52,1552014222762.69.5431.08.873.11063110.3
Dave KriegDave Krieg52,0521814021266.09.7410.48.583.815127110.0
Dan FoutsDan Fouts52,1741913821863.310.0434.88.762.8114.0
Sonny JurgensenSonny Jurgensen52,0871712721060.59.9417.48.1104.8101.0
Philip RiversPhilip Rivers41,6781213217376.39.7419.56.921.2319124.4
Matt RyanMatt Ryan41,7811312217171.310.4445.37.621.2844125.4
Tony RomoTony Romo41,7691511918763.69.5442.38.063.214100107.9
Carson PalmerCarson Palmer41,6671613920368.58.2416.87.952.5973109.4
Drew BledsoeDrew Bledsoe41,7291314221167.38.2432.36.241.9539104.9
Tommy KramerTommy Kramer41,8261511318262.110.0456.58.263.3109.4
Derek CarrDerek Carr31,3671110416961.58.1455.76.521.2526103.8
Jameis WinstonJameis Winston31,319119714566.99.1439.77.653.4535106.7
Nick FolesNick Foles31,305148712569.610.4435.011.221.6642134.3
StatMuse has game-level data for passing touchdowns and passing yards going back to the 1950 season.

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