Tom Brady has the most games when he has had 14 or more (ATT/GP) and with exactly 0 intercepted passes, with 168 games.

most games without an interception, mimimum 14 pass attempts per game
Interpreted as:
most regular-season games without an passing interception by a player, mimimum 14 or more pass attempts per game
BradyBreesRodgersBrunellHasselbeckManningRiversFavreRyanSmithRoethlisbergerJohnsonMontanaHarbaughYoungKriegAndersonTarkentonDeBergManningElwayJaworskiChandler168130128119113112108106999999999694939393939089898885
NAMEGPATTINTATT/GPCMPPCTYDSAVGYDS/GTDTD%INT%SCKSCKYRATE
Tom BradyTom Brady1685,669033.743,70265.344,0547.8262.23556.30.02771,757109.8
Drew BreesDrew Brees1304,419033.993,18572.135,9828.1276.82956.70.01581,046118.3
Aaron RodgersAaron Rodgers1284,045031.62,69966.732,3788.0253.02827.00.02771,913114.3
Mark BrunellMark Brunell1192,312019.431,42661.716,7227.2140.5954.10.01861,18297.3
Matt HasselbeckMatt Hasselbeck1132,096018.551,33163.515,3817.3136.1964.60.0137847100.8
Peyton ManningPeyton Manning1123,594032.092,45368.329,4538.2263.02486.90.0107685116.1
Philip RiversPhilip Rivers1083,242030.022,19667.727,2318.4252.11946.00.01681,041113.5
Brett FavreBrett Favre1063,269030.842,16766.325,5967.8241.52216.80.01731,085112.5
Matt RyanMatt Ryan993,393034.272,29967.826,4497.8267.21755.20.01801,164108.2
Alex SmithAlex Smith992,858028.871,83864.320,6697.2208.81224.30.02331,278100.0
Ben RoethlisbergerBen Roethlisberger993,102031.332,06866.725,2828.2255.42026.50.02011,313113.3
Brad JohnsonBrad Johnson991,638016.551,04563.811,6647.1117.8804.90.090597101.2
Joe MontanaJoe Montana962,108021.961,34063.616,5677.9172.61165.50.0106.1
Jim HarbaughJim Harbaugh941,747018.591,06961.212,0316.9128.0593.40.01801,12093.0
Steve YoungSteve Young931,863020.031,24967.015,4348.3166.01196.40.0151879113.8
Dave KriegDave Krieg931,729018.591,06861.813,4767.8144.91066.10.0106.5
Ken AndersonKen Anderson931,775019.091,11562.814,2648.0153.41055.90.0107.6
Fran TarkentonFran Tarkenton932,202023.681,30459.216,8697.7181.41416.40.0104.7
Steve DeBergSteve DeBerg901,434015.9387460.910,7117.5119.0755.20.0101.4
Eli ManningEli Manning892,824031.731,77462.820,6997.3232.61485.20.0140931102.4
John ElwayJohn Elway892,547028.621,51759.619,3647.6217.61254.90.01851,28299.8
Ron JaworskiRon Jaworski881,289014.6572256.09,4347.3107.2645.00.095.8
Chris ChandlerChris Chandler851,607018.9198461.212,4267.7146.2875.40.01581,103103.4
Dan MarinoDan Marino852,722032.021,68561.920,2187.4237.91395.10.088611101.6
Joe TheismannJoe Theismann851,193014.0471259.78,9137.5104.9736.10.0103.3
StatMuse has game-level data for intercepted passes and passing attempts going back to the 1950 season.

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