It depends on when you do the query. Years ago (mid 2000s) at ITA, Carl wrote code to find the longest possible shortest route between any two airports with scheduled flights. At the time the winner was Wasu, New Guinea to Peawanuck, Ontario, which took a minimum of 90 hours and many flights. There are airports you can only get to at the end of a long line of stops; this drives the number of stops way up.
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