I think The Federated States of Micronesia to Dominica ties Michael’s answer with 5 segments:
You could also do NRT and JFK instead of HNL and ATL if you really like taking the long way. Or you could substitute JFK for ATL while leaving HNL.
Note that while the Wiki pages for Chuuk and other Federated States of Micronesia airports mention flights to HNL, these are all the United “Island Hopper” flight and are not non-stop.
5 flight segments:
From Vientiane to Rio it takes at least 3 flights. Which means that from smaller Lao airports like Luang Namtha nor Oudomsay, which have flights only to VTE, it takes at least 4 hops. Attapeu was worse, since it took two hops to VTE (AOU-PKZ, PKZ-VTE), but it’s closed now.
From Nauru, the only “mainland” airport you can fly to is Brisbane, Australia. From there it is at least two hops to anywhere in Europe or Africa. On the other hand, from the only international airport in Equitorial Guinea you must fly to another airport in Africa, or an airport in Europe, before you can go anywhere else. So I believe that flying from Nauru to Equitorial Guinea will take you at least four hops.
Credit:stackoverflow.com‘