UAL 1 and 2 are (were?) RTW routes. LAX-HKG-DEL-LHR-JFK-LAX or something like that. I've never done a RTW, but did fly that flight from LAX to DEL. I thought it was amusing that they announced it as United flight 1 to Hong Kong with continuing service to Los Angeles.
I believe it's gone now and thus hasn't stood the test of time. But it was easily recognized.
cnk