This is the 14583rd most frequent German word.
längsten
Superlative form of "lang" meaning "longest."
Here, 'längsten' is used in the context of expressing a subjective impression of a very long duration of time.
Ich warte seit längsten auf eine Antwort!
I have been waiting for the longest time for an answer!
In this example, 'längsten' is used to describe the greatest extent of duration among a set of considered periods.
Hast du den Bericht schon über den längsten Zeitraum überprüft?
Have you already checked the report over the longest period?
In this sentence, 'längste' is used as the superlative form of 'lang', referring to physical length in terms of dimension or distance, here describing the river.