Fatto generale: 6723 is a number for which we're missing a fact (submit one to numbersapi at google mail!).
Fatto matematico: 6723 is a value of n for which 3n and 8n together use each digit exactly once.
Trivia: 6723 is a boring number.
Data storica: May 28th is the day in 585 BC that a solar eclipse occurs while Alyattes is battling Cyaxares in the Battle of the Eclipse, leading to a truce.