Mathematical fact: 6668 is the number of trees on 21 vertices with diameter 5.
Trivia: 6668 is a number for which we're missing a fact (submit one to numbersapi at google mail!).
Historical date: April 3rd is the day in 1933 that First flight over Mount Everest, a British expedition, led by the Marquis of Clydesdale, and funded by Lucy, Lady Houston.