Fatto generale: 6740 is a number for which we're missing a fact (submit one to numbersapi at google mail!).
Fatto matematico: 6740 is the number of 13-iamonds that do not tile the plane.
Trivia: 6740 is a boring number.
Data storica: June 14th is the day in 1966 that the Vatican announces the abolition of the Index Librorum Prohibitorum (index of prohibited books), which was originally instituted in 1557.