General fact: 4684 is a number for which we're missing a fact (submit one to numbersapi at google mail!).
Mathematical fact: 4684 is the number of subsets of {1,2,3,...,15} that have a sum divisible by 7.
Trivia: 4684 is an uninteresting number.
Historical date: October 27th is the day in 1964 that Ronald Reagan delivers a speech on behalf of Republican candidate for president, Barry Goldwater.