Mathematical fact: 10514 is an unremarkable number.
Trivia: 10514 is a number for which we're missing a fact (submit one to numbersapi at google mail!).
Historical date: October 13th is the day in 1332 that Rinchinbal Khan, Emperor Ningzong of Yuan becomes the Khagan of the Mongols and Emperor of the Yuan Dynasty, reigning for only 53 days.