Fatto generale: 1113 is a number for which we're missing a fact (submit one to numbersapi at google mail!).
Fatto matematico: 1113 is the number of partitions of 40 into distinct parts.
Trivia: 1113 is a boring number.
Data storica: January 17th is the day in 395 that Emperor Theodosius I dies in Milan, the Roman Empire is re-divided into an eastern and a western half.