Fait mathématique: 5638 is the number of 3×3 sliding puzzle positions that require exactly 17 moves to solve starting with the hole in a corner.
Culture générale: 5638 is a number for which we're missing a fact (submit one to numbersapi at google mail!).
Date historique: June 8th is the day in 1783 that the volcano Laki, in Iceland, begins an eight-month eruption which kills over 9,000 people and starts a seven-year famine.