Fatto matematico: 5638 is the number of 3×3 sliding puzzle positions that require exactly 17 moves to solve starting with the hole in a corner.
Trivia: 5638 is a number for which we're missing a fact (submit one to numbersapi at google mail!).
Data storica: June 8th is the day in 1794 that Robespierre inaugurates the French Revolution's new state religion, the Cult of the Supreme Being, with large organized festivals all across France.