math_fact: 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!).
historical_date: June 8th is the day in 1856 that a group of 194 Pitcairn Islanders, descendants of the mutineers of HMS Bounty, arrives at Norfolk Island commencing the Third Settlement of the Island.