Fait mathématique: 2560 is the number of 2×2 singular matrices mod 8.
Culture générale: 2560 is a number for which we're missing a fact (submit one to numbersapi at google mail!).
Date historique: January 3rd is the day in 1888 that the refracting telescope at the Lick Observatory, measuring 91 cm in diameter, is used for the first time.