Mathematical fact: 4311 is the largest number n known with the property that n-2^{k} is a pseudoprime for all k>0.
Trivia: 4311 is a number for which we're missing a fact (submit one to numbersapi at google mail!).
Historical date: October 20th is the day in 1962 that China launches simultaneous offensives in Ladakh and across the McMahon Line, beginning the Sino-Indian War.