Q. When should the word “century” be capitalized? ... Chicago style treats “century” like “day,” “month,” or “year”; we would lowercase it in all the contexts you cite.
Is the twentieth century capitalized?
However, do not capitalize the names of centuries or decades unless they are part of special names: the twentieth century.
Is 21st century a proper noun?
Historical Periods
A numerical designation of a time period is lowercased unless it is part of a proper name (21st century, the nineties). Some names applied to historical periods are capitalized (Ice Age, Roaring Twenties, Reformation).