21st is usually hyphenated when spelt. Dictionaries list it as 'twenty-first'.
However, as a book/article title, or in company names, it is sometimes written as Twenty First ... as in 'Twenty First Century Poets', but, as this could be interpreted as meaning a book about 1st century poets, a hyphen would remove any ambiguity e.g. written as 'Twenty-first Century Poets' or 'Twenty-First Century Poets' (unless, of course, the book is actually about 1st century poets, in which case a better title would be 'Twenty First-Century Poets'!)
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