Erdős's proof of Sylvester's theorem Sylvester's theorem states that the product of $k$ consecutive integers $>k$ has a prime factor $p>k$. Erdős gave a short proof for it, but I can't find Erdős's proof online. Can anyone give a sketch of the proof? Thanks.

The proof is available on-line here in white on black and here in black on white. And here is a PDF of Erdős’s paper, _A Theorem of Sylvester and Schur_.

**Added:** As Coffee_Table notes in the comments, Paul Erdős’s papers from $1929$ through $1989$ are available here; the site’s front page has a search engine.