I recently worked through Paul Erdos proof on the Sylvester-Schur theorem.
The proof is from 1934 and I was wondering if anyone since then has made progress in simplifying the argument.
It occurred to me that the standard proof for Bertrand's postulate could be repurposed to prove Sylvester-Schur which should be simpler than the Erdos proof.
Is there a standard proof for Sylvester-Schur that is simpler than the classic one by Erdos?