The Theorem of Sylvester and Schur states that for some n>k, one of n+1,...,n+k-1, has a prime divisor exceeding k. While Bertrand's postulate says that for all positive integers n, there exists a prime number between n and 2n.
I see how these are related but I can't make the direct connection between the two, and I'm struggling to understand why Sylvester and Schur's theorem is a generalization of Bertrand's.