On a conjecture of Graham on the p-divisibility of central binomial
coefficients $\binom{2n}{n}$.
In this talk I will discuss some conjectures on which values of n we
have that $\binom{2n}{n}$ is not divisible by sets of primes $p_1,p_2,...,p_r$,
including a conjecture of R. L. Graham. We do not resolve these conjectures,
but have made some progress on some of these conjectures. This is joint with
Hamed Mousavi and Maxie Schmidt.