  We show that the independence number of $ G_{n,p}$ is concentrated on two
values if $ n^{-2/3+ \epsilon} < p \le 1$. This result is roughly best possible
as an argument of Sah and Sawhney shows that the independence number is not, in
general, concentrated on 2 values for $ p = o \left( (\log(n)/n)^{2/3}
\right)$. The extent of concentration of the independence number of $ G_{n,p}$
for $ \omega(1/n) <p \le n^{-2/3}$ remains an interesting open question.
