Let m(n, r) denote the minimal number of edges in an n-uniform hypergraph which is not r-colorable. It is known that for a fixed n one has cnrⁿ < m(n, r) < Cnrⁿ. We prove that for any fixed n the sequence ar:= m(n, r)/rⁿ has a limit, which was conjectured by Alon. We also prove the list colorings analogue of this statement.