Legitimate colorings of projective planes

For a projective plane Pn of order n, let X(Pn) denote the minimum number k, so that there is a coloring of the points of P~ in k colors such that no two distinct lines contain precisely the same number' of points of each color. Answering a question of A. Rosa, we show that for all sufficiently large n, 5 < X(Pn) < 8 for every projective plane P, of order n.