RU-SPB 2010 Problem 114

Natural number $N$ is given. Let $p_N$ - biggest prime, that $\leq N$ . On every move we replace $N$ by $N-p_N$ . We repeat this until we get $0$ or $1$ . If we get $1$ then $N$ is called as good, else is bad. For example, $95$ is good because we get $95 \to 6 \to 1$ . Prove that among numbers from $1$ to $1000000$ there are between one quarter and half good numbers