Solution: The answer is $\ell=13$. The example is the numbers in the form $S=10^{6k_1}+10^{6k_2}+\dots+10^{6k_{63}}$ with $k_1,k_2,\dots, k_{63}$ pairwise distinct positive integers. It's easy to verify that $P_0(S+k)|S+k$ with $k\in \{0,1,\dots,12\}$. Let's look to the final digit, if $\ell \geq 14$, then there are four numbers(in order) which the final digit(s) are in one of the following sequences: $(3,6,9,3),(6,9,3,6)$ or $(9,3,6,9)$. Let $n$ the number that ends in $9$, therefore $3|P_0(n)|n$, but $n+4$ ends in $3$, so $3|P_0(n+4)|n+4 \Rightarrow 3|4$, contradiction.