Limit of the given set

Question

$S=\{ p \: \mathrm{if} \: n=p^r,r>1 \: \mathrm{and} \: 0 \: \mathrm{otherwise}\}$ Where $p$ is prime no. And $n$ is natural no. $S=\{0,0,0,2,0,0,0,2......\}$ my teacher says all $p$ and $0$ are limit point of set $S$ but according to def of limit point every neighborhood of limit point must contain infinite many point of set. so in general this set is $S=\{0,p\}$ where $p$ is prime no. so $0$ has no point in is nbd, as I thinks, so how it could be limit point of set $S$ but my teacher says their is infinite many zero in set so nbd of $0$ contains infinite many point of $S$ , so it is limit point Plz help bcz I am stuck between my thinking and my teacher bcz repeated elements in set can be taken as one