13) Let $X$ be a set of positive integers. It is known that $X$ contains at least one element greater than 1 and that, whenever it contains a certain number $n$, it also contains all numbers greater than $n$ except, possibly, the multiples of $n$. Which of the following statements is certainly correct?

(A) $X$ is a finite set

(B) the set $X$ and the set of positive integers that do not belong to $X$ are both infinite

(C) $X$ contains all prime numbers

(D) there exists a number $m$ such that $X$ contains all integers greater than $m$

(E) $X$ is equal to the set of all positive integers
13) The answer is (D).

Indeed, if $n>1$ is an element of $X$, then $n+1$ is greater than $n$ but is not a multiple of $n$ and therefore belongs to $X$. Similarly, all numbers $n+2, n+3, \ldots$ belong to $X$. For the reasons stated, (A) and (B) are false. Furthermore, the set of integers greater than 10 provides an example of a set that satisfies the required properties but contradicts (C) and (E).