Question 12
For a positive integer $p,$ define the positive integer $n$ to be $p$-*safe* if $n$ differs in absolute value by more than $2$ from all multiples of $p.$ For example, the set of $10$-safe numbers is $\{3,$ $4,$ $5,$ $6,$ $7,$ $13,$ $14,$ $15,$ $16,$ $17,$ $23,$ $\ldots\}.$ Find the number of positive integers less than or equal to $10{,}000$ which are simultaneously $7$-safe, $11$-safe, and $13$-safe.