8. (6 points) From $1,2,3, \cdots, 2016$, if $n$ numbers are arbitrarily taken out, and at least two of the taken numbers are coprime, then the smallest $n$ is $\qquad$ .
【Solution】Solution: According to the analysis, among the numbers $1 \sim 2016$, there are 1008 odd numbers and 1008 even numbers. Since even numbers cannot be coprime with each other, hence:
(1) When $n<1008$, it is possible to select $n$ numbers that are all even, in which case there will not be at least two numbers that are coprime;
(2) When $n=1008$, if the selected numbers are all even, there will also not be at least two numbers that are coprime;
(3) When $n \geqslant 1009$, then among the $n$ selected numbers, there must be at least one odd number. This odd number and its adjacent even number will definitely be coprime,

In summary, the minimum value of $n$ is 1009.
Therefore, the answer is: 1009.