8. If there exists a sufficiently large positive integer $n$, which, apart from not being divisible by two consecutive positive integers $k$, $k+1$ from 1 to 250, is divisible by all other integers from 1 to 250, then $k=$ $\qquad$
8.127

Analysis: First, it is clear that $k \neq 1$. When $2 \leq k \leq 125$, since $k$ does not divide $n$, $2k$ does not divide $n$, and $k+1125$; Second, if $k=r s$, where $(r, s)=1, r \geq 2, s \geq 2, r, s \in N$, since $k$ does not divide $n$, one of $r, s$ must not divide $n$, leading to a contradiction! Therefore, $k$ must be a prime or a power of a prime, and similarly, $k+1$ must also be a prime or a power of a prime; Finally, since one of $k, k+1$ is even, one of them must be a power of 2. In the range from 125 to 250, only 128 is a power of 2, $128=2^{7}$. Since 127 is a prime number and 129 is not a prime number, it follows that $k=127$.