35.3. Find all integers $n$ for which the number $\left|n^{2}-6 n-27\right|$ is prime
35.3. We have: $\left|n^{2}-6 n-27\right|=|n+3| \cdot|n-9|$. The product of the absolute values will be a prime number if one of the absolute values is equal to one, and the other is a prime number at that time. The first absolute value is equal to one at $n=-4$ and $n=-2$, and the second at $n=8$ and $n=10$. It is easy to check that for all the specified values of $n$, the other absolute value is a prime number (11 or 13).