10. What is the largest possible prime value of $n^{2}-12 n+27$, where $n$ ranges over all positive integers?
(A) 91
(B) 37
(C) 23
(D) 17
(E) 7
10. (E)
Note that $n^{2}-12 n+27=(n-9)(n-3)$. For this number to be a prime, either $n=$ 10 , in which case $n^{2}-12 n+27=7$; or $n=2$, in which case $n^{2}-12 n+27=7$. Since a prime number cannot be factorized in other ways, we know that 7 is the only answer.