18. How many squares are exactly four greater than a prime?
A 0
B 1
C 2
D 3
E 4
18. B Let $n^{2}$ be a square which is 4 greater than a prime, $p$.
Then $n^{2}=p+4$. So $p=n^{2}-4=(n+2)(n-2)$.
However, as $p$ is prime, its only factors are $p$ and 1 . So $n+2=p$ and $n-2=1$.
Hence $n=3$ and therefore $p=3+2=5$.
So the only square which is 4 greater than a prime is $3^{2}=9$. It is 4 greater than 5 , which is prime.