Is it possible for a Queen to attack all 18 prime-numbered squares on a Knight's Tour solution? Yes, however the total number of distinct solutions remains unknown.
Note the primes are colored red.
The smallest number C of the form 2a^2 such that C+1 and C-1 are both prime. [Hartley]
18 is the largest value of n less than a thousand such that if L(n) = length of n in base 10, then 2*n^n+1, 2*L(n^n)+1, and 2*L(L(n^n))+1 are all primes greater than 3 (as the expression 2*L(L(L(...(L(x))...)))+1 will converge at 3 for sufficient repetitions of L given any value of x). [Opao]
18 is the only two-digit number m , such that three numbers, m + prime(m), m^2 + prime(m^2) & m^3 + prime(m^3), are primes. [Firoozbakht]
18 equals the product of its prime divisors plus the product of their factorials. [Silva]
The difference between any emirp pair is divisible by 18. [Green]
There are only 18 primes that consist of distinct prime digits. Six of them yield three pairs of emirps. [Loungrides]
(There are 11 curios for this number that have not yet been approved by an editor.)