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• It is possible for a Queen to attack all 18 prime numbered squares on a Knight's Tour solution.
  Here is one example in which the Queen sits on square #35.
  Note the primes are colored red.

  37	24	45	4	39	22	47	62
  44	5	38	23	46	61	40	21
  25	36	43	60	3	20	63	48
  6	59	26	35	64	41	2	19
  27	30	57	42	1	34	49	12
  58	7	54	29	52	13	18	15
  31	28	9	56	33	16	11	50
  8	55	32	53	10	51	14	17

  Click here for more information.

18 is the smallest difference between an emirp and its reverse. [Poo Sung]

18 is the common difference in the arithmetic progression formed by the 5th, 10th, and 15th primes. [Rupinski]

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]

The sum of digits, digital product, and reversal of 18 are perfect powers of its prime divisors. [Silva]