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 |
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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]
18 equals the product of its prime divisors plus the product of their factorials. [Silva]
There are a prime number (197699) of zeros in the set of
all primes whose binary representation is no more than 18
bits, including leading zeros. [Post]
The difference between any emirp pair is divisible by 18. [Green]
(There are 3 curios for this number that have not yet been approved by an editor.) To link to this page use http://primes.utm.edu/curios/page.php?number_id=77
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