18 (another Prime Pages' Curiosity)
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GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits)

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.

Here is the first known 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 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.)

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