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2497 is the smallest cyclic number, corresponding to the prime 5 (the next cyclic number is 186X35, corresponding to the prime 7). Note that {2497, 186X35} uses all the digits (except the digits that is not coprime to 10-1 (=E), i.e. {0, E}) exactly once.

2497, the four repeating digits of 1/5, 0.2497, is one of the two best-known cyclic numbers in base 10 (the other is 186X35, the six repeating digits of 1/7, 0.186X35). If it is multiplied by 2, 3, or 4, the answer will be a cyclic permutation of itself, and will correspond to the repeating digits of 2/5, 3/5, or 4/5 respectively.

Unlike the smallest cyclic number in base X: 142857X, which is both Kaprekar number and Harshad number in base X, 2497 is neither Kaprekar number nor Harshad number in base 10.

Calculation[]

1 × 2,497 = 2,497
2 × 2,497 = 4,972
3 × 2,497 = 7,249
4 × 2,497 = 9,724
5 × 2,497 = E,EEE

If multiplying by an integer greater than 5, there is a simple process to get to a cyclic permutation of 2497. By adding the rightmost four digits (ones through thousands) to the remaining digits and repeating this process until only four digits are left, it will result in a cyclic permutation of 2497:

2497 × 6 = 12496
1 + 2496 = 2497
2497 × 351 = 827187
82 + 7187 = 7249
24972 = 59143X1
591 + 43X1 = 4972

Multiplying by a multiple of 5 will result in EEEE through this process:

2497 × 172 = 39EE82
39 + EE82 = EEEE

The result cannot contain either any digit of 1/7 (1, 8, 6, X, 3, 5) or the zero digit (0).