8666 = 2 x 7 x 619.
8666 has a 9th root whose decimal part starts with the digits 1 to 9 in some order.
8666 is a beastly number (A051003).
8666 is the number of permutations of length 21 that avoid the patterns 123 and 4312 (A116699).
8666 is a number n such that n, n + 1, n + 2, and n + 3 are not divisible by any of their nonzero digits (A244358).
8666 is a number n such that n ends with 6 and is the difference of cubes in at least one way (A038861).
Source: What's Special About This Number?