3666 = 2 x 3 x 13 x 47.
3666 is the number of ways to tile a 4 x 46 room with 1 x 2 Tatami mats, with at most three Tatami mats meeting at a point (A068923).
3666 is the number of partitions of the 33rd decimal palindrome into distinct decimal palindromes (A091585).
3666 divides 956 - 1.
Source: OEIS
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