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There are N = 6670903752021072936960 6.671×1021 valid Sudoku grids. Taking out the factors of 9! and 722 coming from relabelling and the lexicographical reduction of the top row of blocks B2 and B3, and of the left column of blocks B4 and B7, this leaves 3546146300288 = 27×27704267971 arrangements, the last factor being prime.
9^9 x 8^9 x 7^9 x 6^9 x 5^9 x 4^9 x 3^9 x 2^9 x 1^9 = 362880^9
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