We study universal properties of random knotting by making an extensive use of isotopy invariants of knots. We define knotting probability (P K (N )) by the probability of an N -noded random polygon being topologically equivalent to a given knot K. The question is the following: for a given model of random polygon how the knotting probability changes with respect to the number N of polygonal nodes? Through numerical simulation we see that the knotting probability can be expressed by a simple

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... ction of N . From the result we propose a universal exponent of P K (N ), which may be a new numerical invariant of knots.