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The article investigates the detail distribution of RSA modulus’ small divisor in the T3 tree in terms of the divisor-ratio. It proves that, the distribution of the small divisor in T3 tree is completely determined by the divisor-ratio and the parity of the level where the RSA modulus lies, the small divisor of a RSA modulus lying on an even level lies on the same level as where the square root of the modulus is clamped, whereas that of a modulus on an odd level possibly lies on the same level or the higher adjacent level of the square root. Through mathematical induction, it shows that a smaller divisor-ratio results in a closer position of the small divisor to the square root of a RSA modulus.

Distribution of RSA Number’s Divisor on T3 Tree