Number Theory

    

Inverse Long Multiplication Program in the Factorization of Semiprime Numbers

Authors: Silvio Gabbianelli

Semiprime numbers are natural integers obtained from the multiplication of two prime numbers. In attempting to solve the factorization of a semiprime number, I considered the inverse procedure of the long multiplication method we learned in elementary school. After careful reflection, I found it to be both useful and feasible. The only known element in this procedure is the result (which must be an odd integer semiprime). We need to find the two sets [n1,n2,...nk][n1, n2, ... nk] and [m1,m2,...mk][m1, m2, ... mk] that will represent the two unique multiplicands that produce the known result. These sets are reconstructed through a triangular matrix, where the rows represent units, tens, hundreds, and so on, and the columns grow and then shrink in size. This matrix allows us to identify the necessary multiplicative pairs by ensuring the result satisfies the condition of being an odd integer that doesn't end in 5.

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[v1] 2025-01-20 20:16:29

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