Convergence of Natural Numbers to Unity via Prime-Factor Processing and Even Correction

In this paper, we introduce a method to analyze natural numbers by decomposing each number into its prime factors and processing each factor independently. The core idea is to reduce even factors by division by 2, while odd factors are adjusted by adding 1 and then repeatedly dividing by 2 until they reach 1. We tested this method on numbers from 1 to 100,000, and 100% of the numbers successfully converged to 1. The maximum number of steps recorded was 35, and the largest intermediate value reached was 99,992. The purpose of this paper is to clearly present and document this algorithm.