Dynamical Behavior of an Iterative Decimal-Splitting and Prime Factorization Mapping on Primes

This paper defines a new iterative mapping on prime numbers based on decimal splitting and prime factorization. For a given prime p, we split its decimal digits into segments. We then replace any composite segments with their prime factors. The resulting concatenated integer is processed again under the same rules. We model this sequence as a directed graph. In this graph, primes act as nodes and the mapping steps form directed edges. By computing the process for the first 1500 primes (up to 12553), we observe strong convergence and bifurcation phenomena. Specifically, 1160 terminal primes are reached by at least two different starting primes. We call these terminal primes attractors. In addition, 827 starting primes can reach multiple different endpoints via different shortest paths. We also study the termination bounds and investigate whether any absorbing states exist.