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April 10, 2026Open Access

The Prime Jump System: Nine Elementary Theorems and the Universal Termination Conjecture

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Authors

JRJose Luis Roman

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Overview

This research demonstrates nine theorems about predictability in the Prime Jump System, suggesting new insights into primality.

Key Points

  • The aim is to establish foundational theorems about the Prime Jump System and explore its properties.
  • Developed a discrete additive dynamical system over natural numbers.
  • Coupled a Fibonacci recurrence with a primality-stopping condition.
  • Analyzed orbits for predictability, strict monotonicity, and parity.
  • Investigated the role of Mersenne primes as fixed points.
  • Formulated the Universal Termination Conjecture and employed CRT sieves.
  • Proved nine fundamental theorems about the orbits in the Prime Jump System.
  • Demonstrated that Mersenne primes serve as perfect absorbing fixed points.
  • Provided insights into the density of attractors via heuristics linked to CRT.

Cite This Study

Jose Luis Roman (2026) studied this question.

synapsesocial.com/papers/69d895046c1944d70ce05effhttps://doi.org/10.5281/zenodo.19461661
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