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

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.

Abstract