Composite Interval Representations of Primes and Finite-Window Phase Transition

Key Points

• This research aims to develop a representation system for primes using composite integers and explore its behavior with varying window sizes.
• Introduced two representation modes: PURE and R1.
• Examined empirical behavior of these modes under increasing window sizes.
• Developed a computational framework to analyze representations.
• Identified a conjectured phase transition phenomenon in the composite-domain representations.
• Showed that representation modes behave differently as the window size increases.