The Incompressibility Limit of the Prime Sequence
Year: 2025
Type: article
Abstract: We propose a new theory of structural complexity for the prime number sequence, based on a residual compressibility metric λk. By comparing compression ratios of prime sequences and their modeling residuals under various structure-based approxi- mations (e.g., log x, Li(x), Riemann R(x)), we observe that the prime sequence exhibits a compressibility pattern that approaches but never reaches that of true random se- quences. This suggests that primes represent a unique class of boundary structures — neither fully random nor fully ordered — which we formally describe as the Prime Residual Compressibility Limit (PRCL).
Author: Li, Y.Y.N.
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6949810643
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