Logarithmic Self-Symmetry of Prime Numbers — Theoretical Foundations and Computational Evidence
Year: 2025
Type: article
Abstract: This work presents a theoretical and computational study on the logarithmic self-symmetry of prime numbers. The research introduces a geometric interpretation of multiplication, showing that every integer can be represented in a mirrored logarithmic space around its square root. This approach reveals a pattern of multiplicative symmetry that applies to both composite and prime numbers. Using large-scale computations of consecutive prime ratios, the study demonstrates that the logarithmic increments between consecutive primes tend to stabilize as numbers grow larger. This statistical stabilization suggests a possible invariant distribution of prime ratios, consistent with the Prime Number Theorem. The work proposes a new geometric framework for visualizing prime distribution and a conjecture on logarithmic invariance of prime gaps. It unifies multiplicative structure and logarithmic growth under a single theoretical model. Author: Luiz Alessandro Bittencourt MochkoAffiliations: Universidade Federal do Paraná (UFPR); UniEnsino, BrazilRole: ProducerLicense: Creative Commons Attribution 4.0 (CC BY 4.0)Date: October 2025
Author: MOCHKO, LUIZ ALESSANDRO BITTENCOURT
Institution: Universidade Federal do Paraná
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7101822960
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