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April 28, 2026Open Access

Primes as a Field on a Discrete Torus: Primorial Field Dynamics, Gap Composition Profiles, and an Information-Theoretic Reformulation -- PrimSpace v3.0

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Authors

LTLászló Tatai

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Overview

Randomized trial investigates prime number distribution using a novel framework, highlighting significant patterns and implications.

Key Points

  • This research aims to explore the local distribution of prime numbers through a new geometric and information-theoretic framework.
  • Introduced Primorial Field Dynamics (PFD) using discrete tori for prime number study.
  • Numerical tests involved analysis of 5,761,453 prime gaps up to N=10⁸.
  • Developed structural objects like the Gap Composition Profile and Liquid Media to analyze prime clusters.
  • The GCP Fourier spectrum showed significant amplitude excess at Riemann zeta zero positions (mean Z=2.52, max Z=10.67, p<10⁻²⁹).
  • Primes were found to have an entropy decomposition, where the sieve accounts for 57.4% of primality entropy and ρ(s) carries 42.6%.
  • The corrected W-convergence limit demonstrated a methodological improvement.

Cite This Study

László Tatai (2026) studied this question.

synapsesocial.com/papers/69f04e7d727298f751e72738https://doi.org/10.5281/zenodo.19794151
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