| _version_ | 1866901615890399232 |
|---|---|
| author | Romagnoli, Federico |
| author_facet | Romagnoli, Federico |
| contents | <p>This work investigates the structural limits underlying the distribution of prime numbers by shifting the focus from primes to composite numbers. Two families of polynomial sequences defined on discrete domains are analyzed, showing that the set of odd composite numbers admits a complete analytic and geometric description, while prime numbers emerge as a complementary, non-generable residue.</p> <p>The study demonstrates that quadratic polynomial families represent a natural efficiency bound for discrete primality sieves and that higher-degree or sub-linear constructions necessarily lead to redundancy or incompleteness. The absence of complex solutions in the generating families highlights that the observed complexity of primes is not analytic in origin, but arithmetical and discrete.</p> <p>Within this framework, the notion of structural chaos is introduced to describe the prime distribution as a deterministic but non-periodic residue of an underlying ordered structure. The role of the Riemann zeta function is reinterpreted as a global descriptive tool that captures this chaos without generating primes or eliminating their irregularity.</p> <p> </p> <p>Note<br>Access to the file is restricted for editorial copyright reasons.<br>The complete work, including all chapters, proofs, and graphical material, is available in print through the Amazon publishing channel. Editorial reference: https://www.amazon.com/dp/B0GKXMDLRR/</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18443633 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Boundaries and Limits of the Structural Chaos of Prime Numbers Romagnoli, Federico Prime numbers number theory composite numbers discrete structures polynomial sequences structural order deterministic chaos <p>This work investigates the structural limits underlying the distribution of prime numbers by shifting the focus from primes to composite numbers. Two families of polynomial sequences defined on discrete domains are analyzed, showing that the set of odd composite numbers admits a complete analytic and geometric description, while prime numbers emerge as a complementary, non-generable residue.</p> <p>The study demonstrates that quadratic polynomial families represent a natural efficiency bound for discrete primality sieves and that higher-degree or sub-linear constructions necessarily lead to redundancy or incompleteness. The absence of complex solutions in the generating families highlights that the observed complexity of primes is not analytic in origin, but arithmetical and discrete.</p> <p>Within this framework, the notion of structural chaos is introduced to describe the prime distribution as a deterministic but non-periodic residue of an underlying ordered structure. The role of the Riemann zeta function is reinterpreted as a global descriptive tool that captures this chaos without generating primes or eliminating their irregularity.</p> <p> </p> <p>Note<br>Access to the file is restricted for editorial copyright reasons.<br>The complete work, including all chapters, proofs, and graphical material, is available in print through the Amazon publishing channel. Editorial reference: https://www.amazon.com/dp/B0GKXMDLRR/</p> |
| title | Boundaries and Limits of the Structural Chaos of Prime Numbers |
| topic | Prime numbers number theory composite numbers discrete structures polynomial sequences structural order deterministic chaos |
| url | https://doi.org/10.5281/zenodo.18443633 |