Polynomial Constellations in Deep Arithmetic Space: Data, Code, and Figures for Q(n) = n⁴⁷ − (n−1)⁴⁷ Prime k-Tuple Analysis
Fuente:
Zenodo
Saved in:
| Main Author: | |
|---|---|
| Format: | Recurso digital |
| Language: | English |
| Published: |
Zenodo
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866901102291582976 |
|---|---|
| author | Chen, Ruqing |
| author_facet | Chen, Ruqing |
| contents | <p>Companion repository for the paper "Polynomial Constellations in Deep Arithmetic Space: Empirical Analysis of Prime k-Tuples and the Bateman–Horn Heuristic for Q(n) = n⁴⁷ − (n−1)⁴⁷."</p> <p>We searched Q(n) = n⁴⁷ − (n−1)⁴⁷ over n ≤ 2 × 10⁹, accumulating 17,908,247 strong probable primes (25-round Miller–Rabin) with up to 430 decimal digits. The dataset includes:</p> <p>• A proven Structural Exclusion Theorem: (Q(n), Q(n)+2) can never both be prime, since Q(n) ≡ 1 (mod 3) for all n ≥ 2.</p> <p>• 170,346 consecutive pairs, 1,691 triples, and 14 quadruplets — instances where four consecutive integers all generate probable primes exceeding 10⁴⁰⁰.</p> <p>• Bateman–Horn consistency: the correction factor C_Q = 8.7 ± 0.1 yields predictions within 2% of the observed prime count.</p> <p>This repository contains the paper (LaTeX source and compiled PDF), all six figures, data files (quadruplet coordinates and density statistics), and Python verification scripts for independent reproducibility.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18520295 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Polynomial Constellations in Deep Arithmetic Space: Data, Code, and Figures for Q(n) = n⁴⁷ − (n−1)⁴⁷ Prime k-Tuple Analysis Chen, Ruqing Bateman-Horn conjecture polynomial primes prime constellations prime k-tuples experimental number theory Miller-Rabin cyclotomic polynomial singular series Mathematics Number Theory Computational Mathematics <p>Companion repository for the paper "Polynomial Constellations in Deep Arithmetic Space: Empirical Analysis of Prime k-Tuples and the Bateman–Horn Heuristic for Q(n) = n⁴⁷ − (n−1)⁴⁷."</p> <p>We searched Q(n) = n⁴⁷ − (n−1)⁴⁷ over n ≤ 2 × 10⁹, accumulating 17,908,247 strong probable primes (25-round Miller–Rabin) with up to 430 decimal digits. The dataset includes:</p> <p>• A proven Structural Exclusion Theorem: (Q(n), Q(n)+2) can never both be prime, since Q(n) ≡ 1 (mod 3) for all n ≥ 2.</p> <p>• 170,346 consecutive pairs, 1,691 triples, and 14 quadruplets — instances where four consecutive integers all generate probable primes exceeding 10⁴⁰⁰.</p> <p>• Bateman–Horn consistency: the correction factor C_Q = 8.7 ± 0.1 yields predictions within 2% of the observed prime count.</p> <p>This repository contains the paper (LaTeX source and compiled PDF), all six figures, data files (quadruplet coordinates and density statistics), and Python verification scripts for independent reproducibility.</p> |
| title | Polynomial Constellations in Deep Arithmetic Space: Data, Code, and Figures for Q(n) = n⁴⁷ − (n−1)⁴⁷ Prime k-Tuple Analysis |
| topic | Bateman-Horn conjecture polynomial primes prime constellations prime k-tuples experimental number theory Miller-Rabin cyclotomic polynomial singular series Mathematics Number Theory Computational Mathematics |
| url | https://doi.org/10.5281/zenodo.18520295 |