Wedi'i Gadw mewn:
| Prif Awdur: | |
|---|---|
| Fformat: | Recurso digital |
| Iaith: | Saesneg |
| Cyhoeddwyd: |
Zenodo
2026
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| Pynciau: | |
| Mynediad Ar-lein: | https://doi.org/10.5281/zenodo.18520295 |
| Tagiau: |
Ychwanegu Tag
Dim Tagiau, Byddwch y cyntaf i dagio'r cofnod hwn!
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Tabl Cynhwysion:
- <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>