Prime Clustering in Polynomial Q(n) = n^q − (n−1)^q: Quadruplet Distribution, Riemann Zero Correlation, and a 200,000-Digit Q47 Probable Prime (Version 2)

This dataset accompanies the research paper on prime-generating polynomials Q(n) = n^q - (n-1)^q, presenting a comprehensive computational study across seven prime exponents q ∈ {37, 41, 43, 47, 53, 61, 71}. **Key Discoveries:**- **15 quadruplet systems** identified for Q₄₇ (where 47 is a safe prime), compared to at most 2 for all other polynomials- Striking correlation (**r = 0.994**) between quadruplet positions and Riemann zeta zeros under the scaling n^(1/2.74)- Effective modulus q_eff = 15.5 ± 0.5 ≈ q/3, suggesting triplet-induced dimensional reduction- Subgroup Interference Hypothesis: I(q) = d(q-1) - 2 determines clustering stability **Dataset Contents:**- Complete coordinates of all 15 Q₄₇ quadruplet systems (verified)- 18,356,706 prime values for Q₄₇ in range n ∈ [1, 2×10⁹]- Seven-polynomial comparison statistics- Analysis scripts (Python)- Publication-ready figures (PDF/PNG)- Full paper (LaTeX source + PDF) **GitHub Repository:** https://github.com/Ruqing1963/Polynomial-Prime-Quadruplets