Supplementary Material: Experimental Data and Numerical Tables for Affine–Correlated Quadratic Polynomials

This document constitutes the supplementary material supporting the paper
“Affine-correlated quadratic polynomials, an index pre-sieve, and finite truncations of Bateman–Horn local factors”.

The present text is exclusively experimental and documentary in nature. It collects numerical tables, computational parameters, and quantitative summaries of the results obtained, in order to enable verification, reproducibility, and independent analysis of the data.

In particular, the supplement reports the observed counts of prime numbers associated with the quadratic polynomials

d(n) = n² + n + 5 and N(n) = 6n² + 6n + 31;

experimental results broken down by number size (number of digits), number of iterations, and index-filter configurations; reference expected values computed as a function of the number of digits of the candidates, together with the corresponding empirical enrichment factors; and summary tables highlighting the stability and order of magnitude of the observed enrichment as the experimental parameters vary.

The theoretical interpretations, the connection with finite truncations of Bateman–Horn local factors, and the mathematical discussion of the results are developed in the main paper. This supplement is limited to the quantitative documentation of the experimental data, without introducing new theoretical models or proof-oriented arguments.

The document is organized into independent sections, each devoted to a specific experimental configuration, in order to make the consultation of tables and numerical results immediate.