Core Verification Data and Extended Records for Constructive Conjectures on Prime Arithmetic Progressions (Lengths 2 to 13, 100 Instances Each)

This dataset provides the core verification data for the preprint "Constructive Conjectures on Prime Arithmetic Progressions: A Systematic Study Based on the Base Primorial." It systematically presents 100 rigorously verified constructive examples for each prime length from 2 to 13 within the theoretical framework of the "base primorial."The data covers the core parameters involved in Conjectures A through D, including length, first term, common difference, base primorial, base primorial multiplier K, and last term.

These data strongly support the four core conjectures proposed in the paper: the constructability of prime arithmetic progressions of length P with prime first term P (Conjecture A), the construction rules with base primorial as the common difference (Conjecture B), the patterns governing minimal first terms and minimal common differences for any given length (Conjecture C), and the absolute length limit imposed by the factorization of any given common difference (Conjecture D).Additionally, this dataset includes extended exploratory records, such as minimal last term records for lengths 14 to 27 and minimal common difference records for lengths 14 to 21.This is a continuously updated dataset.