A Dataset of Minimal Prime Arithmetic Progressions: Instances within Ranges 10^1–10^9 and 2^1–2^32

The data cover two families of ranges: powers of 10 (from 10^1 to 10^9) and powers of 2 (from 2^1 to 2^32). For each range, and for lengths k = 2 through 16 (or the maximum length achievable within that range), we present the complete sequences of the minimal-difference AP and the minimal-start AP, including the initial prime, common difference, and all term values.

All data were generated by a unified, self-designed two-stage search algorithm and cross-validated against a precomputed prime database to ensure correctness. This dataset offers direct numerical support for structural studies of prime distribution, lower-bound analysis of AP parameters, and verification of constructive theories.