Prime Values of p³ − 2 over Prime Inputs: Reproducible Computational Edition with the p³ + 2 Mirror Lane

This paper studies prime inputs p for which p^3 - 2 or p^3 + 2 is prime and states two corresponding infinitude conjectures. For every prime p > 3, if p mod 3 = 2, then p^3 - 2 is composite. If p mod 3 = 1, then p^3 + 2 is composite. In each case, the expression with the opposite sign is eligible, but not guaranteed, to be prime. A standalone reproduction program regenerated 6,110,100 consecutive prime inputs through p = 106,431,659, reproducing all previously reported minus-lane counts and providing a corresponding plus-lane comparison. A second program independently reproduces the local-density benchmark of 166,343.25 expected prime outputs during the final 5,000,000-input stage, compared with 166,507 observed. These computations are consistent with a Bateman-Horn and local-sieve interpretation but do not prove either infinitude conjecture. The accompanying reproduction package contains the source code, pinned dependencies, computational results, benchmark output, metadata, and SHA-256 checksums required for independent reproduction and auditing.