A Stacked–Residue Prime Prediction Sieve

We formalize a prime–prediction sieve based on stacked residues: an incremental, primorial–layered construction that generates only those integers that survive divisibility by all primes up to a moving base, while preserving a deterministic two–adic ordering for locality and near–monotone drift. Each layer lifts residue classes via the Chinese Remainder Theorem (CRT), culls composites by the next base prime, and streams a candidate sequence in which every prime p beyond the base appears exactly once before any verification step. This differs from a plain wheel sieve by (i) explicit CRT lifting (stacking), (ii) an ordering keyed by two–adic valuation v2(·) to improve traversal, and (iii) a memory–light, restartable stream form suited to hardware/topological layouts. We prove correctness of coverage/uniqueness, give algorithms, and include a worked miniature example