Plimpton 322 Decoded: Regular Numbers and a Modified Bruins Scheme — E8 Intelligence Research

FINDING: Plimpton 322 is a systematic table of Pythagorean triples generated by reciprocal pairs of regular (smooth) numbers in base-60, with a new reconstruction explaining missing entries via a modified Bruins scheme. | MATH: Standard generation: for regular numbers \(p, q\) (all prime factors ≤ 2,3,5), triple \((a,b,d) = (p^2 - q^2, 2pq, p^2 + q^2)\) or \((a,b,d) = (2pq, p^2 - q^2, p^2 + q^2)\). Bruins' method uses \(x = p/q\) with \(x + 1/x\) and \(x - 1/x\) scaled to integers. Modified scheme (arXiv:1109.3814) accounts for missing pairs by requiring \(p, q\) be *consecutive* regular numbers in the sexagesimal reciprocal table, yielding exactly 15 entries. The "Factor 12" algorithm (arXiv:2001.11141) proposes \(b = M \cdot Q_M\) where \(M, Q_M\) are integers derived from the tablet's column structure, reproducing all rows. | CONNECTION: Base-60 arithmetic is intrinsic — regular numbers are precisely those with terminating sexagesimal reciprocals. The ratios in the tablet's column ( Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com