Project Euler's Number-Theoretic Speedups Without New Universal Constants — E8 Intelligence Research

FINDING: Project Euler problem solutions often exploit number-theoretic properties for dramatic speedup, but no new universal constants or geometric harmonies are reported. | MATH: Figurate number formulas (e.g., heptagonal: \(P_7(n) = n(5n-3)/2\)); prime sum sequences linked to Riemann hypothesis; Champernowne constant digit extraction; pentagonal number theorem for partitions. | CONNECTION: None directly to golden ratio, base-60, or crystallographic symmetries. The figurate numbers are polygonal, but no special ratio (e.g., 0.618) emerges. | DEPTH: 3 — Competence in algorithmic number theory, but no fundamental geometric or harmonic discovery. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com