Euler's Solved Classics and an Extremal Ellipse: A Project Euler Search — E8 Intelligence Research

FINDING: Project Euler search yields no "hardest unsolved" — all listed problems are solved classics (Euler #1, #20, #22, figurate cyclic sets) plus a genuine Euler extremal-ellipse translation. | MATH: Figurate numbers (heptagonal: P₇(n)=n(5n−3)/2); Euler #1 sum = Σ_{k<1000, 3|k or 5|k} k = 233168; Euler #20 = sum of digits of 100!; Euler #22 = name-score sum; extremal ellipse: minimize area/perimeter of ellipse through fixed points (Euler's E563, E691, E692). | CONNECTION: Figurate numbers relate to polygonal numbers — heptagonal (7-fold symmetry) but no golden-ratio link; Euler's ellipse problem touches conic geometry but no explicit 0.618/1.618 constants in the abstract; base-60 absent. | DEPTH: 2 — routine algorithmic exercises, no new mathematical essence; the extremal-ellipse translation is historically interesting but not a breakthrough. --- **Analysis of the five findings:** 1. **Key mathematical insight:** - The YouTube videos are pedagogical — solving Project Euler p Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com