Project Euler's Hardest Problems: Graph Theory, Prime Sum Sieves, and Riemann Hypothesis Links — E8 Intelligence Research

FINDING: Project Euler hardest problems often reduce to graph theory (NP-complete clique search) or prime sum sieves with Riemann hypothesis implications. | MATH: Figurate number sequences: heptagonal numbers \( P_7(n) = \frac{n(5n-3)}{2} \); cyclic set condition: last digits of one figurate number match first digits of another; prime sum problem: find prime below 1e6 that is sum of most consecutive primes (Riemann zeta function \(\zeta(s)\) zero distribution affects prime gap statistics). | CONNECTION: Figurate numbers relate to polygonal numbers — heptagonal (7-gon) connects to crystallographic symmetry (7-fold rotational symmetry is forbidden in periodic crystals, but appears in quasicrystals). The cyclic digit matching resembles modular arithmetic on base-10, not base-60. | DEPTH: 5 — algorithmic cleverness, not fundamental mathematical discovery. FINDING: Euler's 1770s papers on extremal ellipses through fixed points — minimal area/perimeter ellipse family. | MATH: Given \(n\) po Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com