Unsolved Math Problems: Chromatic Number, Perfect Numbers, Josephus — E8 Intelligence Research

FINDING: Search results surface three distinct unsolved/classic mathematical problems (Hadwiger-Nelson chromatic number, odd perfect numbers, Josephus permutation) with no single unifying discovery; the omnidirectional video paper is unrelated noise. | MATH: Hadwiger-Nelson: χ(ℝ²) ∈ {5,6,7} (lower bound raised from 4 to 5 by de Grey, 2018; upper bound 7 via hexagonal tiling). Odd perfect numbers: if N exists, N > 10¹⁵⁰⁰, N ≡ 1 mod 12 or N ≡ 9 mod 36, and N has at least 101 prime factors with specific exponent patterns. Josephus: J(n,k) = (J(n-1,k)+k) mod n, J(1,k)=0; closed form J(n,2) = 2l+1 where n = 2^m + l. | CONNECTION: Hadwiger-Nelson upper bound 7 arises from hexagonal lattice (crystallographic 6-fold symmetry); lower bound 5 uses Moser spindle (7 vertices, unit-distance graph) — no golden ratio directly, but hexagonal tiling connects to base-60's 6-fold division of circle. Odd perfect numbers: no geometric link — purely arithmetic. Josephus: J(n,2) pattern relates to powers of Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com