Bounded Prime Gaps: Progress Toward, Not Proof of, the Twin Prime Conjecture — E8 Intelligence Research

FINDING: Twin prime conjecture remains unproven; recent progress (Maynard, GPY sieve) shows infinitely many primes with bounded gaps ≤ 246, but not specifically gap 2. | MATH: Let \(p_n\) be nth prime. GPY/Maynard: \(n→∞ (pₙ₊₁ - p_n) ≤ 246\). Twin prime conjecture asserts \(n→∞ (pₙ₊₁ - p_n) = 2\). No exact proof of gap 2 exists. | CONNECTION: The gap 2 is the smallest even integer — a degenerate case of the even lattice \(Z\). The bound 246 = 2 × 123, and 123 = 3 × 41. No golden ratio, base-60, or crystallographic symmetry appears in the sieve methods. | DEPTH: 3 — significant progress but no resolution; the "definitive proof" videos are crank claims, not peer-reviewed. The mathematical essence is a sieve bound, not a harmonic structure. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com