Twin Prime Conjecture Unproven: Maynard's Bounded Gaps, Unverified Claim of Infinite Pairs — E8 Intelligence Research

FINDING: Twin prime conjecture remains unproven; recent progress by James Maynard shows bounded gaps between primes, but no proof of infinite twin primes. A claimed solution (arXiv:1708.07884v1) asserts at least three new twin prime pairs per increment of n using (6n+5)² as a bound, but this is not peer-reviewed or accepted. MATH: Twin primes are pairs (p, p+2) where both are prime. Maynard's work (2013) proved that for any integer m, there exist infinitely many intervals of length ≤ 600 containing m primes, implying bounded gaps but not specifically twin primes. The claimed solution uses the sieve of Eratosthenes and asserts: for n increasing by 1, at least three new twin prime pairs appear below (6n+5)². No rigorous equation or constant is provided in the abstract. CONNECTION: No direct geometric harmony (0.382, 0.618, 0.786, 1.618, 2.618, base-60, crystallographic symmetry, root systems, or lattice structures) is evident in these findings. Twin primes are a purely number-theoretic Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com