Bounded Gaps at 246, Twin Prime Proof Still Elusive — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Twin prime conjecture remains unproven; recent progress (Maynard) shows infinitely many primes with bounded gaps ≤246, but no proof of infinitely many pairs with gap exactly 2. One arXiv preprint claims a proof via sieve of Eratosthenes, but is not peer-validated. | MATH: Twin primes: \(p, p+2\) both prime. Maynard–Zhang–Tao: \(\liminf_{n\to\infty}(p_{n+1}-p_n) \le 246\). No exact gap-2 infinity proof. The arXiv claim (1708.07884v1) asserts ≥3 new twin pairs per increment of \(n\) near \((6n+5)^2\), but this is unverified and likely flawed. | CONNECTION: The gap 2 is the smallest even gap — relates to the lattice of integers mod 6: all primes >3 are \(6k\pm1\), so twin pairs are \(6k-1, 6k+1\). This is a crystallographic-like residue class symmetry (mod 6 = 2×3), but no golden-ratio or base-60 link emerges from the evidence. | DEPTH: 3/10 — the finding is a status report, not a breakthrough. The 246 bound is real but far from 2; the arXiv "proof" is not credible. No geometric Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204109160
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