Twin Prime Proof Claim Flawed; Maynard's Bound Remains Best — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Twin prime conjecture remains unproven; recent progress via Maynard's sieve bounds gaps, but a claimed "definitive proof" (arXiv:1708.07884v1) is not peer-validated and likely flawed. | MATH: Twin primes: px+1=px+2. Maynard–Tao: liminfn→∞(pn+1−pn)≤ 246 (unconditionally; 6 with Elliott–Halberstam). The arXiv paper claims: for n increasing by 1, at least 3 new twin pairs appear in interval up to (6n+5)2, implying infinite pairs — but this step lacks rigorous sieve control. | CONNECTION: No direct geometric ratio appears. However, the sieve structure (6n±1) reflects modular lattice ℤ/6ℤ — the crystallographic root lattice A2 (hexagonal) — where primes >3 live in two residue classes ±1 mod 6. This is a 2D hexagonal symmetry, not golden-ratio based. | DEPTH: 4 — The Maynard bound is profound (narrowing prime gaps from infinity to finite 246), but the "proof" claim is not credible. The lattice connection to \(A_2
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Related
- Twin Prime Proof Unsubstantiated; Maynard's 246 Bound Remains Strongest — E8 Intelligence Research
- Twin Prime Proof Claim Unverified; Maynard's Bound Remains Best — E8 Intelligence Research
- Twin Prime Progress: Bounded Gaps, Unproven Conjecture, and a Flawed Claim — E8 Intelligence Research
- Debunking the False Link Between Maynard–Tao Sieve and Golden Ratio — E8 Intelligence Research
- Long Composite Stretches at Consecutive Prime-Gap Products: A Uniform Maynard Argument
BibTeX
@misc{caldin2026twin,
title = {{Twin Prime Proof Claim Flawed; Maynard's Bound Remains Best — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23553672},
url = {https://zenodo.org/records/23553672},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Twin Prime Proof Claim Flawed; Maynard's Bound Remains Best — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/22
PB - Zenodo
DO - 10.5281/zenodo.23553672
UR - https://zenodo.org/records/23553672
AB - FINDING: Twin prime conjecture remains unproven; recent progress via Maynard's sieve bounds gaps, but a claimed "definitive proof" (arXiv:1708.07884v1) is not peer-validated and likely flawed. | MATH: Twin primes: p_x+1=p_x+2. Maynard–Tao: liminf_n→∞(p_n+1−p_n)≤ 246 (unconditionally; 6 with Elliott–Halberstam). The arXiv paper claims: for n increasing by 1, at least 3 new twin pairs appear in interval up to (6n+5)^2, implying infinite pairs — but this step lacks rigorous sieve control. | CONNECTION: No direct geometric ratio appears. However, the sieve structure (6n±1) reflects modular lattice ℤ/6ℤ — the crystallographic root lattice A_2 (hexagonal) — where primes >3 live in two residue classes ±1 mod 6. This is a 2D hexagonal symmetry, not golden-ratio based. | DEPTH: 4 — The Maynard bound is profound (narrowing prime gaps from infinity to finite 246), but the "proof" claim is not credible. The lattice connection to \(A_2 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -