Twin Prime Proof Claim Unverified; Bounded Gaps Remain Best Result — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Twin prime conjecture remains unproven; recent progress (Maynard, Zhang) establishes bounded gaps, but no proof exists. The arXiv paper claims a sieve-based proof but is not peer-reviewed/validated.
MATH: - Twin primes: p, p+2 both prime. - Zhang (2013): liminfn→∞ (pn+1−pn) < 7×107. - Maynard (2013): liminfn→∞ (pn+1−pn) ≤ 246 (unconditionally, under Elliott–Halberstam: 12). - No exact constant, ratio, or closed form emerges from these results. - The arXiv paper (1708.07884v1) claims: for n increasing by 1, at least 3 new twin prime pairs appear below (6n+5)2 — this is a *claim*, not a verified theorem. No rigorous equation given.
CONNECTION: - The modulus 6 in the arXiv claim ties to residue classes mod 6: all primes >3 are 6k±1. Twin primes are 6k−1, 6k+1. This is a lattice/residue structure, but **no** golden-ratio, base-60, or crystallographic symmetry appears in any of the cited work.
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026twin,
title = {{Twin Prime Proof Claim Unverified; Bounded Gaps Remain Best Result — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23490625},
url = {https://zenodo.org/records/23490625},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Twin Prime Proof Claim Unverified; Bounded Gaps Remain Best Result — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/20
PB - Zenodo
DO - 10.5281/zenodo.23490625
UR - https://zenodo.org/records/23490625
AB - FINDING: Twin prime conjecture remains unproven; recent progress (Maynard, Zhang) establishes bounded gaps, but no proof exists. The arXiv paper claims a sieve-based proof but is not peer-reviewed/validated. MATH: - Twin primes: p, p+2 both prime. - Zhang (2013): liminf_n→∞ (p_n+1−p_n) < 7×10^7. - Maynard (2013): liminf_n→∞ (p_n+1−p_n) ≤ 246 (unconditionally, under Elliott–Halberstam: 12). - No exact constant, ratio, or closed form emerges from these results. - The arXiv paper (1708.07884v1) claims: for n increasing by 1, at least 3 new twin prime pairs appear below (6n+5)^2 — this is a *claim*, not a verified theorem. No rigorous equation given. CONNECTION: - The modulus 6 in the arXiv claim ties to residue classes mod 6: all primes >3 are 6k±1. Twin primes are 6k−1, 6k+1. This is a lattice/residue structure, but **no** golden-ratio, base-60, or crystallographic symmetry appears in any of the cited work. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -