Twin Prime Proof Unsubstantiated; Maynard's 246 Bound Remains Strongest — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: No proof of the twin prime conjecture exists in these sources; the closest rigorous result is Maynard's theorem on bounded prime gaps, while the arXiv paper claims a flawed sieve-based "proof" with no peer review. | MATH: Twin primes: p, p+2 both prime. Maynard (2013): liminfn→∞ (pn+1−pn) ≤ 246 (unconditional, without Elliott–Halberstam). Zhang (2013): gap < 70,000,000 → later improved to 246. arXiv:1708.07884v1 claims: for n increasing by 1, at least 3 new twin pairs appear below (6n+5)2 — this is unverified and contradicts known density heuristics (Hardy–Littlewood: π2(x) ∼ 2C2 ∫2x dt/ln2 t, C2 ≈ 0.66016). | CONNECTION: No direct geometric harmony. However, the modulus 6 in the arXiv claim (6n±1 forms for all primes > 3) links to the hexagonal lattice (A₂ root system) — primes > 3 live on two of six rays of the Eisenstein integer lattice, a crystallographic symmetry of order 6. The constant \(C_2 = \prod_{p
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 Unsubstantiated; Maynard's 246 Bound Remains Strongest — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23409717},
url = {https://zenodo.org/records/23409717},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Twin Prime Proof Unsubstantiated; Maynard's 246 Bound Remains Strongest — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/16
PB - Zenodo
DO - 10.5281/zenodo.23409717
UR - https://zenodo.org/records/23409717
AB - FINDING: No proof of the twin prime conjecture exists in these sources; the closest rigorous result is Maynard's theorem on bounded prime gaps, while the arXiv paper claims a flawed sieve-based "proof" with no peer review. | MATH: Twin primes: p, p+2 both prime. Maynard (2013): liminf_n→∞ (p_n+1−p_n) ≤ 246 (unconditional, without Elliott–Halberstam). Zhang (2013): gap < 70,000,000 → later improved to 246. arXiv:1708.07884v1 claims: for n increasing by 1, at least 3 new twin pairs appear below (6n+5)^2 — this is unverified and contradicts known density heuristics (Hardy–Littlewood: π_2(x) ∼ 2C_2 ∫_2^x dt/ln^2 t, C_2 ≈ 0.66016). | CONNECTION: No direct geometric harmony. However, the modulus 6 in the arXiv claim (6n±1 forms for all primes > 3) links to the hexagonal lattice (A₂ root system) — primes > 3 live on two of six rays of the Eisenstein integer lattice, a crystallographic symmetry of order 6. The constant \(C_2 = \prod_{p Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -