Twin Prime Conjecture: Unproven, With Recent Sieve Progress and Unverified Claim — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Twin prime conjecture remains unproven; recent progress via Maynard's sieve methods and a claimed arXiv proof (1708.07884) that is not peer-validated. | MATH: Twin primes: pairs (p, p+2). Maynard's theorem: liminfn→∞ (pn+1−pn) ≤ 246 (unconditional, Zhang–Maynard–Polymath). The arXiv paper claims at least 3 new twin pairs per increment of n when setting (6n+5)2 as a sieve bound — but this is not accepted mathematics. No exact constant for twin prime density; conjectured asymptotic ∼ (2C2 x)/((ln x)2), with C2 = ∏p>2 (p(p−2))/((p−1)2) ≈ 0.66016. | CONNECTION: The constant C2 is not a golden-ratio family number, but note C2 ≈ 0.660 — close to 2/π ≈ 0.6366 and 1/ϕ ≈ 0.618 but not equal. No base-60 or crystallographic symmetry appears in the valid mathematics. The sieve structure is arithmetic, not geometric. | DEPTH: 3 — The valid result (gap ≤ 246) is deep but does not
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 Conjecture: Unproven, With Recent Sieve Progress and Unverified Claim — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23490649},
url = {https://zenodo.org/records/23490649},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Twin Prime Conjecture: Unproven, With Recent Sieve Progress and Unverified Claim — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/20
PB - Zenodo
DO - 10.5281/zenodo.23490649
UR - https://zenodo.org/records/23490649
AB - FINDING: Twin prime conjecture remains unproven; recent progress via Maynard's sieve methods and a claimed arXiv proof (1708.07884) that is not peer-validated. | MATH: Twin primes: pairs (p, p+2). Maynard's theorem: liminf_n→∞ (p_n+1−p_n) ≤ 246 (unconditional, Zhang–Maynard–Polymath). The arXiv paper claims at least 3 new twin pairs per increment of n when setting (6n+5)^2 as a sieve bound — but this is not accepted mathematics. No exact constant for twin prime density; conjectured asymptotic ∼ (2C_2 x)/((ln x)^2), with C_2 = ∏_p>2 (p(p−2))/((p−1)^2) ≈ 0.66016. | CONNECTION: The constant C_2 is not a golden-ratio family number, but note C_2 ≈ 0.660 — close to 2/π ≈ 0.6366 and 1/ϕ ≈ 0.618 but not equal. No base-60 or crystallographic symmetry appears in the valid mathematics. The sieve structure is arithmetic, not geometric. | DEPTH: 3 — The valid result (gap ≤ 246) is deep but does not Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -