Bounded Prime Gaps: Progress Toward, But Not Proof of, the Twin Prime Conjecture — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Twin prime conjecture remains unproven; recent progress via Maynard's sieve methods shows infinitely many primes with bounded gaps (≤246), but no proof of infinitely many pairs at gap exactly 2. | MATH: Maynard–Tao theorem: \(\liminf_{n\to\infty} (p_{n+m} - p_n) \leq C_m\), with \(C_1 = 246\) (unconditional, Zhang–Maynard–Polymath). Twin prime conjecture requires \(C_1 = 2\). No equation, constant, or ratio in the listed sources yields a new exact result. The arXiv paper (1708.07884) claims a sieve-based proof but is not peer-reviewed and likely flawed (no known valid proof exists). | CONNECTION: None found. No occurrence of 0.382, 0.618, 0.786, 1.618, 2.618, base-60, or crystallographic symmetry in any of the sources. The prime gaps relate to additive number theory, not geometric harmony. | DEPTH: 2 — the finding is a status report, not a breakthrough. The only mathematically substantive item is the bounded-gap result (gap 246), which is profound in analytic number theory but 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: W7212082451
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