Polymath and AI Collaboration Narrows Prime Gap Bounds to 246 — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Polymath collaboration demonstrates that distributed human-AI mathematical effort can crack problems like bounded prime gaps, with Tao's equational theories project scaling to industrial-level theorem exploration. | MATH: Hm := liminfn → ∞ (pn+m − pn); twin prime conjecture ⇔ H1 = 2; Zhang's bound H1 < 7×107 reduced via Polymath to H1 ≤ 246 (unconditionally), H1 ≤ 6 under Elliott–Halberstam. | CONNECTION: Prime gaps Hm relate to the distribution of primes modulo small integers — the structure of ℤ/qℤ for smooth q mirrors lattice/root-system periodicity (e.g., q=6 gives residues 1,5 — the twin-prime pairs sit on a 6-periodic lattice, echoing hexagonal close-packing symmetry). The gap sequence pn+1−pn statistically obeys Poisson-like spacing, but the *extremal* gaps Hm probe the fine structure of the sieve — a discrete analogue of spectral gaps in quasi-crystals. | DEPTH: 7 — Profound for methodology (
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026polymath,
title = {{Polymath and AI Collaboration Narrows Prime Gap Bounds to 246 — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23635120},
url = {https://zenodo.org/records/23635120},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Polymath and AI Collaboration Narrows Prime Gap Bounds to 246 — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/25
PB - Zenodo
DO - 10.5281/zenodo.23635120
UR - https://zenodo.org/records/23635120
AB - FINDING: Polymath collaboration demonstrates that distributed human-AI mathematical effort can crack problems like bounded prime gaps, with Tao's equational theories project scaling to industrial-level theorem exploration. | MATH: H_m := liminf_n → ∞ (p_n+m − p_n); twin prime conjecture ⇔ H_1 = 2; Zhang's bound H_1 < 7×10^7 reduced via Polymath to H_1 ≤ 246 (unconditionally), H_1 ≤ 6 under Elliott–Halberstam. | CONNECTION: Prime gaps H_m relate to the distribution of primes modulo small integers — the structure of ℤ/qℤ for smooth q mirrors lattice/root-system periodicity (e.g., q=6 gives residues 1,5 — the twin-prime pairs sit on a 6-periodic lattice, echoing hexagonal close-packing symmetry). The gap sequence p_n+1−p_n statistically obeys Poisson-like spacing, but the *extremal* gaps H_m probe the fine structure of the sieve — a discrete analogue of spectral gaps in quasi-crystals. | DEPTH: 7 — Profound for methodology ( Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -