Polymath Collaboration and AI Advance Prime Gap Bounds — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Polymath collaboration demonstrates that large-scale distributed problem-solving can crack hard number-theory problems, notably bounding prime gaps via Zhang's method, while AI now augments experimental mathematics. | MATH: Hm := liminfn → ∞ (pn+m − pn); twin prime conjecture ⇔ H1 = 2; Zhang's breakthrough gave finite bound for H1 (later Polymath reduced to H1 ≤ 246 under Elliott–Halberstam, H1 ≤ 6 unconditionally for m=1 via Maynard–Tao). No explicit new constants or ratios appear in the raw findings beyond the prime-gap framework. | CONNECTION: No direct geometric harmony (0.382, 0.618, 0.786, 1.618, 2.618, base-60, crystallographic symmetry) is present in the cited material. Prime gaps relate to additive number theory, not to ratio-based or lattice symmetries. The "Golden Square" episode title is a red herring — no mathematical content linking to φ is provided in the search results. | DEPTH: 6 — The Polymath method itself is a profound me
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 Collaboration and AI Advance Prime Gap Bounds — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23658179},
url = {https://zenodo.org/records/23658179},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Polymath Collaboration and AI Advance Prime Gap Bounds — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/26
PB - Zenodo
DO - 10.5281/zenodo.23658179
UR - https://zenodo.org/records/23658179
AB - FINDING: Polymath collaboration demonstrates that large-scale distributed problem-solving can crack hard number-theory problems, notably bounding prime gaps via Zhang's method, while AI now augments experimental mathematics. | MATH: H_m := liminf_n → ∞ (p_n+m − p_n); twin prime conjecture ⇔ H_1 = 2; Zhang's breakthrough gave finite bound for H_1 (later Polymath reduced to H_1 ≤ 246 under Elliott–Halberstam, H_1 ≤ 6 unconditionally for m=1 via Maynard–Tao). No explicit new constants or ratios appear in the raw findings beyond the prime-gap framework. | CONNECTION: No direct geometric harmony (0.382, 0.618, 0.786, 1.618, 2.618, base-60, crystallographic symmetry) is present in the cited material. Prime gaps relate to additive number theory, not to ratio-based or lattice symmetries. The "Golden Square" episode title is a red herring — no mathematical content linking to φ is provided in the search results. | DEPTH: 6 — The Polymath method itself is a profound me Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -