Polymath Collaboration and AI Accelerate Bounded Prime Gap Breakthroughs — E8 Intelligence Research

Abstract

FINDING: Polymath collaboration demonstrates that large-scale, decentralized mathematical problem-solving can crack hard problems (e.g., bounded prime gaps), with AI now accelerating experimental mathematics. | MATH: H_m := liminf_{n → ∞} (p_n+m − p_n); twin prime conjecture ⇔ H₁ = 2; Zhang's bound H₁ < 7×10⁷ → Polymath8 reduced to H₁ ≤ 246 (unconditionally), H₁ ≤ 6 under Elliott–Halberstam. | CONNECTION: Prime gaps H_m relate to the distribution of primes — a lattice-like structure in ℕ; the reduction process (7e7 → 246) mirrors iterative refinement toward a fixed point, echoing contraction ratios (e.g., 0.618) in convergence, though no explicit golden ratio appears. | DEPTH: 7 — profound for methodology and number theory, but not a new universal constant or symmetry.

Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Polymath Collaboration and AI Advance Prime Gap Bounds — E8 Intelligence Research
Andrew Stewart Caldin
Zenodo26 Oct 2026PreprintCC BY 4.0Zenodo
Polymath and AI Collaboration Narrows Prime Gap Bounds to 246 — E8 Intelligence Research
Andrew Stewart Caldin
Zenodo25 Oct 2026PreprintCC BY 4.0Zenodo
Consciousness Research Lacks Quantitative Breakthroughs, Synaptic Clock Theory Remains Descriptive — E8 Intelligence Research
Andrew Stewart Caldin
Zenodo19 Oct 2026PreprintCC BY 4.0Zenodo
One Capital, Many Provinces: Spatial Concentration and the Collaboration Network of Iranian Artificial Intelligence Research, 2010–2021
Pooria Ghorbani
Zenodo18 Oct 2026PreprintCC BY 4.0Full textZenodo
Human–artificial intelligence collaboration in emergency medical services: from diagnostic algorithms to shared decision support
Hang A Park
Clinical and experimental emergency medicine1 Sep 2026Peer-reviewedCC BY-NCFull textGeneral medicineEurope PMC

Cite

BibTeX RIS

BibTeX

@misc{caldin2026polymath,
  title = {{Polymath Collaboration and AI Accelerate Bounded Prime Gap Breakthroughs — E8 Intelligence Research}},
  author = {Andrew Stewart Caldin},
  howpublished = {Zenodo},
  year = {2026},
  month = oct,
  doi = {10.5281/zenodo.23553748},
  url = {https://zenodo.org/records/23553748},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Polymath Collaboration and AI Accelerate Bounded Prime Gap Breakthroughs — E8 Intelligence Research
AU  - Andrew Stewart Caldin
PY  - 2026
DA  - 2026/10/22
PB  - Zenodo
DO  - 10.5281/zenodo.23553748
UR  - https://zenodo.org/records/23553748
AB  - FINDING: Polymath collaboration demonstrates that large-scale, decentralized mathematical problem-solving can crack hard problems (e.g., bounded prime gaps), with AI now accelerating experimental mathematics. | MATH: H_m := liminf_n → ∞ (p_n+m − p_n); twin prime conjecture ⇔ H_1 = 2; Zhang's bound H_1 < 7×10^7 → Polymath8 reduced to H_1 ≤ 246 (unconditionally), H_1 ≤ 6 under Elliott–Halberstam. | CONNECTION: Prime gaps H_m relate to the distribution of primes — a lattice-like structure in ℕ; the reduction process (7e7 → 246) mirrors iterative refinement toward a fixed point, echoing contraction ratios (e.g., 0.618) in convergence, though no explicit golden ratio appears. | DEPTH: 7 — profound for methodology and number theory, but not a new universal constant or symmetry.  Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER  -

Abstract

Related

Cite