What question did this study set out to answer?

The aim is to refine the upper bound for the twin prime gap through collaborative proof techniques.

July 22, 2026Open Access

Polymath Project Narrows Twin Prime Gap Bound to 246 via Collaborative Proof-Refinement — E8 Intelligence Research

Key Points

The aim is to refine the upper bound for the twin prime gap through collaborative proof techniques.
Collaborative proof-refinement using distributed efforts among mathematicians
Analysis of the Maynard–Tao sieve and its implications on prime gaps
Application of the Elliott–Halberstam conjecture to further narrow bounds.
The twin prime gap upper bound is reduced from 70,000,000 to 246
Under the Elliott–Halberstam conjecture, the gap could be as small as 6
No new universal constants or geometric symmetries were discovered.

Abstract

FINDING: Polymath project on bounded gaps between primes reduces upper bound for \ (H₁\) (twin prime gap) via collaborative, distributed proof-refinement. | MATH: \ (H₁ = ₍ (p₍+₁ - pₙ) \) ; Zhang's original bound \ (H₁ 70, 000, 000\) reduced to \ (H₁ 246\) (and to \ (H₁ 6\) under Elliott–Halberstam conjecture). Key constant: the Maynard–Tao sieve yields \ (Hₘ m e^4m\). | CONNECTION: No direct geometric harmony ratios (0. 382, 0. 618, etc. ) appear. The prime gap distribution relates to the Selberg sieve, which has no crystallographic or base-60 link. | DEPTH: 7 — Profound for analytic number theory and collaborative methodology, but not revealing new universal constants or geometric symmetries. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com

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