What question did this study set out to answer?

To reduce the bounded gap between prime numbers, from Zhang's original bound of 70 million to a new bound of 246.

July 27, 2026Open Access

Polymath8 Reduces Prime Gap Bound from 70 Million to 246 — E8 Intelligence Research

Key Points

To reduce the bounded gap between prime numbers, from Zhang's original bound of 70 million to a new bound of 246.
Collaborative proof utilizing combinatorial number theory and sieve methods.
Application of the Maynard–Tao sieve with multidimensional weights.
Established that H_1 ≤ 246, significantly less than the previous limit of 70 million.
Refined known bounds in the distribution of prime numbers without introducing new geometric constants.

Abstract

FINDING: Polymath project retrospective on bounded gaps between primes — collaborative proof that \ (H₁ 246 \) (reduced from Zhang's 70 million), using combinatorial number theory and sieve methods. | MATH: \ (Hₘ = ₍ (p₍+₌ - pₙ) \) ; Zhang's original bound: \ (H₁ 70, 000, 000 \) ; Polymath8 reduction to 246; key tool: Maynard–Tao sieve with multidimensional weights. | CONNECTION: No direct geometric ratio or crystallographic symmetry. The prime gaps are arithmetic, not harmonic. However, the underlying distribution of primes relates to the Riemann zeta function's zeros, which exhibit spectral rigidity — a subtle connection to eigenvalue spacing in quantum chaos and random matrix theory (GUE). | DEPTH: 6 — Profound in collaborative methodology and number theory, but no new constants or geometric ratios emerge. The result refines known bounds, not a paradigm shift. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com

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