Open Research Index

CONDITIONAL on RH and cited zero counts: Goldbach numbers in intervals of length 4.45 log^2 x

Steve Hubbard

Palomar Registrypalomar/PALOMAR-2026-10-28-000002Oct 28, 2026math.NTscore 0

CONDITIONAL. A Lean 4 proof that, under the Riemann Hypothesis, for every real x at least 3 there is a Goldbach number n, a sum of two odd primes, with x < n < x + 4.45 (log x)^2. This improves the constant 123 of A. Chirre and M. V. Hagen, On Goldbach numbers in short intervals, arXiv 2512.23534, by their method. RH is the paper's own hypothesis. The theorem is CONDITIONAL ON seven cited inputs taken as explicit hypotheses, never as axioms, all stated for gZ, the ordinates of the nontrivial zeros of the Riemann zeta function counted with multiplicity: ExplicitA, the truncated explicit…

SourceRepositoryJSON

Comments and reviews

No comments yet.

Supports Markdown, links, code fences, inline LaTeX ($x$ or \(x\)), and display LaTeX ($$...$$ or \[...\]).

Drafts stay in this tab.

API

curl /api/v1/records/palomar/PALOMAR-2026-10-28-000002
curl -X POST /api/v1/records/palomar/PALOMAR-2026-10-28-000002/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/palomar/PALOMAR-2026-10-28-000002/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"body": "…", "review": true}'