Not evaluated
The Ford–Konyagin–Luca conjecture on prime predecessors (family 011)
The gist
On October 6, 2026, OpenAI announced three manuscripts from an unreleased internal model, linked to the Ford–Konyagin–Luca conjecture on prime predecessors.
DiscoverIA status on October 12, 2026: not evaluated, meaning no third-party evaluation found.
AI draft, not reviewedWhat has not been reviewed?
Text written by an AI (DiscoverIA pipeline), on . The status and its sources come from the registry; only the explanatory text has not been reviewed. A reported error is corrected, then the text is reviewed.
Cite this entry
A single status snapshot since Oct 12, 2026: a citation always points to a dated snapshot.
Cite snapshot 1, Oct 12, 2026
APA citation with the dated link
BibTeX @misc, key discoveria-oai-fam-011-fordkonyaginluca-conjecture-prime-r1
@misc{discoveria-oai-fam-011-fordkonyaginluca-conjecture-prime-r1,
author = {{DiscoverIA}},
title = {The Ford–Konyagin–Luca conjecture on prime predecessors (family 011)},
howpublished = {DiscoverIA registry, entry oai-fam-011-fordkonyaginluca-conjecture-prime},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-011-fordkonyaginluca-conjecture-prime#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
If the three manuscripts were correct, they would bring new results on the prime factors of these numbers, the subject of the Ford–Konyagin–Luca conjecture.
What remains unclear
No Lean proof (checkable by computer) is supplied for this family, and no third-party assessment is recorded. The sources read do not say whether the manuscripts claim the conjecture itself or neighbouring results.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · README.md
Step 1 of 4 on the scale: not evaluated. Next step: under review.
- Announced
- Recordednot evaluated
- nextTo follow
What this status means
Source reading : Source read word for word (level 3 of 3)
The result is declared neither right nor wrong.
To move to “Under review”: a public review under way. To “Peer reviewed”: a journal publication or a review by named experts.
Sources
- Main sourcegithub.com · CONTENTS.mdlink only, reading not recorded
- Repositorygithub.com · Weighted-Dilation-Graphs…link only, reading not recorded
- Repositorygithub.com · The-Poisson-Dirichlet-Law…link only, reading not recorded
- Repositorygithub.com · Prime-Predecessors-with…link only, reading not recorded
Method
The openai/math repository contains three manuscripts: “Weighted dilation graphs, smooth shifted primes and totient fibers” (September 24, 2026), “The Poisson-Dirichlet law for prime predecessors” (September 24, 2026) and “Prime Predecessors with an Even Number of Prime Factors” (September 17, 2026). The absence of Lean is inferred from the absence of a lean/docs/011.md file; history.md reports no revision of these manuscripts. DiscoverIA status: not evaluated, meaning that no third-party evaluation has been found in the sources read. Set on October 12, 2026 from github.com (page read, quotation checked word for word: “Not all have accompanying Lean formalizations.”).
Limits
DiscoverIA has not checked this result itself.
Key facts
- Claimed by
- OpenAI (unreleased internal model)
announced on Oct 6, 2026 - Nature
- new result
- Field
- Mathematics (Number theory)
- In openai/math
- family 011, section “Number theory”, 3 manuscripts dated Sep 17, 2026
- Lean proof
- none supplied
- Revisions
- none reported by the claimant
- Checked by
- no verifier identified
- Sources
- 4 : 4 links only
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
Family with no Lean proof supplied. No third-party evaluation read.
Source: github.comread word for word
An observation is added; none is ever erased.
In the same set
openai/math: 719 manuscripts in 372 families from an unreleased internal model · entry 11 of 372, by family number
- Not evaluated : The Deligne–Drinfeld conjecture (family 008)
- Not evaluated : Bogomolov–Pop and Milnor K-theoretic reconstruction (family 009)
- Not evaluated : Fontaine–Mazur modularity at the prime 2 and 2-adic pro-modularity (family 010)
- Not evaluated : The Ford–Konyagin–Luca conjecture on prime predecessors (family 011)
- Not evaluated : Independent largest prime factors of consecutive integers (family 012)
- Not evaluated : Ostmann's inverse Goldbach conjecture (family 013)
- Not evaluated : Restricted geometric Langlands, generic Ramanujan and Arthur parameters (family 014)
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