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PrimeGaps186

PrimeGaps186 is an open-source repository by OpenAI containing a conditional Lean formalization and numerical certificate for prime gaps at most 186. Mathematicians or formal verification engineers can use the proof and certificate to verify or extend related conclusions when studying prime distributions. AI receives mathematical propositions and proof tasks, performs formal reasoning and numerical verification, and delivers machine-checkable proof files and certificates. Specific workflows and deliverables require further verification.

Not a business yet Early Open-source projectInfrastructureMathematical researchMathematiciansFormal verification engineersCross-market opportunityOpen-source traction 164
Team / maker
openai
First tracked here
2026-09-03
Last updated here
2026-09-21
Product site
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01

Why this would be needed

Start inside the user's day · Public facts + observable behavior · 2026-09-15

Use case

Mathematicians or formal verification engineers advancing research on prime gap upper bounds need to turn a conditional proof plus numerical certificate into a Lean machine-checkable form so others can reproduce it or extend the result.

The current alternative is a paper appendix plus informal numerical scripts, or independently recomputing with Sage, PARI/GP or Python and comparing by hand; the Lean ecosystem previously lacked a ready formalization and certificate for this specific bound.

Results on prime gap upper bounds rest on heavy numerical computation and conditional assumptions; manual review cannot check every step, so without machine-checkable proofs and certificates peer reproduction is costly, errors are hard to localize, and credibility rests on trusting the authors.

xOcto's call

Demand is evidenced

Trend: AI for formal mathematical proofs may accelerate mathematical discovery and verification. Entry: Target the mathematical research community with formal proof services or tools, but user willingness to pay needs clarification.

Reason to use it

Why users would choose it

Inference: versus rewriting the Lean proof from scratch or only reading the paper, the repository supplies a compilable Lean formalization and numerical certificate, sparing users the step of building the formal framework and recomputing the certificate while yielding a machine-checkable result; hence mathematicians and formal verification engineers formalizing prime distribution or reusing this bound would choose it when reproducing or extending the result.

Where the easy answer breaks down

The tension worth following

An English validation note will follow from the public evidence.

If this is your job

Worth trying. Inference: versus rewriting the Lean proof from scratch or only reading the paper, the repository supplies a compilable Lean formalization and numerical certificate, sparing users the step of building the formal framework and recomputing the certificate while yielding a machine-checkable result; hence mathematicians and formal verification engineers formalizing prime distribution or reusing this bound would choose it when reproducing or extending the result.

Entry and what to borrow

Trend: AI for formal mathematical proofs may accelerate mathematical discovery and verification. Entry: Target the mathematical research community with formal proof services or tools, but user willingness to pay needs clarification.

What this judgment rests on
Public fact

PrimeGaps186 is an open-source repository by OpenAI containing a conditional Lean formalization and numerical certificate for prime gaps at most 186. Mathematicians or formal verification engineers can use the proof and certificate to verify or extend related conclusions when studying prime distributions. AI receives mathematical propositions and proof tasks, performs formal reasoning and numerical verification, and delivers machine-checkable proof files and certificates. Specific workflows and deliverables require further verification.

Workflow reasoning

Inference: versus rewriting the Lean proof from scratch or only reading the paper, the repository supplies a compilable Lean formalization and numerical certificate, sparing users the step of building the formal framework and recomputing the certificate while yielding a machine-checkable result; hence mathematicians and formal verification engineers formalizing prime distribution or reusing this bound would choose it when reproducing or extending the result.

The unknown that could change the call

An English validation note will follow from the public evidence.

01 · Value Supported

The assessment is recorded; an English explanation is pending.

02 · Consensus Insufficient evidence

The assessment is recorded; an English explanation is pending.

03 · Model Insufficient evidence

The assessment is recorded; an English explanation is pending.

04 · Truth Insufficient evidence

The assessment is recorded; an English explanation is pending.

02

Chinese and English ecosystems

Market comparison · Cross-market opportunity

English ecosystem · English-language market

Local supply: Emerging
Demand evidence: Not yet verified

Public coverage has been recorded for this market. · 2026-09-21

Chinese ecosystem · CN

Local supply: Not found in covered sources
Demand evidence: Not yet verified

Public coverage has been recorded for this market. · 2026-09-21

There is no full analysis yet. Start with the direction above.

Public information is limited; this view will update as more evidence appears. It was recently added and does not yet have verifiable usage data.

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04

Verifiable public evidence

Evidence trail

05

Go from the product name to primary material

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