Claude (via Claude Code)
The paper describes itself as a human-AI collaboration and says the tools contributed substantially to the Lean formalisation.
Provider: Anthropic · Prompt public: unknown · Independence: unknown
Problem detail · source-aware
The Erdos-Graham Semiprime Unit Fraction Problem
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Precise statement
Every natural number is a finite sum of distinct unit fractions whose denominators are semiprimes. This is the $\omega = 2$ integer case of a problem of Erdos and Graham, left as a conjecture by Butler, Erdos and Graham, who proved the $\omega = 3$ analogue.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.
What AI did
Verification boundary
A Lean formalisation accompanies the work, with the model credited as a substantial contributor to it. We have not compiled it. arXiv preprint, not peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
Timeline
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arXiv:2606.15159 - Every natural number is a sum of distinct semiprime unit fractions
the omega = 2 integer case, the one Butler, Erdos and Graham left open
Known method families
argument (source-reported)
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
What remains uncertain
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.
- VibeMath has not independently verified the mathematical claim.
- AI-attempt independence and training-data exposure are unknown unless explicitly documented.
- VibeMath has not independently audited the mathematical statement, proof, or novelty claim.