Problem detail · source-aware

Erdős Problem #1196: Primitive Sets

resolvedconfidence 70%

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

Bounds the weighted sum $\sum 1/(a \log a)$ taken over primitive sets of integers (sets where no element divides another).

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

GPT-5.4 Pro

Price, an amateur with no advanced math training, fed GPT-5.4 Pro the bare problem statement with no historical context. It found the key move: reweighting the random walk via the von Mangoldt function.

Provider: OpenAI · Prompt public: unknown · Independence: unknown

Verification boundary

lean verified statement audited

The raw output needed cleanup, but the underlying idea held up. Examined, corrected, generalized and written up in a joint account by Alexeev, Barreto, Li, Lichtman, Price, Shah, Tang and Tao. Formalised in Lean.

Correctness: supported · statement fidelity: audited · peer review: none

Timeline

  1. erdosproblems.com

    VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.

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.