Erdős Problem #1196: Primitive Sets
Erdős problem #1196 · erdosproblems.com/1196
Bounds the weighted sum taken over primitive sets of integers (sets where no element divides another).
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI-discovered
- Method
- Argument
- Field
- Number Theory
- Posed by
- Paul Erdős, András Sárközy, Endre Szemerédi
- Year posed
- 1966
- Years open
- 60y
- Solved
- 2026-04
- Model
- GPT-5.4 Pro
- Vendor
- OpenAI
- Collaborators
- Boris Alexeev, Kevin Barreto, Yanyang Li, Jared Duker Lichtman, Liam Price, Jibran Iqbal Shah, Quanyu Tang, Terence Tao
- Verification
- Lean-verified
- Publication
- Announced
- Significance
- 15 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
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.
Verification
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.
Sources
- PaperAlexeev et al., the paper behind this solve
- Problem recorderdosproblems.com