Erdős Problem #1196 — Primitive Sets
Erdős problem #1196 · erdosproblems.com/1196
Bounds the weighted sum ∑ 1/(a log a) taken over primitive sets of integers (sets where no element divides another).
- Result
- Proved
- Field
- Number Theory
- Posed by
- Paul Erdős, András Sárközy, Endre Szemerédi
- Year posed
- 1968
- Years open
- 58y
- Solved
- 2026-04
- Model
- GPT-5.4 Pro
- Vendor
- OpenAI
- Collaborators
- Boris Alexeev, Kevin Barreto, Li, Jared Duker Lichtman, Liam Price, Shah, Tang, Terence Tao
- Verification
- Expert-verified
- Notability
- 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.