The board / number theory / #699
Erdős Problem #699
FALSIFIABLEdatabase updated 2025-08-31
Still open — but if it is false, a finite counterexample exists, so a computer search could in principle disprove it. A search can't prove it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Sylvester and Schur: for \(1 \le i \le n/2\) there is a prime \(p > i\) dividing `n.choose i`.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 2 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/699.Attempts
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The live page (accessed 2026-07-28) has status FALSIFIABLE/open, lists 2 claimed partial proofs (one accepted by the site), and names conglu, Woett, and ster as currently working; the mandatory no-dup
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