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from every problem. erdosproblems.com no longer shows statuses (Bloom's reasons); this is the database's record, not our verdict.
908 of 1221 statements are formalized in Lean (Formal Conjectures) · 107 carry an Erdős prize · 3 are independent of ZFC and 9 more can't be proved, or can't be disproved, from ZFC alone · “open” counts the computable and Lean-checked ones too.
OPENnumber theory · base representations · complete sequences
Let \(3 \le d_1 < d_2 < \dots < d_r\) be integers such that \[\sum_{1 \le i \le r}\frac 1{d_i - 1} \ge 1.\] Can all sufficiently large integers be written as a sum of the shape \(\sum_i c_ia_i\) where \(c_i \in \{0, 1\}\) and \(a_i\) has…
DISPROVED LEANnumber theory · base representations
Let \(A\) be the set of integers which have only the digits \(0, 1\) when written base 3, -/ local notation "A" => { x : ℕ | (digits 3 x).toFinset ⊆ {0, 1} } /-- and \(B\) be the set of integers which have only the digits \(0, 1\) when…
SOLVEDSKIPPEDnumber theory · binomial coefficients · base representations
Are there infinitely many pairs of integers \(n < m\) such that \(\binom{2n}{n}\) and \(\binom{2m}{m}\) have the same set of prime divisors? Yes: there are infinitely many consecutive pairs \((n, n+1)\). The formal proof registered as…
Source: teorth/erdosproblems (its own interactive table), Apache-2.0, pulled 2026-10-21. A status here is what that database records, not an independent verification by us, except where a problem page says so.