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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.
A set \(A\subset \mathbb{N}\) is primitive if no member of \(A\) divides another. Is the sum \[\sum_{n\in A}\frac{1}{n\log n}\] maximised over all primitive sets when \(A\) is the set of primes? Erdős [Er35] proved that this sum always…
Let \(A \subseteq \mathbb{N}\), and for each \(n \in A\) choose some \(X_n \subseteq \mathbb{Z}/n\mathbb{Z}\). Let \(B = \{m \in \mathbb{N} : m \not\in X_n \pmod{n} \text{ for all } n \in A \text{ with } m > n\}\). Must \(B\) have a…
Let \(A\subseteq \{1,\ldots,N\}\) be such that there is no solution to \(at=b\) with \(a,b\in A\) and the smallest prime factor of \(t\) is \(>a\). Estimate the maximum of \[\frac{1}{\log N}\sum_{n\in A}\frac{1}{n}.\] This has been solved…
Erdős Problem 872, part (i) (weak form): there exists a constant \(\epsilon > 0\) such that the game length is at least \(\epsilon \cdot n\) for all sufficiently large \(n\).
What is the size of the largest \(A\subseteq \{1,\ldots,n\}\) such that in the set \[\left\{ \sum_{a\in S} a : \emptyset\neq S\subseteq A\right\}\] no two distinct elements divide each other? A problem of Erdős and Sárközy. The answer is…
Is it true that, for any \(x\), if \(A\subset [x,\infty)\) is a primitive set of integers (so that no distinct elements of \(A\) divide each other) then\[\sum_{a\in A}\frac{1}{a\log a}< 1+o(1),\]where the \(o(1)\) term \(\to 0\) 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.