Regenerated from the community database (Apache-2.0), dated, and linked back to it
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.
Let \(\alpha>0\) be an irrational number. Is the set \[A=\left\{ n\geq 1: \| \alpha n^2\| < \frac{1}{\log n}\right\},\] where \(\|\cdot\|\) denotes the distance to the nearest integer, an additive basis of order \(2\)? This was disproved…
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.