All 1221 problems · community database as of Nov 12, 2026
The status of every Erdős problem, kept in public.
On 6 October 2026 erdosproblems.com stopped showing which of its problems are solved
(here's why). The
community database beside it still records a status for every one.
This site shows that record — dated, sourced, and explained — with a page for each problem.
Two questions decide where a problem sits: what people have concluded about it, and whether a machine has checked a solution.
They don't always agree. Each square is one problem.
Is there a function \(f\) with \(f(n)\to\infty\) as \(n\to\infty\) such that, for all large \(n\), there is a composite number \(m\) such that \[ n + f(n) < m < n + p(m) \] Here \(p(m)\) is the least prime factor of \(m\).
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/463.
Erdős offered money for solutions and paid it by personal cheque — several recipients framed the cheque instead of cashing it.
55 open problems still carry one.
You have an AI subscription. That's most of what it takes to try.
The guide covers picking a problem, briefing a model, making it compute instead of narrate, and checking what comes back.
Then send what you found: we read it the way we read our own work and publish it, with your consent, under an honest verdict.
The site's authors — Patrick White and Claude, an AI — have taken a run at 617 of these problems since July 2026.
Every attempt is logged, including the ones that hit a wall. These are our verdicts, not the database's.
12 NOV · CHEN'S 12n IS NOT OURS; THE WINDOW LEMMA IS · ERDŐS–SURÁNYI: HOW MANY OF max(A) CONSECUTIVE INTEGERS DOES IT TAKE TO HAVE A PRODUCT DIVISIBLE BY ∏A? · ERDŐS ($100): IS (2+o(1))n ENOUGH? · H. CHEN, SEP 2026: 12n, LEAN 4 · STATEMENT AUDIT + STATEMENT AUDIT + OUR KERNEL REPLAY: CLEAN · AI REFEREE INSTANCE: ONE SLIP (THE THRESHOLD-2 BARRIER'S EXAMPLE), THE FLOOR SURVIVES · OURS: g(n) ≥ ⌊3n/2⌋ − 1 FOR EVERY n ≥ 4 (A RECORD ONLY AT SMALL n; 1959'S 2n − O(√n) WINS LATER)
11 NOV · GESSEL'S COUNTEREXAMPLE — NOT OURS; THE EXPLICIT CERTIFICATES ARE · ERDŐS: IS M(m)/m < 2·M(n)/n WHENEVER m > n ≥ max A (M COUNTS MULTIPLES OF A)? · NO: D. GESSEL, 5 SEP 2026, LEAN VIA JIG · AI REFEREE INSTANCE: NO GAP · OUR KERNEL REPLAY + STATEMENT BRIDGE TO FORMAL CONJECTURES: CLEAN · OURS: n = 2⁶⁴ IN HIS FAMILY, n ≈ 1.1·10¹⁵ IN ONE OF LIU'S BANDS (EARLIEST EXPLICIT WE FOUND: 10¹¹⁸) · CERTIFIED BY COUNTING BOUNDS FROM TWO PROGRAMS, NOT LEAN