teorth/erdosproblems

A community database for the problems on the erdosproblems.com site

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Sep 9, 2026

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README

Erdős problem database

Browse the interactive table - Sort, filter, and search all the problems in the database

A community database for the problems on the erdosproblems.com site. We are particularly seeking community contributions regarding the integer sequences associated with these problems, and linking them to the OEIS.

The table below is auto-generated from the YAML file data/problems.yaml, which is the "ground truth" for this data as far as this repository is concerned.

To propose changes, open a PR editing data/problems.yaml.
See CONTRIBUTING.md for guidelines and field definitions.

For further discussion of this project, see this blog post (from Sep 1, 2025).

Several of the problems have received assistance from various AI tools. A list of such assistance can be found here. This wiki is no longer updated as of June 30, 2026, and is retained as a historical record; please do not open issues proposing additions to it.

Progress

Table

There are 1217 problems in total, of which

106 are attached to a monetary prize.
330 have been proved.
- 172 of these proofs have been formalized in Lean.
132 have been disproved.
- 86 of these disproofs have been formalized in Lean.
94 have been otherwise solved.
- 28 of these solutions have been formalized in Lean.
3 appear to be open, but cannot be proven from the axioms of ZFC. (not provable)
4 appear to be open, but cannot be disproven from the axioms of ZFC. (not disprovable)
3 are known to be independent of the ZFC axioms of mathematics. (independent)
9 appear to be open, but have been reduced to a finite computation. (decidable)
27 appear to be open, but can be disproven by a finite computation if false. (falsifiable)
7 appear to be open, but can be proven by a finite computation if true. (verifiable)
608 appear to be completely open.
10 have ambiguous statements.
0 have a literature review requested.
291 have a solution formalized in Lean. This need not be a subset of the solved problems above: a formalized solution that has not yet been digested by a human reader keeps its informal status (so can appear as, e.g., "open (Lean)").
612 have their statements formalized in Lean in the Formal Conjectures Repository.
321 have been linked to 412 distinct OEIS sequences, with a total of 492 links created.
- 80 of these OEIS sequences were added since the creation of this database (A387000 onwards).
324 are potentially related to an OEIS sequence not already listed.
- 269 of these problems are not currently linked to any existing OEIS sequence.
0 have a related sequence currently being submitted to the OEIS.
1 have a related sequence whose generation is currently in progress.

#	Prize	Status	Statement formalized	AI Attempts	OEIS	Tags	Comments
1	$500	open	yes	view	A276661	number theory, additive combinatorics
2	$1000	disproved (Lean)	yes	view	A160559	number theory, covering systems
3	$5000	open	yes	view	A003002, A003003, A003004, A003005	number theory, additive combinatorics, arithmetic progressions
4	$10000	proved	yes	view	A002386	number theory, primes
5	no	open	yes	view	A001223	number theory, primes
6	$100	proved (Lean)	yes	view	A335277	number theory, primes
7	no	verifiable	yes	view	N/A	number theory, covering systems
8	no	disproved (Lean)	no	view	N/A	number theory, covering systems
9	no	open	yes	view	A006286	number theory, additive basis, primes
10	no	open	yes	view	A387053	number theory, additive basis, primes
11	no	open	yes	view	A001220, A377587	number theory, additive basis
12	no	open	yes	view	N/A	number theory
13	$100	proved (Lean)	yes	view	A002264	number theory
14	no	open	yes	view	A143824, possible	number theory, sidon sets, additive combinatorics
15	no	open	yes	view	N/A	number theory, primes
16	no	disproved (Lean)	yes	view	A006285	number theory, additive basis, primes
17	no	open	yes	view	A038133	number theory, primes	cluster primes
18	no	open	yes	view	A005153	number theory, divisors, factorials	practical numbers
19	$500	decidable	no	view	N/A	graph theory, chromatic number
20	$1000	open	yes	view	A332077	combinatorics	sunflower conjecture
21	$500	proved (Lean)	no	view	A391599	combinatorics, intersecting family
22	no	proved (Lean)	yes	view	possible	graph theory
23	no	falsifiable	yes	view	A389646	graph theory
24	no	proved (Lean)	yes	view	possible	graph theory
25	no	open	yes	view	N/A	number theory
26	no	disproved (Lean)	yes	view	N/A	number theory, divisors
27	$100	disproved	no	view	N/A	number theory, covering systems
28	$500	open	yes	view	N/A	number theory, additive basis
29	$100	proved (Lean)	no	view	N/A	number theory, additive basis
30	$1000	open	yes	view	A143824, A227590, A003022	number theory, sidon sets, additive combinatorics
31	no	proved (Lean)	yes	view	N/A	number theory, additive basis
32	no	open	yes	view	N/A	number theory, additive basis
33	no	open	yes	view	N/A	number theory, additive basis
34	no	disproved (Lean)	yes	view	A389241, A234813, A390187	number theory
35	no	proved (Lean)	no	view	N/A	number theory, additive basis
36	no	open	yes	view	A393584, possible	number theory, additive combinatorics	minimum overlap problem
37	no	disproved (Lean)	no	view	N/A	number theory, additive combinatorics
38	no	proved (Lean)	yes	view	N/A	number theory
39	$500	open	yes	view	N/A	number theory, sidon sets, additive combinatorics
40	$500	open	yes	view	N/A	number theory, additive basis
41	$500	open	yes	view	N/A	number theory, sidon sets, additive combinatorics
42	no	solved (Lean)	yes	view	N/A	number theory, sidon sets, additive combinatorics
43	$100	disproved (Lean)	yes	view	A143824, A227590, A003022, possible	number theory, sidon sets, additive combinatorics
44	no	open	yes	view	N/A	number theory, sidon sets, additive combinatorics
45	no	proved (Lean)	yes	view	possible	number theory, unit fractions, ramsey theory
46	no	proved (Lean)	yes	view	N/A	number theory, unit fractions, ramsey theory
47	$100	proved (Lean)	yes	view	N/A	number theory, unit fractions
48	no	proved (Lean)	yes	view	N/A	number theory
49	no	proved (Lean)	no	view	A365339, A365474	number theory, primes
50	$250	open	yes	view	N/A	number theory
51	no	open	yes	view	A002202, A014197	number theory
52	$250	open	yes	view	A263996	number theory, additive combinatorics	sum-product problem
53	no	proved (Lean)	no	view	possible	number theory, additive combinatorics
54	$100	solved	no	view	N/A	number theory, ramsey theory
55	$250	solved	no	view	N/A	number theory, ramsey theory
56	$10	disproved (Lean)	yes	view	N/A	number theory, intersecting family
57	no	proved (Lean)	no	view	N/A	graph theory, chromatic number, cycles
58	no	proved	no	view	N/A	graph theory, chromatic number, cycles
59	no	disproved (Lean)	no	view	N/A	graph theory, turan number
60	no	open	yes	view	A006855	graph theory, cycles
61	no	open	yes	view	N/A	graph theory
62	no	open	no	view	N/A	graph theory
63	no	proved (Lean)	no	view	N/A	graph theory, chromatic number, cycles
64	$1000	falsifiable	yes	view	N/A	graph theory, cycles
65	no	open	no	view	N/A	graph theory, cycles
66	$500	open	yes	view	N/A	number theory, additive basis
67	$500	proved	yes	view	A181740, A237695	discrepancy	Erdős discrepancy problem
68	no	open	yes	view	A331373	number theory, irrationality
69	no	proved	yes	view	A262153	number theory, irrationality
70	no	open	yes	view	N/A	graph theory, ramsey theory, set theory
71	no	proved (Lean)	yes	view	N/A	graph theory, cycles
72	$100	proved	no	view	N/A	graph theory, cycles
73	no	proved	no	view	N/A	graph theory
74	$500	open	yes	view	N/A	graph theory, chromatic number, cycles
75	no	open	yes	view	N/A	graph theory, chromatic number
76	no	proved	no	view	A060407	graph theory, ramsey theory
77	$250	open	no	view	A059442	graph theory, ramsey theory
78	$100	open	no	view	A059442	graph theory, ramsey theory
79	no	proved	no	view	N/A	graph theory, ramsey theory
80	no	open	yes	view	N/A	graph theory, ramsey theory
81	no	open	no	view	possible	graph theory
82	no	open	yes	view	A120414, A390256, A390257, A390919, A392636, A394400, A394462, A394539, A394563, A394564, A394573, A394574, A394930, A394933	graph theory
83	$500	proved (Lean)	no	view	A071799, A387635	combinatorics
84	no	open	no	view	possible	graph theory, cycles
85	no	open	yes	view	A006672, possible	graph theory
86	$100	open	no	view	A245762	graph theory
87	no	open	no	view	A059442, possible	graph theory, ramsey theory
88	$100	proved	no	view	N/A	graph theory, ramsey theory
89	$500	open	yes	view	A186704, A131628	geometry, distances	Erdős distance problem
90	$500	disproved (Lean)	yes	view	A186705	geometry, distances	unit distance problem
91	no	open	yes	view	A186704, possible	geometry, distances
92	$500	disproved	yes	view	possible	geometry, distances
93	no	proved (Lean)	yes	view	N/A	geometry, convex, distances
94	£25	proved (Lean)	yes	view	A387858	geometry, convex, distances
95	$500	proved (Lean)	no	view	possible	geometry, convex, distances
96	no	open	yes	view	possible	geometry, distances, convex
97	$100	falsifiable	yes	view	N/A	geometry, distances, convex
98	no	open	yes	view	possible	geometry, distances
99	$100	open	yes	view	N/A	geometry, distances
100	no	open	yes	view	N/A	geometry, distances
101	$100	open	yes	view	A006065, possible	geometry
102	no	open	no	view	N/A	geometry
103	no	open	no	view	possible	geometry, distances
104	$100	open	no	view	A003829	geometry
105	$50	disproved (Lean)	yes	view	N/A	geometry
106	no	falsifiable	no	view	N/A	geometry
107	$500	falsifiable	yes	view	A000051	geometry, convex	'Happy Ending' problem
108	no	open	yes	view	possible	graph theory, chromatic number, cycles
109	no	proved (Lean)	yes	view	N/A	additive combinatorics	Erdős sumset conjecture
110	no	disproved	no	view	N/A	graph theory, chromatic number, cycles
111	no	open	no	view	N/A	graph theory, chromatic number, set theory
112	no	open	no	view	possible	graph theory, ramsey theory
113	$500	disproved (Lean)	no	view	N/A	graph theory, turan number
114	$250	falsifiable	no	view	N/A	polynomials, analysis
115	no	proved (Lean)	yes	view	N/A	polynomials, analysis
116	no	proved (Lean)	no	view	N/A	polynomials, analysis
117	no	open	no	view	possible	group theory
118	no	disproved	no	view	N/A	set theory, ramsey theory
119	$100	solved (Lean)	yes	view	N/A	analysis, polynomials
120	$100	open	yes	view	N/A	combinatorics	Erdős similarity problem
121	no	disproved (Lean)	no	view	A028391, A013928, A372306, A373319, A372306, A373178, A360659, A373114, A143301	number theory, squares
122	no	open	no	view	N/A	number theory
123	$250	proved (Lean)	yes	view	N/A	number theory
124	no	open	yes	view	N/A	number theory, base representations
125	no	disproved (Lean)	yes	view	A367090	number theory, base representations
126	$250	open	yes	view	possible	number theory
127	no	proved (Lean)	no	view	possible	graph theory
128	$250	falsifiable	yes	view	N/A	graph theory
129	no	open	no	view	possible	graph theory, ramsey theory	ambiguous statement
130	no	open	yes	view	N/A	graph theory, chromatic number
131	no	open	no	view	A068063	number theory
132	$100	open	no	view	N/A	distances
133	no	disproved	no	view	possible	graph theory
134	no	proved (Lean)	yes	view	N/A	graph theory
135	$250	disproved (Lean)	no	view	possible	distances, geometry
136	no	solved	no	view	possible	graph theory
137	no	open	yes	view	N/A	number theory
138	$500	open	yes	view	A005346	additive combinatorics
139	$1000	proved (Lean)	yes	view	A003002, A003003, A003004, A003005	additive combinatorics, arithmetic progressions	Szemerédi's theorem
140	$500	proved (Lean)	no	view	A003002	additive combinatorics, arithmetic progressions
141	no	open	yes	view	A006560	additive combinatorics, primes, arithmetic progressions
142	$10000	open	yes	view	A003002, A003003, A003004, A003005	additive combinatorics, arithmetic progressions
143	$500	open	yes	view	N/A	primitive sets
144	$250	proved (Lean)	no	view	A005279	number theory, divisors
145	no	open	yes	view	A005117	number theory
146	$500	open (Lean)	yes	view	N/A	graph theory, turan number
147	$500	disproved (Lean)	no	view	N/A	graph theory, turan number
148	no	open	no	view	A076393, A006585	number theory, unit fractions
149	no	open	no	view	N/A	graph theory
150	no	proved (Lean)	yes	view	possible	graph theory
151	no	open	no	view	possible	graph theory
152	no	proved (Lean)	yes	view	N/A	sidon sets
153	no	open	yes	view	N/A	sidon sets
154	no	proved (Lean)	yes	view	N/A	sidon sets
155	no	open	yes	view	A143824, A227590, A003022	additive combinatorics, sidon sets
156	no	open	yes	view	A382397	sidon sets
157	no	proved	no	view	N/A	sidon sets
158	no	open	yes	view	N/A	sidon sets
159	no	open	no	view	possible	graph theory, ramsey theory
160	no	open	yes	view	possible	additive combinatorics, arithmetic progressions
161	$500	open	no	view	N/A	combinatorics, ramsey theory, discrepancy
162	no	open	no	view	N/A	combinatorics, ramsey theory, discrepancy
163	no	proved	no	view	N/A	graph theory, ramsey theory	Burr-Erdős conjecture
164	no	proved (Lean)	yes	view	A137245	number theory, primitive sets
165	$250	open	no	view	A000791	graph theory, ramsey theory
166	$250	proved	no	view	A059442	graph theory, ramsey theory
167	no	falsifiable	no	view	N/A	graph theory
168	no	open	yes	view	A004059, A057561, A094708, A386439	additive combinatorics
169	no	open	no	view	A005346	additive combinatorics, arithmetic progressions
170	no	open	yes	view	A046693	additive combinatorics	sparse ruler problem
171	no	proved (Lean)	no	view	A156989	additive combinatorics, combinatorics	density Hales-Jewett
172	no	open	yes	view	N/A	additive combinatorics, ramsey theory
173	no	open	no	view	N/A	geometry, ramsey theory
174	no	open	no	view	N/A	geometry, ramsey theory
175	no	proved (Lean)	no	view	N/A	number theory, binomial coefficients
176	no	open	no	view	possible	additive combinatorics, arithmetic progressions, discrepancy
177	no	open	no	view	N/A	discrepancy, arithmetic progressions
178	no	proved (Lean)	yes	view	N/A	discrepancy
179	no	proved	no	view	possible	additive combinatorics, arithmetic progressions
180	no	open (Lean)	yes	view	N/A	graph theory, turan number
181	no	open	no	view	possible	graph theory, ramsey theory
182	no	proved	no	view	possible	graph theory
183	$250	open (Lean)	yes	view	A003323	graph theory, ramsey theory
184	no	open	yes	view	possible	graph theory, cycles
185	no	proved (Lean)	no	view	A003142	additive combinatorics
186	no	solved	no	view	A389784	additive combinatorics
187	no	open	no	view	N/A	additive combinatorics, ramsey theory
188	no	open	yes	view	N/A	geometry, ramsey theory
189	no	disproved (Lean)	yes	view	N/A	geometry, ramsey theory
190	no	solved	no	view	possible	additive combinatorics, arithmetic progressions
191	no	proved (Lean)	no	view	N/A	combinatorics, ramsey theory
192	no	solved (Lean)	no	view	N/A	arithmetic progressions, combinatorics
193	no	open	yes	view	A231255	geometry
194	no	disproved (Lean)	yes	view	N/A	arithmetic progressions
195	no	open	yes	view	N/A	arithmetic progressions
196	no	open	yes	view	N/A	arithmetic progressions
197	no	open	yes	view	N/A	arithmetic progressions
198	no	disproved (Lean)	yes	view	N/A	additive combinatorics, sidon sets, arithmetic progressions
199	no	disproved (Lean)	yes	view	N/A	arithmetic progressions
200	no	open	yes	view	A005115	primes, arithmetic progressions
201	no	open	no	view	A003002, A003003, A003004, A003005, possible	additive combinatorics, arithmetic progressions
202	no	solved (Lean)	yes	view	A389975	covering systems
203	no	open	yes	view	N/A	primes, covering systems
204	no	disproved (Lean)	yes	view	N/A	covering systems
205	no	disproved (Lean)	yes	view	possible	number theory
206	no	disproved (Lean)	yes	view	N/A	number theory, unit fractions
207	no	proved	no	view	N/A	combinatorics, hypergraphs
208	no	open	yes	view	A005117, A076259	number theory
209	no	disproved (Lean)	yes	view	N/A	geometry
210	no	proved	no	view	A003034	geometry
211	$100	proved	no	view	N/A	geometry
212	no	open	yes	view	N/A	geometry, distances
213	no	open	yes	view	N/A	geometry, distances
214	no	proved (Lean)	yes	view	N/A	geometry, distances
215	no	proved (Lean)	no	view	N/A	geometry
216	no	disproved	no	view	A381776	geometry, convex
217	no	open	no	view	possible	geometry, distances
218	no	open	yes	view	A333230, A333231, A064113	number theory, primes
219	no	proved (Lean)	yes	view	A005115, A113827, A123556	number theory, additive combinatorics, primes, arithmetic progressions	Green-Tao theorem
220	$500	proved (Lean)	no	view	A322144	number theory
221	no	proved (Lean)	yes	view	N/A	number theory, additive basis
222	no	open	no	view	A001481, A256435	number theory, squares
223	no	solved	no	view	possible	geometry, distances
224	no	proved (Lean)	yes	view	N/A	geometry
225	no	proved	no	view	N/A	analysis
226	no	proved (Lean)	yes	view	N/A	analysis
227	no	disproved	no	view	N/A	analysis
228	no	proved (Lean)	yes	view	N/A	analysis, polynomials
229	no	proved (Lean)	yes	view	N/A	analysis, iterated functions
230	no	disproved (Lean)	no	view	N/A	analysis, polynomials
231	no	disproved (Lean)	no	view	N/A	combinatorics
232	no	proved	no	view	N/A	geometry, distances
233	no	open	yes	view	A074741	number theory, primes
234	no	open	yes	view	N/A	number theory, primes
235	no	proved	no	view	N/A	number theory
236	no	open	yes	view	A039669, A109925	number theory, primes
237	no	proved (Lean)	no	view	N/A	number theory, primes
238	no	open	yes	view	N/A	number theory, primes
239	no	proved (Lean)	yes	view	N/A	number theory
240	no	proved	no	view	N/A	number theory, primes
241	$100	open	yes	view	A387704	additive combinatorics, sidon sets
242	no	falsifiable	yes	view	A073101, A075245, A075246, A075247, A075248, A287116	number theory, unit fractions	Erdős-Straus conjecture
243	no	open	yes	view	A000058	number theory
244	no	open	yes	view	N/A	number theory, primes
245	no	proved	yes	view	N/A	additive combinatorics
246	no	proved (Lean)	yes	view	N/A	number theory
247	no	open	yes	view	N/A	number theory, irrationality
248	no	proved (Lean)	yes	view	N/A	number theory
249	no	open	yes	view	A256936	number theory, irrationality
250	no	proved (Lean)	yes	view	A066766	number theory, irrationality
251	no	open	yes	view	A098990	number theory, irrationality
252	no	open	yes	view	A227988, A227989, A307036, A359060, possible	number theory, irrationality
253	no	disproved (Lean)	yes	view	N/A	number theory
254	no	open	yes	view	N/A	number theory
255	no	proved (Lean)	no	view	N/A	discrepancy
256	no	open	no	view	N/A	analysis
257	no	open	yes	view	N/A	irrationality
258	no	proved (Lean)	yes	view	N/A	irrationality
259	no	proved (Lean)	yes	view	A371134	irrationality
260	no	open	yes	view	N/A	irrationality
261	no	open	no	view	N/A	number theory
262	no	solved (Lean)	no	view	N/A	irrationality
263	no	open	yes	view	N/A	irrationality
264	no	open	yes	view	N/A	irrationality
265	no	open	no	view	N/A	irrationality	ambiguous statement
266	no	disproved (Lean)	yes	view	N/A	irrationality
267	no	open	yes	view	N/A	irrationality
268	no	proved (Lean)	yes	view	N/A	number theory
269	no	open	yes	view	N/A	irrationality
270	no	disproved (Lean)	no	view	A073016	irrationality
271	no	open	no	view	A005487	additive combinatorics, arithmetic progressions	Stanley sequences
272	no	open	yes	view	possible	additive combinatorics, arithmetic progressions
273	no	open	yes	view	N/A	number theory, covering systems
274	no	open	yes	view	N/A	group theory, covering systems	Herzog-Schönheim conjecture
275	no	proved (Lean)	yes	view	N/A	number theory, covering systems
276	no	open	yes	view	N/A	number theory, covering systems
277	no	proved (Lean)	yes	view	N/A	number theory, covering systems
278	no	open	no	view	N/A	number theory, covering systems
279	no	open	yes	view	N/A	number theory, covering systems, primes
280	no	disproved (Lean)	yes	view	N/A	number theory, covering systems
281	no	proved (Lean)	yes	view	N/A	number theory, covering systems
282	no	open	yes	view	N/A	number theory, unit fractions
283	no	proved (Lean)	yes	view	A380791	number theory, unit fractions
284	no	proved	no	view	possible	number theory, unit fractions
285	no	proved (Lean)	yes	view	A030659	number theory, unit fractions
286	no	proved	no	view	N/A	number theory, unit fractions
287	no	falsifiable	yes	view	N/A	number theory, unit fractions
288	no	open	yes	view	N/A	number theory, unit fractions
289	no	open	yes	view	N/A	number theory, unit fractions
290	no	proved (Lean)	yes	view	A375081	number theory, unit fractions
291	no	open	yes	view	A110566	number theory, unit fractions
292	no	proved	no	view	A092671	number theory, unit fractions
293	no	open	no	view	possible	number theory, unit fractions	ambiguous statement
294	no	proved	no	view	possible	number theory, unit fractions
295	no	open	yes	view	A192881	number theory, unit fractions
296	no	proved (Lean)	yes	view	possible	number theory, unit fractions
297	no	solved	no	view	A092670	number theory, unit fractions
298	no	proved (Lean)	yes	view	N/A	number theory, unit fractions
299	no	disproved (Lean)	yes	view	N/A	number theory, unit fractions
300	no	solved (Lean)	no	view	A390393	number theory, unit fractions
301	no	open	no	view	A390394	number theory, unit fractions
302	no	open	yes	view	A390395	number theory, unit fractions
303	no	proved (Lean)	yes	view	N/A	number theory, unit fractions
304	no	open	yes	view	A097847, A097849	number theory, unit fractions
305	no	proved	no	view	possible	number theory, unit fractions
306	no	open	yes	view	N/A	number theory, unit fractions
307	no	verifiable	yes	view	N/A	number theory, unit fractions
308	no	proved	no	view	possible	number theory, unit fractions
309	no	disproved (Lean)	no	view	A217693	number theory, unit fractions
310	no	proved (Lean)	no	view	N/A	number theory, unit fractions
311	no	open	no	view	N/A	number theory, unit fractions
312	no	open	yes	view	N/A	number theory, unit fractions
313	no	open	yes	view	A054377	number theory, unit fractions
314	no	proved (Lean)	yes	view	N/A	number theory, unit fractions
315	no	proved (Lean)	yes	view	A000058, A076393	number theory, unit fractions
316	no	disproved (Lean)	yes	view	N/A	number theory, unit fractions
317	no	open	yes	view	N/A	number theory, unit fractions
318	no	solved	yes	view	N/A	number theory, unit fractions
319	no	open	yes	view	possible	number theory, unit fractions
320	no	solved	no	view	A072207	number theory, unit fractions
321	no	solved	yes	view	A384927, A391592	number theory, unit fractions
322	no	open	no	view	A025456, A025418	number theory, powers
323	no	open	yes	view	A004825, A004831, A004832, A004833, A004842, A004843, A004844, A004845, A004857, A004869, possible	number theory, powers
324	no	open	yes	view	N/A	number theory, powers
325	no	open	yes	view	A004825, A004832, A004843, A004854, A004865, possible	number theory, powers
326	no	open	yes	view	N/A	number theory, additive basis
327	no	open	no	view	A384927	number theory, unit fractions
328	no	disproved (Lean)	yes	view	N/A	number theory, additive combinatorics
329	no	open	yes	view	possible	number theory
330	no	proved (Lean)	yes	view	N/A	number theory, additive basis
331	no	disproved (Lean)	yes	view	N/A	number theory, additive combinatorics
332	no	open	yes	view	N/A	number theory
333	no	disproved (Lean)	yes	view	N/A	number theory, additive basis
334	no	open	no	view	A062241, A045535	number theory
335	no	open	no	view	N/A	number theory, additive combinatorics
336	no	open	no	view	possible	number theory, additive basis
337	no	disproved (Lean)	yes	view	N/A	number theory, additive combinatorics, additive basis
338	no	open	no	view	N/A	number theory, additive basis
339	no	proved	no	view	N/A	number theory, additive basis
340	no	open	yes	view	A080200, A005282	number theory, additive combinatorics, sidon sets
341	no	open	yes	view	N/A	number theory
342	no	open	yes	view	A002858	number theory
343	no	proved	no	view	N/A	number theory, complete sequences
344	no	proved	no	view	N/A	number theory, complete sequences
345	no	open	no	view	A001661	number theory, complete sequences
346	no	open	yes	view	N/A	number theory, complete sequences
347	no	proved (Lean)	yes	view	N/A	number theory, complete sequences
348	no	open	yes	view	N/A	number theory, complete sequences
349	no	open	yes	view	N/A	number theory, complete sequences
350	no	proved (Lean)	yes	view	N/A	number theory, additive combinatorics
351	no	proved (Lean)	yes	view	N/A	number theory, complete sequences
352	no	open	yes	view	N/A	geometry
353	no	proved (Lean)	yes	view	N/A	geometry
354	no	open	yes	view	N/A	number theory
355	no	proved (Lean)	yes	view	N/A	number theory, unit fractions
356	no	proved (Lean)	no	view	possible	number theory
357	no	open	yes	view	A364132, A364153, possible	number theory
358	no	proved (Lean)	yes	view	possible	number theory, additive basis, primes
359	no	open	yes	view	A002048	number theory	segmented numbers
360	no	solved	no	view	possible	number theory
361	no	open	yes	view	possible	number theory
362	no	proved (Lean)	no	view	possible	number theory
363	no	disproved (Lean)	yes	view	N/A	number theory
364	no	verifiable	yes	view	A060355, A076445	number theory
365	no	open	no	view	A060355, A060859, A175155	number theory
366	no	verifiable	yes	view	A060355	number theory	ambiguous statement
367	no	open	yes	view	A057521	number theory
368	no	open	no	view	A074399	number theory
369	no	proved (Lean)	yes	view	N/A	number theory
370	no	proved (Lean)	yes	view	N/A	number theory
371	no	open	yes	view	A070089	number theory
372	no	proved	yes	view	A071870	number theory
373	no	open	yes	view	A003135	number theory, factorials
374	no	open	no	view	A388851, A387184, A389117, A389148	number theory
375	no	falsifiable	yes	view	N/A	number theory
376	no	open	yes	view	A030979	number theory, binomial coefficients, base representations
377	no	open	yes	view	N/A	number theory, binomial coefficients
378	no	proved	no	view	N/A	number theory, binomial coefficients
379	no	proved (Lean)	yes	view	possible	number theory, binomial coefficients
380	no	proved	no	view	A070003, A388654, A387054, A389100	number theory
381	no	disproved	no	view	A002182	number theory, divisors
382	no	open	no	view	A388850	number theory
383	no	open	yes	view	N/A	number theory
384	no	proved (Lean)	no	view	N/A	number theory, binomial coefficients
385	no	open	yes	view	A322292	number theory
386	no	open	yes	view	A280992	number theory, binomial coefficients
387	no	solved	yes	view	N/A	number theory, binomial coefficients
388	no	open	no	view	N/A	number theory
389	no	open	yes	view	A375071	number theory
390	no	open (Lean)	yes	view	A193429	number theory, factorials
391	no	proved (Lean)	no	view	A034258, A034259	number theory, factorials
392	no	proved (Lean)	yes	view	possible	number theory, factorials
393	no	open	no	view	A388302	number theory, factorials
394	no	open	yes	view	A344005	number theory
395	no	proved (Lean)	no	view	N/A	analysis	reverse Littlewood-Offord problem
396	no	open	yes	view	A375077	number theory, binomial coefficients
397	no	disproved (Lean)	yes	view	N/A	number theory, binomial coefficients
398	no	falsifiable	yes	view	A146968, A141399	number theory, factorials	Brocard-Ramanujan conjecture
399	no	disproved (Lean)	yes	view	N/A	number theory, factorials
400	no	open	yes	view	possible	number theory, factorials
401	no	proved (Lean)	yes	view	N/A	number theory, factorials
402	no	proved	yes	view	N/A	number theory
403	no	proved (Lean)	yes	view	N/A	number theory, factorials
404	no	open	no	view	N/A	number theory, factorials
405	no	proved (Lean)	no	view	N/A	number theory, factorials
406	no	open	yes	view	N/A	number theory, base representations
407	no	proved	no	view	possible, A387688	number theory
408	no	open	no	view	A049108	number theory, iterated functions
409	no	open	yes	view	A039651, A229487	number theory, iterated functions
410	no	open	yes	view	A007497, possible	number theory, iterated functions
411	no	open	no	view	A383044, possible	number theory, iterated functions
412	no	open	yes	view	A007497, A051572	number theory, iterated functions
413	no	open	yes	view	A005236	number theory, iterated functions
414	no	open	yes	view	A064491, possible	number theory, iterated functions
415	no	open	no	view	possible	number theory
416	no	open	yes	view	A264810	number theory
417	no	open	yes	view	A264810, A061070	number theory
418	no	proved (Lean)	yes	view	A005278, A263958	number theory
419	no	solved (Lean)	yes	view	N/A	number theory, factorials
420	no	open	no	view	N/A	number theory
421	no	open	yes	view	A389544, A390848	number theory
422	no	open	yes	view	A005185	number theory
423	no	open	no	view	A005243	number theory
424	no	open	yes	view	A005244	number theory
425	no	open	no	view	possible	number theory, sidon sets
426	$25	disproved (Lean)	yes	view	possible	graph theory
427	no	proved (Lean)	yes	view	N/A	number theory, primes
428	no	open	yes	view	N/A	number theory, primes
429	no	disproved (Lean)	yes	view	N/A	number theory
430	no	open	no	view	possible	number theory
431	no	open	no	view	N/A	number theory, primes	inverse Goldbach problem
432	no	open	no	view	N/A	number theory
433	no	proved (Lean)	no	view	possible	number theory
434	no	proved (Lean)	yes	view	possible	number theory
435	no	proved (Lean)	yes	view	A389479	number theory
436	no	open	no	view	A000445, possible	number theory
437	no	proved	no	view	possible	number theory
438	no	solved	no	view	A363069	number theory
439	no	proved	no	view	N/A	number theory, ramsey theory
440	no	solved	no	view	N/A	number theory
441	no	disproved	no	view	A068509	number theory
442	no	disproved (Lean)	yes	view	N/A	number theory
443	no	proved (Lean)	yes	view	N/A	number theory
444	no	proved	no	view	N/A	number theory, divisors
445	no	open	yes	view	N/A	number theory
446	no	solved	no	view	A074738	number theory, divisors
447	no	proved (Lean)	yes	view	possible	combinatorics
448	no	disproved (Lean)	yes	view	A397433	number theory, divisors
449	no	disproved	no	view	possible	number theory, divisors
450	no	open	yes	view	N/A	number theory, divisors
451	no	open	no	view	A386620	number theory
452	no	open	no	view	possible	number theory
453	no	disproved (Lean)	yes	view	N/A	number theory
454	no	open	yes	view	A389676, A389677	number theory, primes
455	no	open	yes	view	N/A	number theory
456	no	open	yes	view	A034694, A061026, possible	number theory
457	no	proved (Lean)	yes	view	A391668	number theory
458	no	falsifiable	yes	view	A056604	number theory, primes
459	no	solved (Lean)	yes	view	A289280	number theory, primes
460	no	open	no	view	N/A	number theory	ambiguous statement
461	no	open	no	view	possible	number theory, primes
462	no	open	no	view	A032742, possible	number theory, primes
463	no	open	yes	view	possible	number theory, primes
464	no	proved (Lean)	yes	view	N/A	number theory
465	no	proved	no	view	N/A	number theory
466	no	proved	no	view	N/A	number theory
467	no	open	no	view	N/A	number theory	ambiguous statement
468	no	open	no	view	A167485, A387502, A387503	number theory, divisors
469	no	proved (Lean)	yes	view	A006036, A119425, possible	number theory, divisors
470	$10	open	yes	view	A006037, A002975	number theory, divisors
471	no	proved	no	view	possible	number theory
472	no	open	no	view	A389713, possible	number theory
473	no	proved	no	view	A055265	number theory
474	$100	not provable	no	view	N/A	set theory, ramsey theory
475	no	decidable	no	view	N/A	number theory, additive combinatorics
476	no	proved (Lean)	yes	view	N/A	number theory, additive combinatorics
477	no	open	yes	view	N/A	number theory
478	no	open	no	view	A210184	number theory, factorials
479	no	open	yes	view	A036236, A015919, A050259, A015921, A006521, A006517, A015940	number theory
480	no	proved (Lean)	yes	view	N/A	number theory
481	no	proved (Lean)	yes	view	N/A	number theory
482	no	solved	no	view	A004539	number theory
483	no	open	no	view	A030126	number theory, additive combinatorics, ramsey theory
484	no	proved (Lean)	yes	view	N/A	number theory, additive combinatorics, ramsey theory
485	no	proved	no	view	possible	analysis, polynomials
486	no	open	yes	view	N/A	number theory, primitive sets
487	no	proved (Lean)	yes	view	N/A	number theory
488	no	falsifiable	yes	view	N/A	number theory
489	no	open	yes	view	N/A	number theory
490	no	proved (Lean)	no	view	A397205	number theory
491	no	proved	no	view	N/A	number theory
492	no	disproved	no	view	N/A	number theory
493	no	proved (Lean)	yes	view	N/A	number theory
494	no	proved	yes	view	N/A	analysis, additive combinatorics
495	no	open	yes	view	N/A	diophantine approximation, number theory	Littlewood conjecture
496	no	proved	no	view	N/A	number theory, diophantine approximation
497	no	solved (Lean)	yes	view	A000372	combinatorics	Dedekind's problem
498	no	proved (Lean)	yes	view	N/A	combinatorics, analysis	strong Littlewood-Offord problem
499	no	proved (Lean)	yes	view	N/A	combinatorics
500	$500	open	no	view	A140462	graph theory, hypergraphs, turan number
501	no	open	yes	view	N/A	combinatorics, set theory
502	no	solved (Lean)	yes	view	A027627	geometry, distances
503	no	open	yes	view	A175769	geometry, distances
504	no	solved	no	view	N/A	geometry	Blumenthal's problem
505	no	disproved (Lean)	yes	view	possible	geometry	Borsuk's problem
506	no	decidable	yes	view	possible	geometry
507	no	open	yes	view	N/A	geometry	Heilbronn's triangle problem
508	no	open	yes	view	N/A	geometry, ramsey theory	Hadwiger-Nelson problem
509	no	open	yes	view	N/A	analysis
510	no	open	yes	view	N/A	analysis	Chowla's cosine problem
511	no	disproved	no	view	N/A	analysis
512	no	proved (Lean)	yes	view	N/A	analysis	Littlewood's conjecture
513	no	open	yes	view	N/A	analysis
514	no	open	no	view	N/A	analysis
515	no	proved	no	view	N/A	analysis
516	no	proved (Lean)	yes	view	N/A	analysis
517	no	open	yes	view	N/A	analysis
518	no	proved	no	view	N/A	graph theory, ramsey theory
519	no	proved (Lean)	yes	[view](https://m

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A community database for the problems on the erdosproblems.com site

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README

Erdős problem database

Browse the interactive table - Sort, filter, and search all the problems in the database

The table below is auto-generated from the YAML file data/problems.yaml, which is the "ground truth" for this data as far as this repository is concerned.

To propose changes, open a PR editing data/problems.yaml.
See CONTRIBUTING.md for guidelines and field definitions.

For further discussion of this project, see this blog post (from Sep 1, 2025).

Progress

Table

There are 1217 problems in total, of which

106 are attached to a monetary prize.
330 have been proved.
- 172 of these proofs have been formalized in Lean.
132 have been disproved.
- 86 of these disproofs have been formalized in Lean.
94 have been otherwise solved.
- 28 of these solutions have been formalized in Lean.
3 appear to be open, but cannot be proven from the axioms of ZFC. (not provable)
4 appear to be open, but cannot be disproven from the axioms of ZFC. (not disprovable)
3 are known to be independent of the ZFC axioms of mathematics. (independent)
9 appear to be open, but have been reduced to a finite computation. (decidable)
27 appear to be open, but can be disproven by a finite computation if false. (falsifiable)
7 appear to be open, but can be proven by a finite computation if true. (verifiable)
608 appear to be completely open.
10 have ambiguous statements.
0 have a literature review requested.
291 have a solution formalized in Lean. This need not be a subset of the solved problems above: a formalized solution that has not yet been digested by a human reader keeps its informal status (so can appear as, e.g., "open (Lean)").
612 have their statements formalized in Lean in the Formal Conjectures Repository.
321 have been linked to 412 distinct OEIS sequences, with a total of 492 links created.
- 80 of these OEIS sequences were added since the creation of this database (A387000 onwards).
324 are potentially related to an OEIS sequence not already listed.
- 269 of these problems are not currently linked to any existing OEIS sequence.
0 have a related sequence currently being submitted to the OEIS.
1 have a related sequence whose generation is currently in progress.

#	Prize	Status	Statement formalized	AI Attempts	OEIS	Tags	Comments
1	$500	open	yes	view	A276661	number theory, additive combinatorics
2	$1000	disproved (Lean)	yes	view	A160559	number theory, covering systems
3	$5000	open	yes	view	A003002, A003003, A003004, A003005	number theory, additive combinatorics, arithmetic progressions
4	$10000	proved	yes	view	A002386	number theory, primes
5	no	open	yes	view	A001223	number theory, primes
6	$100	proved (Lean)	yes	view	A335277	number theory, primes
7	no	verifiable	yes	view	N/A	number theory, covering systems
8	no	disproved (Lean)	no	view	N/A	number theory, covering systems
9	no	open	yes	view	A006286	number theory, additive basis, primes
10	no	open	yes	view	A387053	number theory, additive basis, primes
11	no	open	yes	view	A001220, A377587	number theory, additive basis
12	no	open	yes	view	N/A	number theory
13	$100	proved (Lean)	yes	view	A002264	number theory
14	no	open	yes	view	A143824, possible	number theory, sidon sets, additive combinatorics
15	no	open	yes	view	N/A	number theory, primes
16	no	disproved (Lean)	yes	view	A006285	number theory, additive basis, primes
17	no	open	yes	view	A038133	number theory, primes	cluster primes
18	no	open	yes	view	A005153	number theory, divisors, factorials	practical numbers
19	$500	decidable	no	view	N/A	graph theory, chromatic number
20	$1000	open	yes	view	A332077	combinatorics	sunflower conjecture
21	$500	proved (Lean)	no	view	A391599	combinatorics, intersecting family
22	no	proved (Lean)	yes	view	possible	graph theory
23	no	falsifiable	yes	view	A389646	graph theory
24	no	proved (Lean)	yes	view	possible	graph theory
25	no	open	yes	view	N/A	number theory
26	no	disproved (Lean)	yes	view	N/A	number theory, divisors
27	$100	disproved	no	view	N/A	number theory, covering systems
28	$500	open	yes	view	N/A	number theory, additive basis
29	$100	proved (Lean)	no	view	N/A	number theory, additive basis
30	$1000	open	yes	view	A143824, A227590, A003022	number theory, sidon sets, additive combinatorics
31	no	proved (Lean)	yes	view	N/A	number theory, additive basis
32	no	open	yes	view	N/A	number theory, additive basis
33	no	open	yes	view	N/A	number theory, additive basis
34	no	disproved (Lean)	yes	view	A389241, A234813, A390187	number theory
35	no	proved (Lean)	no	view	N/A	number theory, additive basis
36	no	open	yes	view	A393584, possible	number theory, additive combinatorics	minimum overlap problem
37	no	disproved (Lean)	no	view	N/A	number theory, additive combinatorics
38	no	proved (Lean)	yes	view	N/A	number theory
39	$500	open	yes	view	N/A	number theory, sidon sets, additive combinatorics
40	$500	open	yes	view	N/A	number theory, additive basis
41	$500	open	yes	view	N/A	number theory, sidon sets, additive combinatorics
42	no	solved (Lean)	yes	view	N/A	number theory, sidon sets, additive combinatorics
43	$100	disproved (Lean)	yes	view	A143824, A227590, A003022, possible	number theory, sidon sets, additive combinatorics
44	no	open	yes	view	N/A	number theory, sidon sets, additive combinatorics
45	no	proved (Lean)	yes	view	possible	number theory, unit fractions, ramsey theory
46	no	proved (Lean)	yes	view	N/A	number theory, unit fractions, ramsey theory
47	$100	proved (Lean)	yes	view	N/A	number theory, unit fractions
48	no	proved (Lean)	yes	view	N/A	number theory
49	no	proved (Lean)	no	view	A365339, A365474	number theory, primes
50	$250	open	yes	view	N/A	number theory
51	no	open	yes	view	A002202, A014197	number theory
52	$250	open	yes	view	A263996	number theory, additive combinatorics	sum-product problem
53	no	proved (Lean)	no	view	possible	number theory, additive combinatorics
54	$100	solved	no	view	N/A	number theory, ramsey theory
55	$250	solved	no	view	N/A	number theory, ramsey theory
56	$10	disproved (Lean)	yes	view	N/A	number theory, intersecting family
57	no	proved (Lean)	no	view	N/A	graph theory, chromatic number, cycles
58	no	proved	no	view	N/A	graph theory, chromatic number, cycles
59	no	disproved (Lean)	no	view	N/A	graph theory, turan number
60	no	open	yes	view	A006855	graph theory, cycles
61	no	open	yes	view	N/A	graph theory
62	no	open	no	view	N/A	graph theory
63	no	proved (Lean)	no	view	N/A	graph theory, chromatic number, cycles
64	$1000	falsifiable	yes	view	N/A	graph theory, cycles
65	no	open	no	view	N/A	graph theory, cycles
66	$500	open	yes	view	N/A	number theory, additive basis
67	$500	proved	yes	view	A181740, A237695	discrepancy	Erdős discrepancy problem
68	no	open	yes	view	A331373	number theory, irrationality
69	no	proved	yes	view	A262153	number theory, irrationality
70	no	open	yes	view	N/A	graph theory, ramsey theory, set theory
71	no	proved (Lean)	yes	view	N/A	graph theory, cycles
72	$100	proved	no	view	N/A	graph theory, cycles
73	no	proved	no	view	N/A	graph theory
74	$500	open	yes	view	N/A	graph theory, chromatic number, cycles
75	no	open	yes	view	N/A	graph theory, chromatic number
76	no	proved	no	view	A060407	graph theory, ramsey theory
77	$250	open	no	view	A059442	graph theory, ramsey theory
78	$100	open	no	view	A059442	graph theory, ramsey theory
79	no	proved	no	view	N/A	graph theory, ramsey theory
80	no	open	yes	view	N/A	graph theory, ramsey theory
81	no	open	no	view	possible	graph theory
82	no	open	yes	view	A120414, A390256, A390257, A390919, A392636, A394400, A394462, A394539, A394563, A394564, A394573, A394574, A394930, A394933	graph theory
83	$500	proved (Lean)	no	view	A071799, A387635	combinatorics
84	no	open	no	view	possible	graph theory, cycles
85	no	open	yes	view	A006672, possible	graph theory
86	$100	open	no	view	A245762	graph theory
87	no	open	no	view	A059442, possible	graph theory, ramsey theory
88	$100	proved	no	view	N/A	graph theory, ramsey theory
89	$500	open	yes	view	A186704, A131628	geometry, distances	Erdős distance problem
90	$500	disproved (Lean)	yes	view	A186705	geometry, distances	unit distance problem
91	no	open	yes	view	A186704, possible	geometry, distances
92	$500	disproved	yes	view	possible	geometry, distances
93	no	proved (Lean)	yes	view	N/A	geometry, convex, distances
94	£25	proved (Lean)	yes	view	A387858	geometry, convex, distances
95	$500	proved (Lean)	no	view	possible	geometry, convex, distances
96	no	open	yes	view	possible	geometry, distances, convex
97	$100	falsifiable	yes	view	N/A	geometry, distances, convex
98	no	open	yes	view	possible	geometry, distances
99	$100	open	yes	view	N/A	geometry, distances
100	no	open	yes	view	N/A	geometry, distances
101	$100	open	yes	view	A006065, possible	geometry
102	no	open	no	view	N/A	geometry
103	no	open	no	view	possible	geometry, distances
104	$100	open	no	view	A003829	geometry
105	$50	disproved (Lean)	yes	view	N/A	geometry
106	no	falsifiable	no	view	N/A	geometry
107	$500	falsifiable	yes	view	A000051	geometry, convex	'Happy Ending' problem
108	no	open	yes	view	possible	graph theory, chromatic number, cycles
109	no	proved (Lean)	yes	view	N/A	additive combinatorics	Erdős sumset conjecture
110	no	disproved	no	view	N/A	graph theory, chromatic number, cycles
111	no	open	no	view	N/A	graph theory, chromatic number, set theory
112	no	open	no	view	possible	graph theory, ramsey theory
113	$500	disproved (Lean)	no	view	N/A	graph theory, turan number
114	$250	falsifiable	no	view	N/A	polynomials, analysis
115	no	proved (Lean)	yes	view	N/A	polynomials, analysis
116	no	proved (Lean)	no	view	N/A	polynomials, analysis
117	no	open	no	view	possible	group theory
118	no	disproved	no	view	N/A	set theory, ramsey theory
119	$100	solved (Lean)	yes	view	N/A	analysis, polynomials
120	$100	open	yes	view	N/A	combinatorics	Erdős similarity problem
121	no	disproved (Lean)	no	view	A028391, A013928, A372306, A373319, A372306, A373178, A360659, A373114, A143301	number theory, squares
122	no	open	no	view	N/A	number theory
123	$250	proved (Lean)	yes	view	N/A	number theory
124	no	open	yes	view	N/A	number theory, base representations
125	no	disproved (Lean)	yes	view	A367090	number theory, base representations
126	$250	open	yes	view	possible	number theory
127	no	proved (Lean)	no	view	possible	graph theory
128	$250	falsifiable	yes	view	N/A	graph theory
129	no	open	no	view	possible	graph theory, ramsey theory	ambiguous statement
130	no	open	yes	view	N/A	graph theory, chromatic number
131	no	open	no	view	A068063	number theory
132	$100	open	no	view	N/A	distances
133	no	disproved	no	view	possible	graph theory
134	no	proved (Lean)	yes	view	N/A	graph theory
135	$250	disproved (Lean)	no	view	possible	distances, geometry
136	no	solved	no	view	possible	graph theory
137	no	open	yes	view	N/A	number theory
138	$500	open	yes	view	A005346	additive combinatorics
139	$1000	proved (Lean)	yes	view	A003002, A003003, A003004, A003005	additive combinatorics, arithmetic progressions	Szemerédi's theorem
140	$500	proved (Lean)	no	view	A003002	additive combinatorics, arithmetic progressions
141	no	open	yes	view	A006560	additive combinatorics, primes, arithmetic progressions
142	$10000	open	yes	view	A003002, A003003, A003004, A003005	additive combinatorics, arithmetic progressions
143	$500	open	yes	view	N/A	primitive sets
144	$250	proved (Lean)	no	view	A005279	number theory, divisors
145	no	open	yes	view	A005117	number theory
146	$500	open (Lean)	yes	view	N/A	graph theory, turan number
147	$500	disproved (Lean)	no	view	N/A	graph theory, turan number
148	no	open	no	view	A076393, A006585	number theory, unit fractions
149	no	open	no	view	N/A	graph theory
150	no	proved (Lean)	yes	view	possible	graph theory
151	no	open	no	view	possible	graph theory
152	no	proved (Lean)	yes	view	N/A	sidon sets
153	no	open	yes	view	N/A	sidon sets
154	no	proved (Lean)	yes	view	N/A	sidon sets
155	no	open	yes	view	A143824, A227590, A003022	additive combinatorics, sidon sets
156	no	open	yes	view	A382397	sidon sets
157	no	proved	no	view	N/A	sidon sets
158	no	open	yes	view	N/A	sidon sets
159	no	open	no	view	possible	graph theory, ramsey theory
160	no	open	yes	view	possible	additive combinatorics, arithmetic progressions
161	$500	open	no	view	N/A	combinatorics, ramsey theory, discrepancy
162	no	open	no	view	N/A	combinatorics, ramsey theory, discrepancy
163	no	proved	no	view	N/A	graph theory, ramsey theory	Burr-Erdős conjecture
164	no	proved (Lean)	yes	view	A137245	number theory, primitive sets
165	$250	open	no	view	A000791	graph theory, ramsey theory
166	$250	proved	no	view	A059442	graph theory, ramsey theory
167	no	falsifiable	no	view	N/A	graph theory
168	no	open	yes	view	A004059, A057561, A094708, A386439	additive combinatorics
169	no	open	no	view	A005346	additive combinatorics, arithmetic progressions
170	no	open	yes	view	A046693	additive combinatorics	sparse ruler problem
171	no	proved (Lean)	no	view	A156989	additive combinatorics, combinatorics	density Hales-Jewett
172	no	open	yes	view	N/A	additive combinatorics, ramsey theory
173	no	open	no	view	N/A	geometry, ramsey theory
174	no	open	no	view	N/A	geometry, ramsey theory
175	no	proved (Lean)	no	view	N/A	number theory, binomial coefficients
176	no	open	no	view	possible	additive combinatorics, arithmetic progressions, discrepancy
177	no	open	no	view	N/A	discrepancy, arithmetic progressions
178	no	proved (Lean)	yes	view	N/A	discrepancy
179	no	proved	no	view	possible	additive combinatorics, arithmetic progressions
180	no	open (Lean)	yes	view	N/A	graph theory, turan number
181	no	open	no	view	possible	graph theory, ramsey theory
182	no	proved	no	view	possible	graph theory
183	$250	open (Lean)	yes	view	A003323	graph theory, ramsey theory
184	no	open	yes	view	possible	graph theory, cycles
185	no	proved (Lean)	no	view	A003142	additive combinatorics
186	no	solved	no	view	A389784	additive combinatorics
187	no	open	no	view	N/A	additive combinatorics, ramsey theory
188	no	open	yes	view	N/A	geometry, ramsey theory
189	no	disproved (Lean)	yes	view	N/A	geometry, ramsey theory
190	no	solved	no	view	possible	additive combinatorics, arithmetic progressions
191	no	proved (Lean)	no	view	N/A	combinatorics, ramsey theory
192	no	solved (Lean)	no	view	N/A	arithmetic progressions, combinatorics
193	no	open	yes	view	A231255	geometry
194	no	disproved (Lean)	yes	view	N/A	arithmetic progressions
195	no	open	yes	view	N/A	arithmetic progressions
196	no	open	yes	view	N/A	arithmetic progressions
197	no	open	yes	view	N/A	arithmetic progressions
198	no	disproved (Lean)	yes	view	N/A	additive combinatorics, sidon sets, arithmetic progressions
199	no	disproved (Lean)	yes	view	N/A	arithmetic progressions
200	no	open	yes	view	A005115	primes, arithmetic progressions
201	no	open	no	view	A003002, A003003, A003004, A003005, possible	additive combinatorics, arithmetic progressions
202	no	solved (Lean)	yes	view	A389975	covering systems
203	no	open	yes	view	N/A	primes, covering systems
204	no	disproved (Lean)	yes	view	N/A	covering systems
205	no	disproved (Lean)	yes	view	possible	number theory
206	no	disproved (Lean)	yes	view	N/A	number theory, unit fractions
207	no	proved	no	view	N/A	combinatorics, hypergraphs
208	no	open	yes	view	A005117, A076259	number theory
209	no	disproved (Lean)	yes	view	N/A	geometry
210	no	proved	no	view	A003034	geometry
211	$100	proved	no	view	N/A	geometry
212	no	open	yes	view	N/A	geometry, distances
213	no	open	yes	view	N/A	geometry, distances
214	no	proved (Lean)	yes	view	N/A	geometry, distances
215	no	proved (Lean)	no	view	N/A	geometry
216	no	disproved	no	view	A381776	geometry, convex
217	no	open	no	view	possible	geometry, distances
218	no	open	yes	view	A333230, A333231, A064113	number theory, primes
219	no	proved (Lean)	yes	view	A005115, A113827, A123556	number theory, additive combinatorics, primes, arithmetic progressions	Green-Tao theorem
220	$500	proved (Lean)	no	view	A322144	number theory
221	no	proved (Lean)	yes	view	N/A	number theory, additive basis
222	no	open	no	view	A001481, A256435	number theory, squares
223	no	solved	no	view	possible	geometry, distances
224	no	proved (Lean)	yes	view	N/A	geometry
225	no	proved	no	view	N/A	analysis
226	no	proved (Lean)	yes	view	N/A	analysis
227	no	disproved	no	view	N/A	analysis
228	no	proved (Lean)	yes	view	N/A	analysis, polynomials
229	no	proved (Lean)	yes	view	N/A	analysis, iterated functions
230	no	disproved (Lean)	no	view	N/A	analysis, polynomials
231	no	disproved (Lean)	no	view	N/A	combinatorics
232	no	proved	no	view	N/A	geometry, distances
233	no	open	yes	view	A074741	number theory, primes
234	no	open	yes	view	N/A	number theory, primes
235	no	proved	no	view	N/A	number theory
236	no	open	yes	view	A039669, A109925	number theory, primes
237	no	proved (Lean)	no	view	N/A	number theory, primes
238	no	open	yes	view	N/A	number theory, primes
239	no	proved (Lean)	yes	view	N/A	number theory
240	no	proved	no	view	N/A	number theory, primes
241	$100	open	yes	view	A387704	additive combinatorics, sidon sets
242	no	falsifiable	yes	view	A073101, A075245, A075246, A075247, A075248, A287116	number theory, unit fractions	Erdős-Straus conjecture
243	no	open	yes	view	A000058	number theory
244	no	open	yes	view	N/A	number theory, primes
245	no	proved	yes	view	N/A	additive combinatorics
246	no	proved (Lean)	yes	view	N/A	number theory
247	no	open	yes	view	N/A	number theory, irrationality
248	no	proved (Lean)	yes	view	N/A	number theory
249	no	open	yes	view	A256936	number theory, irrationality
250	no	proved (Lean)	yes	view	A066766	number theory, irrationality
251	no	open	yes	view	A098990	number theory, irrationality
252	no	open	yes	view	A227988, A227989, A307036, A359060, possible	number theory, irrationality
253	no	disproved (Lean)	yes	view	N/A	number theory
254	no	open	yes	view	N/A	number theory
255	no	proved (Lean)	no	view	N/A	discrepancy
256	no	open	no	view	N/A	analysis
257	no	open	yes	view	N/A	irrationality
258	no	proved (Lean)	yes	view	N/A	irrationality
259	no	proved (Lean)	yes	view	A371134	irrationality
260	no	open	yes	view	N/A	irrationality
261	no	open	no	view	N/A	number theory
262	no	solved (Lean)	no	view	N/A	irrationality
263	no	open	yes	view	N/A	irrationality
264	no	open	yes	view	N/A	irrationality
265	no	open	no	view	N/A	irrationality	ambiguous statement
266	no	disproved (Lean)	yes	view	N/A	irrationality
267	no	open	yes	view	N/A	irrationality
268	no	proved (Lean)	yes	view	N/A	number theory
269	no	open	yes	view	N/A	irrationality
270	no	disproved (Lean)	no	view	A073016	irrationality
271	no	open	no	view	A005487	additive combinatorics, arithmetic progressions	Stanley sequences
272	no	open	yes	view	possible	additive combinatorics, arithmetic progressions
273	no	open	yes	view	N/A	number theory, covering systems
274	no	open	yes	view	N/A	group theory, covering systems	Herzog-Schönheim conjecture
275	no	proved (Lean)	yes	view	N/A	number theory, covering systems
276	no	open	yes	view	N/A	number theory, covering systems
277	no	proved (Lean)	yes	view	N/A	number theory, covering systems
278	no	open	no	view	N/A	number theory, covering systems
279	no	open	yes	view	N/A	number theory, covering systems, primes
280	no	disproved (Lean)	yes	view	N/A	number theory, covering systems
281	no	proved (Lean)	yes	view	N/A	number theory, covering systems
282	no	open	yes	view	N/A	number theory, unit fractions
283	no	proved (Lean)	yes	view	A380791	number theory, unit fractions
284	no	proved	no	view	possible	number theory, unit fractions
285	no	proved (Lean)	yes	view	A030659	number theory, unit fractions
286	no	proved	no	view	N/A	number theory, unit fractions
287	no	falsifiable	yes	view	N/A	number theory, unit fractions
288	no	open	yes	view	N/A	number theory, unit fractions
289	no	open	yes	view	N/A	number theory, unit fractions
290	no	proved (Lean)	yes	view	A375081	number theory, unit fractions
291	no	open	yes	view	A110566	number theory, unit fractions
292	no	proved	no	view	A092671	number theory, unit fractions
293	no	open	no	view	possible	number theory, unit fractions	ambiguous statement
294	no	proved	no	view	possible	number theory, unit fractions
295	no	open	yes	view	A192881	number theory, unit fractions
296	no	proved (Lean)	yes	view	possible	number theory, unit fractions
297	no	solved	no	view	A092670	number theory, unit fractions
298	no	proved (Lean)	yes	view	N/A	number theory, unit fractions
299	no	disproved (Lean)	yes	view	N/A	number theory, unit fractions
300	no	solved (Lean)	no	view	A390393	number theory, unit fractions
301	no	open	no	view	A390394	number theory, unit fractions
302	no	open	yes	view	A390395	number theory, unit fractions
303	no	proved (Lean)	yes	view	N/A	number theory, unit fractions
304	no	open	yes	view	A097847, A097849	number theory, unit fractions
305	no	proved	no	view	possible	number theory, unit fractions
306	no	open	yes	view	N/A	number theory, unit fractions
307	no	verifiable	yes	view	N/A	number theory, unit fractions
308	no	proved	no	view	possible	number theory, unit fractions
309	no	disproved (Lean)	no	view	A217693	number theory, unit fractions
310	no	proved (Lean)	no	view	N/A	number theory, unit fractions
311	no	open	no	view	N/A	number theory, unit fractions
312	no	open	yes	view	N/A	number theory, unit fractions
313	no	open	yes	view	A054377	number theory, unit fractions
314	no	proved (Lean)	yes	view	N/A	number theory, unit fractions
315	no	proved (Lean)	yes	view	A000058, A076393	number theory, unit fractions
316	no	disproved (Lean)	yes	view	N/A	number theory, unit fractions
317	no	open	yes	view	N/A	number theory, unit fractions
318	no	solved	yes	view	N/A	number theory, unit fractions
319	no	open	yes	view	possible	number theory, unit fractions
320	no	solved	no	view	A072207	number theory, unit fractions
321	no	solved	yes	view	A384927, A391592	number theory, unit fractions
322	no	open	no	view	A025456, A025418	number theory, powers
323	no	open	yes	view	A004825, A004831, A004832, A004833, A004842, A004843, A004844, A004845, A004857, A004869, possible	number theory, powers
324	no	open	yes	view	N/A	number theory, powers
325	no	open	yes	view	A004825, A004832, A004843, A004854, A004865, possible	number theory, powers
326	no	open	yes	view	N/A	number theory, additive basis
327	no	open	no	view	A384927	number theory, unit fractions
328	no	disproved (Lean)	yes	view	N/A	number theory, additive combinatorics
329	no	open	yes	view	possible	number theory
330	no	proved (Lean)	yes	view	N/A	number theory, additive basis
331	no	disproved (Lean)	yes	view	N/A	number theory, additive combinatorics
332	no	open	yes	view	N/A	number theory
333	no	disproved (Lean)	yes	view	N/A	number theory, additive basis
334	no	open	no	view	A062241, A045535	number theory
335	no	open	no	view	N/A	number theory, additive combinatorics
336	no	open	no	view	possible	number theory, additive basis
337	no	disproved (Lean)	yes	view	N/A	number theory, additive combinatorics, additive basis
338	no	open	no	view	N/A	number theory, additive basis
339	no	proved	no	view	N/A	number theory, additive basis
340	no	open	yes	view	A080200, A005282	number theory, additive combinatorics, sidon sets
341	no	open	yes	view	N/A	number theory
342	no	open	yes	view	A002858	number theory
343	no	proved	no	view	N/A	number theory, complete sequences
344	no	proved	no	view	N/A	number theory, complete sequences
345	no	open	no	view	A001661	number theory, complete sequences
346	no	open	yes	view	N/A	number theory, complete sequences
347	no	proved (Lean)	yes	view	N/A	number theory, complete sequences
348	no	open	yes	view	N/A	number theory, complete sequences
349	no	open	yes	view	N/A	number theory, complete sequences
350	no	proved (Lean)	yes	view	N/A	number theory, additive combinatorics
351	no	proved (Lean)	yes	view	N/A	number theory, complete sequences
352	no	open	yes	view	N/A	geometry
353	no	proved (Lean)	yes	view	N/A	geometry
354	no	open	yes	view	N/A	number theory
355	no	proved (Lean)	yes	view	N/A	number theory, unit fractions
356	no	proved (Lean)	no	view	possible	number theory
357	no	open	yes	view	A364132, A364153, possible	number theory
358	no	proved (Lean)	yes	view	possible	number theory, additive basis, primes
359	no	open	yes	view	A002048	number theory	segmented numbers
360	no	solved	no	view	possible	number theory
361	no	open	yes	view	possible	number theory
362	no	proved (Lean)	no	view	possible	number theory
363	no	disproved (Lean)	yes	view	N/A	number theory
364	no	verifiable	yes	view	A060355, A076445	number theory
365	no	open	no	view	A060355, A060859, A175155	number theory
366	no	verifiable	yes	view	A060355	number theory	ambiguous statement
367	no	open	yes	view	A057521	number theory
368	no	open	no	view	A074399	number theory
369	no	proved (Lean)	yes	view	N/A	number theory
370	no	proved (Lean)	yes	view	N/A	number theory
371	no	open	yes	view	A070089	number theory
372	no	proved	yes	view	A071870	number theory
373	no	open	yes	view	A003135	number theory, factorials
374	no	open	no	view	A388851, A387184, A389117, A389148	number theory
375	no	falsifiable	yes	view	N/A	number theory
376	no	open	yes	view	A030979	number theory, binomial coefficients, base representations
377	no	open	yes	view	N/A	number theory, binomial coefficients
378	no	proved	no	view	N/A	number theory, binomial coefficients
379	no	proved (Lean)	yes	view	possible	number theory, binomial coefficients
380	no	proved	no	view	A070003, A388654, A387054, A389100	number theory
381	no	disproved	no	view	A002182	number theory, divisors
382	no	open	no	view	A388850	number theory
383	no	open	yes	view	N/A	number theory
384	no	proved (Lean)	no	view	N/A	number theory, binomial coefficients
385	no	open	yes	view	A322292	number theory
386	no	open	yes	view	A280992	number theory, binomial coefficients
387	no	solved	yes	view	N/A	number theory, binomial coefficients
388	no	open	no	view	N/A	number theory
389	no	open	yes	view	A375071	number theory
390	no	open (Lean)	yes	view	A193429	number theory, factorials
391	no	proved (Lean)	no	view	A034258, A034259	number theory, factorials
392	no	proved (Lean)	yes	view	possible	number theory, factorials
393	no	open	no	view	A388302	number theory, factorials
394	no	open	yes	view	A344005	number theory
395	no	proved (Lean)	no	view	N/A	analysis	reverse Littlewood-Offord problem
396	no	open	yes	view	A375077	number theory, binomial coefficients
397	no	disproved (Lean)	yes	view	N/A	number theory, binomial coefficients
398	no	falsifiable	yes	view	A146968, A141399	number theory, factorials	Brocard-Ramanujan conjecture
399	no	disproved (Lean)	yes	view	N/A	number theory, factorials
400	no	open	yes	view	possible	number theory, factorials
401	no	proved (Lean)	yes	view	N/A	number theory, factorials
402	no	proved	yes	view	N/A	number theory
403	no	proved (Lean)	yes	view	N/A	number theory, factorials
404	no	open	no	view	N/A	number theory, factorials
405	no	proved (Lean)	no	view	N/A	number theory, factorials
406	no	open	yes	view	N/A	number theory, base representations
407	no	proved	no	view	possible, A387688	number theory
408	no	open	no	view	A049108	number theory, iterated functions
409	no	open	yes	view	A039651, A229487	number theory, iterated functions
410	no	open	yes	view	A007497, possible	number theory, iterated functions
411	no	open	no	view	A383044, possible	number theory, iterated functions
412	no	open	yes	view	A007497, A051572	number theory, iterated functions
413	no	open	yes	view	A005236	number theory, iterated functions
414	no	open	yes	view	A064491, possible	number theory, iterated functions
415	no	open	no	view	possible	number theory
416	no	open	yes	view	A264810	number theory
417	no	open	yes	view	A264810, A061070	number theory
418	no	proved (Lean)	yes	view	A005278, A263958	number theory
419	no	solved (Lean)	yes	view	N/A	number theory, factorials
420	no	open	no	view	N/A	number theory
421	no	open	yes	view	A389544, A390848	number theory
422	no	open	yes	view	A005185	number theory
423	no	open	no	view	A005243	number theory
424	no	open	yes	view	A005244	number theory
425	no	open	no	view	possible	number theory, sidon sets
426	$25	disproved (Lean)	yes	view	possible	graph theory
427	no	proved (Lean)	yes	view	N/A	number theory, primes
428	no	open	yes	view	N/A	number theory, primes
429	no	disproved (Lean)	yes	view	N/A	number theory
430	no	open	no	view	possible	number theory
431	no	open	no	view	N/A	number theory, primes	inverse Goldbach problem
432	no	open	no	view	N/A	number theory
433	no	proved (Lean)	no	view	possible	number theory
434	no	proved (Lean)	yes	view	possible	number theory
435	no	proved (Lean)	yes	view	A389479	number theory
436	no	open	no	view	A000445, possible	number theory
437	no	proved	no	view	possible	number theory
438	no	solved	no	view	A363069	number theory
439	no	proved	no	view	N/A	number theory, ramsey theory
440	no	solved	no	view	N/A	number theory
441	no	disproved	no	view	A068509	number theory
442	no	disproved (Lean)	yes	view	N/A	number theory
443	no	proved (Lean)	yes	view	N/A	number theory
444	no	proved	no	view	N/A	number theory, divisors
445	no	open	yes	view	N/A	number theory
446	no	solved	no	view	A074738	number theory, divisors
447	no	proved (Lean)	yes	view	possible	combinatorics
448	no	disproved (Lean)	yes	view	A397433	number theory, divisors
449	no	disproved	no	view	possible	number theory, divisors
450	no	open	yes	view	N/A	number theory, divisors
451	no	open	no	view	A386620	number theory
452	no	open	no	view	possible	number theory
453	no	disproved (Lean)	yes	view	N/A	number theory
454	no	open	yes	view	A389676, A389677	number theory, primes
455	no	open	yes	view	N/A	number theory
456	no	open	yes	view	A034694, A061026, possible	number theory
457	no	proved (Lean)	yes	view	A391668	number theory
458	no	falsifiable	yes	view	A056604	number theory, primes
459	no	solved (Lean)	yes	view	A289280	number theory, primes
460	no	open	no	view	N/A	number theory	ambiguous statement
461	no	open	no	view	possible	number theory, primes
462	no	open	no	view	A032742, possible	number theory, primes
463	no	open	yes	view	possible	number theory, primes
464	no	proved (Lean)	yes	view	N/A	number theory
465	no	proved	no	view	N/A	number theory
466	no	proved	no	view	N/A	number theory
467	no	open	no	view	N/A	number theory	ambiguous statement
468	no	open	no	view	A167485, A387502, A387503	number theory, divisors
469	no	proved (Lean)	yes	view	A006036, A119425, possible	number theory, divisors
470	$10	open	yes	view	A006037, A002975	number theory, divisors
471	no	proved	no	view	possible	number theory
472	no	open	no	view	A389713, possible	number theory
473	no	proved	no	view	A055265	number theory
474	$100	not provable	no	view	N/A	set theory, ramsey theory
475	no	decidable	no	view	N/A	number theory, additive combinatorics
476	no	proved (Lean)	yes	view	N/A	number theory, additive combinatorics
477	no	open	yes	view	N/A	number theory
478	no	open	no	view	A210184	number theory, factorials
479	no	open	yes	view	A036236, A015919, A050259, A015921, A006521, A006517, A015940	number theory
480	no	proved (Lean)	yes	view	N/A	number theory
481	no	proved (Lean)	yes	view	N/A	number theory
482	no	solved	no	view	A004539	number theory
483	no	open	no	view	A030126	number theory, additive combinatorics, ramsey theory
484	no	proved (Lean)	yes	view	N/A	number theory, additive combinatorics, ramsey theory
485	no	proved	no	view	possible	analysis, polynomials
486	no	open	yes	view	N/A	number theory, primitive sets
487	no	proved (Lean)	yes	view	N/A	number theory
488	no	falsifiable	yes	view	N/A	number theory
489	no	open	yes	view	N/A	number theory
490	no	proved (Lean)	no	view	A397205	number theory
491	no	proved	no	view	N/A	number theory
492	no	disproved	no	view	N/A	number theory
493	no	proved (Lean)	yes	view	N/A	number theory
494	no	proved	yes	view	N/A	analysis, additive combinatorics
495	no	open	yes	view	N/A	diophantine approximation, number theory	Littlewood conjecture
496	no	proved	no	view	N/A	number theory, diophantine approximation
497	no	solved (Lean)	yes	view	A000372	combinatorics	Dedekind's problem
498	no	proved (Lean)	yes	view	N/A	combinatorics, analysis	strong Littlewood-Offord problem
499	no	proved (Lean)	yes	view	N/A	combinatorics
500	$500	open	no	view	A140462	graph theory, hypergraphs, turan number
501	no	open	yes	view	N/A	combinatorics, set theory
502	no	solved (Lean)	yes	view	A027627	geometry, distances
503	no	open	yes	view	A175769	geometry, distances
504	no	solved	no	view	N/A	geometry	Blumenthal's problem
505	no	disproved (Lean)	yes	view	possible	geometry	Borsuk's problem
506	no	decidable	yes	view	possible	geometry
507	no	open	yes	view	N/A	geometry	Heilbronn's triangle problem
508	no	open	yes	view	N/A	geometry, ramsey theory	Hadwiger-Nelson problem
509	no	open	yes	view	N/A	analysis
510	no	open	yes	view	N/A	analysis	Chowla's cosine problem
511	no	disproved	no	view	N/A	analysis
512	no	proved (Lean)	yes	view	N/A	analysis	Littlewood's conjecture
513	no	open	yes	view	N/A	analysis
514	no	open	no	view	N/A	analysis
515	no	proved	no	view	N/A	analysis
516	no	proved (Lean)	yes	view	N/A	analysis
517	no	open	yes	view	N/A	analysis
518	no	proved	no	view	N/A	graph theory, ramsey theory
519	no	proved (Lean)	yes	[view](https://m