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Erdős problem 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.

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

Table

There are 1080 problems in total, of which

  • 98 are attached to a monetary prize.
  • 254 have been proved.
    • 2 of these proofs have been formalized in Lean.
  • 88 have been disproved.
    • 1 of these disproofs have been formalized in Lean.
  • 43 have been otherwise solved.
  • 4 appear to be open, but cannot be proven from the axioms of ZFC. (not provable)
  • 0 appear to be open, but cannot be disproven from the axioms of ZFC. (not disprovable)
  • 0 are independent of the ZFC axioms of mathematics. (independent)
  • 6 appear to be open, but have been reduced to a finite computation. (decidable)
  • 39 appear to be open, but can be disproven by a finite computation if false. (falsifiable)
  • 8 appear to be open, but can be proven by a finite computation if true. (verifiable)
  • 638 appear to be completely open.
  • 4 have ambiguous statements.
  • 7 have a literature review requested.
  • 185 have their statements formalized in Lean in the Formal Conjectures Repository.
  • 209 have been linked to 255 distinct OEIS sequences, with a total of 305 links created.
    • 22 of these OEIS sequences were added since the creation of this database (A387000 onwards).
  • 329 are potentially related to an OEIS sequence not already listed.
    • 303 of these problems are not currently linked to any existing OEIS sequence.
  • 1 have a related sequence currently being submitted to the OEIS.
  • 2 have a related sequence whose generation is currently in progress.
# Prize Status Formalized OEIS Tags Comments
1 $500 open yes A276661 number theory, additive combinatorics
2 $1000 disproved no N/A number theory, covering systems
3 $5000 open yes A003002, A003003, A003004, A003005 number theory, additive combinatorics, arithmetic progressions
4 $10000 proved yes A002386 number theory, primes
5 no open no N/A number theory, primes
6 $100 proved yes A335277 number theory, primes
7 no verifiable no N/A number theory, covering systems
8 no disproved no N/A number theory, covering systems
9 no open yes A006286 number theory, additive basis, primes
10 no open yes N/A number theory, additive basis, primes
11 no falsifiable yes A001220, A377587 number theory, additive basis
12 no open yes N/A number theory
13 $100 proved no A002264 number theory
14 no open no possible number theory, sidon sets, additive combinatorics
15 no open no N/A number theory, primes
16 no disproved no A006285 number theory, additive basis, primes
17 no open yes A038133 number theory, primes cluster primes
18 no open no A005153 number theory, divisors, factorials practical numbers
19 $500 decidable no N/A graph theory, chromatic number
20 $1000 open yes A332077 combinatorics sunflower conjecture
21 $500 proved no possible combinatorics, intersecting family
22 no proved no possible graph theory
23 no falsifiable no possible graph theory
24 no proved no possible graph theory
25 no open no N/A number theory
26 no disproved no N/A number theory, divisors
27 $100 disproved no N/A number theory, covering systems
28 $500 open yes N/A number theory, additive basis
29 $100 proved no N/A number theory, additive basis
30 $1000 open yes A143824, A227590, A003022 number theory, sidon sets, additive combinatorics
31 no proved no N/A number theory, additive basis
32 no open no N/A number theory, additive basis
33 no open yes N/A number theory, additive basis
34 no disproved no A389241, A234813, submitted number theory
35 no proved no N/A number theory, additive basis
36 no open yes possible number theory, additive combinatorics minimum overlap problem
37 no disproved no N/A number theory, additive combinatorics
38 no open no N/A number theory
39 $500 open yes N/A number theory, sidon sets, additive combinatorics
40 $500 open yes N/A number theory, additive basis
41 $500 open yes N/A number theory, sidon sets, additive combinatorics
42 no open no N/A number theory, sidon sets, additive combinatorics
43 $100 open no A143824, A227590, A003022, possible number theory, sidon sets, additive combinatorics
44 no open yes N/A number theory, sidon sets, additive combinatorics
45 no proved no possible number theory, unit fractions, ramsey theory
46 no proved no N/A number theory, unit fractions, ramsey theory
47 $100 proved no N/A number theory, unit fractions
48 no proved yes N/A number theory
49 no proved no A365339, A365474 number theory, primes
50 $250 open no N/A number theory
51 no open yes N/A number theory
52 $250 open no A263996 number theory, additive combinatorics sum-product problem
53 no proved no possible number theory, additive combinatorics
54 $100 solved no N/A number theory, ramsey theory
55 $250 solved no N/A number theory, ramsey theory
56 $10 disproved yes N/A number theory, intersecting family
57 no proved no N/A graph theory, chromatic number, cycles
58 no proved no N/A graph theory, chromatic number, cycles
59 no disproved no N/A graph theory, turan number
60 no open no possible graph theory, cycles
61 no open yes N/A graph theory
62 no open no N/A graph theory
63 no proved no N/A graph theory, chromatic number, cycles
64 $1000 falsifiable yes N/A graph theory, cycles
65 no open no N/A graph theory, cycles
66 $500 open yes N/A number theory, additive basis
67 $500 proved no A181740, A237695 discrepancy Erdős discrepancy problem
68 no open yes A331373 number theory, irrationality
69 no open yes A262153 number theory, irrationality
70 no open no N/A graph theory, ramsey theory, set theory
71 no proved no N/A graph theory, cycles
72 $100 proved no N/A graph theory, cycles
73 no proved no N/A graph theory
74 $500 open yes N/A graph theory, chromatic number, cycles
75 no open no N/A graph theory, chromatic number
76 no proved no A060407 graph theory, ramsey theory
77 $250 open no A059442 graph theory, ramsey theory
78 $100 open no A059442 graph theory, ramsey theory
79 no proved no N/A graph theory, ramsey theory
80 no open no N/A graph theory, ramsey theory
81 no open no possible graph theory
82 no open no A120414, in progress graph theory
83 $500 proved no A071799, A387635 combinatorics
84 no open no possible graph theory, cycles
85 no falsifiable no possible graph theory
86 $100 open no A245762 graph theory
87 no open no A059442, possible graph theory, ramsey theory
88 $100 proved no N/A graph theory, ramsey theory
89 $500 open no A186704, A131628 geometry, distances Erdős distance problem
90 $500 open yes A186705 geometry, distances unit distance problem
91 no open no A186704, possible geometry, distances
92 $500 open yes possible geometry, distances
93 no proved no N/A geometry, convex
94 £25 open no A387858 geometry, convex
95 $500 proved no possible geometry, convex, distances
96 no open no possible geometry, distances, convex
97 $100 falsifiable no N/A geometry, distances, convex
98 no open no possible geometry, distances
99 $100 open no N/A geometry, distances
100 no open no N/A geometry, distances
101 $100 open no A006065, possible geometry
102 no open no N/A geometry
103 no open no possible geometry, distances
104 $100 open no A003829 geometry
105 $50 falsifiable no N/A geometry
106 no falsifiable no N/A geometry
107 $500 falsifiable yes A000051 geometry, convex 'Happy Ending' problem
108 no open no possible graph theory, chromatic number, cycles
109 no proved no N/A additive combinatorics Erdős sumset conjecture
110 no not provable no N/A graph theory, chromatic number, cycles
111 no open no N/A graph theory, chromatic number, set theory
112 no open no possible graph theory, ramsey theory
113 $500 disproved no N/A graph theory, turan number
114 no falsifiable no N/A polynomials, analysis
115 no proved no N/A polynomials, analysis
116 no proved no N/A polynomials, analysis
117 no open no possible group theory
118 no disproved no N/A set theory, ramsey theory
119 $100 open no N/A analysis, polynomials
120 $100 open no N/A combinatorics Erdős similarity problem
121 no disproved no A028391, A013928, A372306, A373319, A372306, A373178, A360659, A373114, A143301 number theory, squares
122 no open no N/A number theory
123 $250 open no N/A number theory
124 no open no N/A number theory, base representations
125 no open no A367090 number theory, base representations
126 $250 open yes possible number theory
127 no proved no possible graph theory
128 $250 open yes N/A graph theory
129 no open no possible graph theory, ramsey theory
130 no open no N/A graph theory, chromatic number
131 no open no A068063 number theory
132 $100 open no N/A distances
133 no disproved no possible graph theory
134 no proved no N/A graph theory
135 $250 disproved no possible distances, geometry
136 no solved no possible graph theory
137 no open yes N/A number theory
138 $500 open yes A005346 additive combinatorics
139 $1000 proved yes A003002, A003003, A003004, A003005 additive combinatorics, arithmetic progressions Szemerédi's theorem
140 $500 proved no A003002 additive combinatorics, arithmetic progressions
141 no open yes A006560 additive combinatorics, primes, arithmetic progressions
142 $10000 open yes A003002, A003003, A003004, A003005 additive combinatorics, arithmetic progressions
143 $500 open yes N/A primitive sets
144 $250 proved no A005279 number theory, divisors
145 no open yes A005117 number theory
146 $500 open no N/A graph theory, turan number
147 $500 disproved no N/A graph theory, turan number
148 no open no A076393, A006585 number theory, unit fractions
149 no open no N/A graph theory
150 no proved no possible graph theory
151 no open no possible graph theory
152 no open no N/A sidon sets
153 no open no N/A sidon sets
154 no proved no N/A sidon sets
155 no open yes A143824, A227590, A003022 additive combinatorics, sidon sets
156 no open no A382397 sidon sets
157 no proved no N/A sidon sets
158 no open no N/A sidon sets
159 no open no possible graph theory, ramsey theory
160 no open yes possible additive combinatorics, arithmetic progressions
161 $500 open no N/A combinatorics, ramsey theory, discrepancy
162 no open no N/A combinatorics, ramsey theory, discrepancy
163 no proved no N/A graph theory, ramsey theory Burr-Erdős conjecture
164 no proved no A137245 number theory, primitive sets
165 $250 open no A000791 graph theory, ramsey theory
166 $250 proved no possible graph theory, ramsey theory
167 no falsifiable no N/A graph theory
168 no open yes A004059, A057561, A094708, A386439 additive combinatorics
169 no open no A005346 additive combinatorics, arithmetic progressions
170 no open no A046693 additive combinatorics sparse ruler problem
171 no proved no A156989 additive combinatorics, combinatorics density Hales-Jewett
172 no open no N/A additive combinatorics, ramsey theory
173 no open no N/A geometry, ramsey theory
174 no open no N/A geometry, ramsey theory
175 no proved no N/A number theory, binomial coefficients
176 no open no possible additive combinatorics, arithmetic progressions, discrepancy
177 no open no N/A discrepancy, arithmetic progressions
178 no proved no N/A discrepancy
179 no proved no possible additive combinatorics, arithmetic progressions
180 no open no N/A graph theory, turan number
181 no open no possible graph theory, ramsey theory
182 no proved no possible graph theory
183 $250 open no A003323 graph theory, ramsey theory
184 no open no possible graph theory, cycles
185 no proved no A003142 additive combinatorics
186 no solved no in progress additive combinatorics
187 no open no N/A additive combinatorics, ramsey theory
188 no open yes N/A geometry, ramsey theory
189 no disproved yes N/A geometry, ramsey theory
190 no open no possible additive combinatorics, arithmetic progressions
191 no proved no N/A combinatorics, ramsey theory
192 no solved no N/A arithmetic progressions, combinatorics
193 no open no A231255 geometry
194 no disproved no N/A arithmetic progressions
195 no open no N/A arithmetic progressions
196 no open yes N/A arithmetic progressions
197 no open no N/A arithmetic progressions
198 no disproved yes N/A additive combinatorics, sidon sets, arithmetic progressions
199 no disproved no N/A arithmetic progressions
200 no open yes A005115 primes, arithmetic progressions
201 no open no A003002, A003003, A003004, A003005, possible additive combinatorics, arithmetic progressions
202 no open no possible covering systems
203 no open yes N/A primes, covering systems
204 no disproved no N/A covering systems
205 no open no possible number theory
206 no disproved no N/A number theory, unit fractions
207 no proved no N/A combinatorics, hypergraphs
208 no open yes A005117, A076259 number theory
209 no disproved no N/A geometry
210 no proved no A003034 geometry
211 $100 proved no N/A geometry
212 no open yes N/A geometry, distances
213 no open yes N/A geometry, distances
214 no proved no N/A geometry, distances
215 no proved no N/A geometry
216 no disproved no A381776 geometry, convex
217 no open no possible geometry, distances
218 no open yes A333230, A333231, A064113 number theory, primes
219 no proved yes A005115, A113827, A123556 number theory, additive combinatorics, primes, arithmetic progressions Green-Tao theorem
220 $500 proved no A322144 number theory
221 no proved no N/A number theory, additive basis
222 no open no A256435 number theory, squares
223 no open no possible geometry, distances
224 no proved no N/A geometry
225 no proved no N/A analysis
226 no proved no N/A analysis
227 no disproved no N/A analysis
228 no proved yes N/A analysis, polynomials
229 no proved yes N/A analysis, iterated functions
230 no disproved no N/A analysis, polynomials
231 no disproved no N/A combinatorics
232 no proved no N/A geometry, distances
233 no open yes A074741 number theory, primes
234 no open no N/A number theory, primes
235 no proved no N/A number theory
236 no open yes A039669, A109925 number theory, primes
237 no proved no N/A number theory, primes
238 no open no N/A number theory, primes
239 no proved no N/A number theory
240 no proved no N/A number theory, primes
241 $100 open no possible additive combinatorics, sidon sets
242 no falsifiable yes A073101, A075245, A075246, A075247, A075248, A287116 number theory, unit fractions Erdős-Straus conjecture
243 no open yes A000058 number theory
244 no open yes N/A number theory, primes
245 no proved yes N/A additive combinatorics
246 no proved no N/A number theory
247 no open yes N/A number theory, irrationality
248 no open yes N/A number theory
249 no open yes A256936 number theory, irrationality
250 no proved yes A066766 number theory, irrationality
251 no open yes A098990 number theory, irrationality
252 no open no A227988, A227989, possible number theory, irrationality
253 no disproved yes N/A number theory
254 no open no N/A number theory
255 no proved no N/A discrepancy
256 no open no N/A analysis
257 no open yes N/A irrationality
258 no open yes N/A irrationality
259 no proved yes A371134 irrationality
260 no open no N/A irrationality
261 no open no N/A number theory
262 no solved no N/A irrationality
263 no open no N/A irrationality
264 no open yes N/A irrationality
265 no open no N/A irrationality
266 no disproved yes N/A irrationality
267 no open yes N/A irrationality
268 no proved no N/A number theory
269 no open yes N/A irrationality
270 no disproved no A073016 irrationality
271 no open no A005487 additive combinatorics, arithmetic progressions
272 no open no possible additive combinatorics, arithmetic progressions
273 no open yes N/A number theory, covering systems
274 no open yes N/A group theory, covering systems Herzog-Schönheim conjecture
275 no proved no N/A number theory, covering systems
276 no open no N/A number theory, covering systems
277 no proved no N/A number theory, covering systems
278 no open no N/A number theory, covering systems
279 no open no N/A number theory, covering systems, primes
280 no disproved no N/A number theory, covering systems
281 no open no N/A number theory, covering systems
282 no open no N/A number theory, unit fractions
283 no open no A380791 number theory, unit fractions
284 no proved no possible number theory, unit fractions
285 no proved yes possible number theory, unit fractions
286 no proved no N/A number theory, unit fractions
287 no open no N/A number theory, unit fractions
288 no open yes N/A number theory, unit fractions
289 no open yes N/A number theory, unit fractions
290 no proved no A375081 number theory, unit fractions
291 no open no A110566 number theory, unit fractions
292 no proved no A092671 number theory, unit fractions
293 no open no possible number theory, unit fractions
294 no proved no possible number theory, unit fractions
295 no open yes possible number theory, unit fractions
296 no proved no possible number theory, unit fractions
297 no solved no A092670 number theory, unit fractions
298 no proved yes N/A number theory, unit fractions
299 no disproved yes N/A number theory, unit fractions
300 no solved no possible number theory, unit fractions
301 no open no possible number theory, unit fractions
302 no open no possible number theory, unit fractions
303 no proved yes N/A number theory, unit fractions
304 no open yes possible number theory, unit fractions
305 no proved no possible number theory, unit fractions
306 no open yes N/A number theory, unit fractions
307 no verifiable yes N/A number theory, unit fractions
308 no proved no possible number theory, unit fractions
309 no disproved no A217693 number theory, unit fractions
310 no proved no N/A number theory, unit fractions
311 no open no N/A number theory, unit fractions
312 no open yes N/A number theory, unit fractions
313 no open yes A054377 number theory, unit fractions
314 no proved no N/A number theory, unit fractions
315 no proved no A000058, A076393 number theory, unit fractions
316 no disproved (Lean) yes N/A number theory, unit fractions
317 no open no N/A number theory, unit fractions
318 no open no N/A number theory, unit fractions
319 no open yes possible number theory, unit fractions
320 no open no A072207 number theory, unit fractions
321 no open yes possible number theory, unit fractions
322 no open no A025456, possible number theory, powers
323 no open no possible number theory, powers
324 no open yes N/A number theory, powers
325 no open yes possible number theory, powers
326 no open yes N/A number theory, additive basis
327 no open no possible number theory, unit fractions
328 no disproved no N/A number theory, additive combinatorics
329 no open yes possible number theory
330 no open yes N/A number theory, additive basis
331 no disproved no N/A number theory, additive combinatorics
332 no open no N/A number theory
333 no open no N/A number theory, additive basis
334 no open no possible number theory
335 no open no N/A number theory, additive combinatorics
336 no open no possible number theory, additive basis
337 no disproved no N/A number theory, additive combinatorics, additive basis
338 no open no N/A number theory, additive basis
339 no open no N/A number theory, additive basis
340 no open yes A080200, A005282 number theory, additive combinatorics, sidon sets
341 no open no N/A number theory
342 no open no A002858 number theory
343 no proved no N/A number theory, complete sequences
344 no proved no N/A number theory, complete sequences
345 no open no possible number theory, complete sequences
346 no open no N/A number theory, complete sequences
347 no open yes N/A number theory, complete sequences
348 no open yes N/A number theory, complete sequences
349 no open yes N/A number theory, complete sequences
350 no proved yes N/A number theory, additive combinatorics
351 no open no N/A number theory, complete sequences
352 no open yes N/A geometry
353 no proved no N/A geometry
354 no open yes N/A number theory
355 no proved yes N/A number theory, unit fractions
356 no proved no possible number theory
357 no open no possible number theory
358 no open yes possible number theory, additive basis, primes
359 no open no A002048 number theory segmented numbers
360 no solved no possible number theory
361 no open yes possible number theory
362 no proved no possible number theory
363 no disproved no N/A number theory
364 no verifiable yes A060355 number theory
365 no open no A060355, A060859, A175155 number theory
366 no verifiable yes A060355 number theory
367 no open no A057521 number theory
368 no open no A074399 number theory
369 no open no N/A number theory
370 no proved yes N/A number theory literature review sought
371 no open no A070089 number theory
372 no proved no A071870 number theory
373 no open yes A003135 number theory, factorials
374 no open no A388851, A387184, A389117, A389148 number theory
375 no falsifiable no N/A number theory
376 no open yes A030979 number theory, binomial coefficients, base representations
377 no open yes N/A number theory, binomial coefficients
378 no proved no N/A number theory, binomial coefficients
379 no proved (Lean) yes possible number theory, binomial coefficients
380 no open no A070003, A388654, A387054, A389100 number theory
381 no disproved no A002182 number theory, divisors
382 no open no A388850 number theory
383 no open yes N/A number theory
384 no proved no N/A number theory, binomial coefficients
385 no open no A322292 number theory
386 no open no A280992 number theory, binomial coefficients
387 no open no N/A number theory, binomial coefficients
388 no open no N/A number theory
389 no open yes A375071 number theory
390 no open no A193429 number theory, factorials
391 no proved no A034258, A034259 number theory, factorials
392 no proved yes possible number theory, factorials
393 no open no A388302 number theory, factorials
394 no proved no A344005 number theory
395 no proved no N/A analysis reverse Littlewood-Offord problem
396 no open no A375077 number theory, binomial coefficients
397 no open no N/A number theory, binomial coefficients
398 no falsifiable yes A146968 number theory, factorials Brocard-Ramanujan conjecture
399 no disproved no N/A number theory, factorials
400 no open no possible number theory, factorials
401 no open no N/A number theory, factorials
402 no proved yes N/A number theory
403 no proved no N/A number theory, factorials
404 no open no N/A number theory, factorials
405 no proved no N/A number theory, factorials
406 no open yes N/A number theory, base representations
407 no proved no possible, A387688 number theory
408 no open no A049108 number theory, iterated functions
409 no open yes A039651, A229487 number theory, iterated functions
410 no open yes A007497, possible number theory, iterated functions
411 no open no A383044, possible number theory, iterated functions
412 no open yes A007497, A051572 number theory, iterated functions
413 no open no A005236 number theory, iterated functions
414 no open no possible number theory, iterated functions
415 no open no possible number theory
416 no open yes A264810 number theory
417 no open no A264810, A061070 number theory
418 no proved yes possible number theory
419 no solved no N/A number theory, factorials
420 no open no N/A number theory
421 no open yes N/A number theory
422 no open no A005185 number theory
423 no open no A005243 number theory
424 no open no A005244 number theory
425 no open no possible number theory, sidon sets
426 $25 disproved no possible graph theory
427 no proved yes N/A number theory, primes
428 no open no N/A number theory, primes
429 no disproved no N/A number theory
430 no open no possible number theory
431 no open no N/A number theory, primes inverse Goldbach problem
432 no open no N/A number theory
433 no open no possible number theory
434 no open yes possible number theory
435 no proved no possible number theory
436 no open no possible number theory
437 no proved no possible number theory
438 no solved no A363069 number theory
439 no proved no N/A number theory, ramsey theory
440 no open no N/A number theory
441 no disproved no A068509 number theory
442 no disproved yes N/A number theory
443 no proved no N/A number theory
444 no proved no N/A number theory, divisors
445 no open no N/A number theory
446 no solved no A074738 number theory, divisors
447 no proved no possible combinatorics
448 no disproved no possible number theory, divisors
449 no disproved no possible number theory, divisors
450 no open no N/A number theory, divisors
451 no open no possible number theory
452 no open no possible number theory
453 no disproved no N/A number theory
454 no open no possible number theory, primes
455 no open no N/A number theory
456 no open no possible number theory
457 no open yes possible number theory
458 no falsifiable no A056604 number theory, primes
459 no solved no possible number theory, primes
460 no open no N/A number theory
461 no open no possible number theory, primes
462 no open no A032742, possible number theory, primes
463 no open yes possible number theory, primes
464 no proved no N/A number theory
465 no proved no N/A number theory
466 no proved no N/A number theory
467 no open no N/A number theory ambiguous statement
468 no open no A167485, A387502, A387503 number theory, divisors
469 no open yes A006036, A119425, possible number theory, divisors
470 no open yes A006037, A002975 number theory, divisors
471 no proved no possible number theory
472 no open no possible number theory
473 no proved no A055265 number theory
474 $100 not provable no N/A set theory, ramsey theory
475 no falsifiable no N/A number theory, additive combinatorics
476 no proved no N/A number theory, additive combinatorics
477 no open yes N/A number theory
478 no open no A210184 number theory, factorials
479 no open yes A036236 number theory
480 no proved yes N/A number theory
481 no open no N/A number theory
482 no solved no A004539 number theory
483 no open no A030126 number theory, additive combinatorics, ramsey theory
484 no proved no N/A number theory, additive combinatorics, ramsey theory
485 no proved no possible analysis, polynomials
486 no open no N/A number theory, primitive sets
487 no proved no N/A number theory
488 no disproved yes N/A number theory
489 no open no N/A number theory
490 no proved no N/A number theory
491 no proved no N/A number theory
492 no disproved no N/A number theory
493 no proved no N/A number theory
494 no open no N/A analysis, additive combinatorics
495 no open no N/A diophantine approximation, number theory Littlewood conjecture
496 no proved no N/A number theory, diophantine approximation
497 no solved no A000372 combinatorics Dedekind's problem
498 no proved no N/A combinatorics, analysis strong Littlewood-Offord problem
499 no proved yes N/A combinatorics
500 $500 open no A140462 graph theory, hypergraphs, turan number
501 no open no N/A combinatorics, set theory
502 no solved no A027627 geometry, distances
503 no open no A175769 geometry, distances
504 no solved no N/A geometry Blumenthal's problem
505 no disproved no possible geometry Borsuk's problem
506 no decidable no possible geometry
507 no open no N/A geometry Heilbronn's triangle problem
508 no open no N/A geometry, ramsey theory Hadwiger-Nelson problem
509 no open yes N/A analysis
510 no open no N/A analysis Chowla's cosine problem
511 no disproved no N/A analysis
512 no proved no N/A analysis Littlewood's conjecture
513 no open no N/A analysis
514 no open no N/A analysis
515 no open no N/A analysis
516 no open no N/A analysis
517 no open no N/A analysis
518 no proved no N/A graph theory, ramsey theory
519 no proved no N/A analysis
520 no open no N/A number theory, probability
521 no open no N/A analysis, polynomials
522 no proved yes N/A analysis, polynomials, probability
523 no proved no N/A analysis, probability, polynomials
524 no open no N/A analysis, probability, polynomials
525 no proved no possible analysis, probability, polynomials
526 no solved no N/A probability, geometry
527 no proved no N/A analysis, probability
528 no open no A387897, A156816 geometry
529 no open no N/A geometry, probability
530 no open no possible number theory, sidon sets
531 no open no possible number theory, ramsey theory
532 no proved no N/A number theory, ramsey theory
533 no open no N/A graph theory
534 no solved no A387543, A387698 number theory, intersecting family
535 no open no possible number theory
536 no open no possible number theory
537 no disproved no possible number theory
538 no open no N/A number theory
539 no open no possible number theory
540 no proved no A034463 number theory
541 no proved yes N/A number theory
542 no solved no N/A number theory
543 no open no possible number theory, group theory
544 no open no A000791 graph theory, ramsey theory
545 no falsifiable no A059442, possible graph theory, ramsey theory
546 no proved no possible graph theory, ramsey theory
547 no decidable no N/A graph theory, ramsey theory
548 no falsifiable no N/A graph theory
549 no disproved no N/A graph theory, ramsey theory
550 no open no N/A graph theory, ramsey theory
551 no decidable no N/A graph theory, ramsey theory
552 no open no A006672 graph theory, ramsey theory
553 no proved no A000791, possible graph theory, ramsey theory
554 no open no possible graph theory, ramsey theory
555 no open no possible graph theory, ramsey theory
556 no decidable no A389335 graph theory, ramsey theory
557 no open no N/A graph theory, ramsey theory
558 no open no possible graph theory, ramsey theory
559 no disproved no possible graph theory, ramsey theory
560 no open no possible graph theory, ramsey theory
561 no open no N/A graph theory, ramsey theory
562 no open no possible graph theory, ramsey theory, hypergraphs
563 no open no N/A graph theory, ramsey theory, hypergraphs
564 $500 open no possible graph theory, ramsey theory, hypergraphs
565 no proved no possible graph theory, ramsey theory
566 no open no N/A graph theory, ramsey theory
567 no open no N/A graph theory, ramsey theory
568 no open no N/A graph theory, ramsey theory
569 no open no N/A graph theory, ramsey theory
570 no falsifiable no N/A graph theory, ramsey theory
571 no open no N/A graph theory, turan number
572 no open no possible graph theory, turan number
573 no open no possible graph theory, turan number
574 no open no possible graph theory, turan number
575 no open no N/A graph theory, turan number
576 no open no possible graph theory, turan number
577 no proved no N/A graph theory
578 no proved no N/A graph theory
579 no open no N/A graph theory, turan number
580 no falsifiable no N/A graph theory
581 no solved no possible graph theory
582 $100 proved no N/A graph theory, ramsey theory
583 no falsifiable no N/A graph theory
584 no open no N/A graph theory, cycles
585 no open no possible graph theory, cycles
586 no disproved no N/A number theory, covering systems
587 no solved yes A372040 number theory
588 $100 open no possible geometry
589 no open no possible geometry
590 $250 proved yes N/A set theory, ramsey theory
591 $250 open yes N/A set theory, ramsey theory
592 $1000 open yes N/A set theory, ramsey theory
593 $500 open no N/A set theory, graph theory, hypergraphs, chromatic number
594 no proved no N/A graph theory, set theory
595 $250 open no N/A graph theory, set theory
596 no open no N/A graph theory, ramsey theory, set theory
597 no open no N/A graph theory, ramsey theory, set theory
598 no open no N/A set theory, ramsey theory
599 no proved no N/A graph theory, set theory Erdős-Menger conjecture
600 no open no possible graph theory
601 $500 open no N/A graph theory, set theory
602 no open no N/A combinatorics, set theory Property B
603 no open no N/A combinatorics, set theory
604 $500 open no possible geometry, distances pinned distance problem
605 no proved no possible geometry, distances
606 no solved no N/A geometry
607 $250 proved no possible geometry
608 no falsifiable no N/A graph theory
609 no open no possible graph theory, ramsey theory
610 no open no possible graph theory
611 no open no N/A graph theory
612 no open no N/A graph theory
613 no falsifiable no N/A graph theory
614 no open no possible graph theory
615 no disproved no possible graph theory, ramsey theory
616 no open no N/A graph theory
617 no falsifiable no N/A graph theory
618 no proved no N/A graph theory
619 no open no N/A graph theory
620 no open no possible graph theory Erdős-Rogers problem
621 no falsifiable no N/A graph theory
622 no proved no possible graph theory
623 no open no N/A set theory
624 no open no possible combinatorics
625 $1000 open no N/A graph theory, chromatic number
626 no open no possible graph theory, chromatic number, cycles
627 no open no possible graph theory, chromatic number
628 no falsifiable no N/A graph theory, chromatic number
629 no open no possible graph theory, chromatic number
630 no proved no N/A graph theory, chromatic number
631 no proved no N/A graph theory, chromatic number
632 no disproved no N/A graph theory, chromatic number
633 $25 open no N/A geometry
634 $25 open no possible geometry
635 no open no N/A number theory
636 no proved no N/A graph theory, ramsey theory
637 no proved no N/A graph theory, ramsey theory
638 no open no N/A graph theory, ramsey theory
639 no proved no N/A graph theory, ramsey theory
640 no open no N/A graph theory, chromatic number
641 no disproved no N/A graph theory
642 no open no possible graph theory, cycles
643 no open no possible graph theory, hypergraphs
644 no open no possible combinatorics
645 no proved yes N/A number theory, additive combinatorics, ramsey theory
646 no proved no N/A number theory, factorials
647 £25 verifiable no A062249, A087280 number theory
648 no solved no possible number theory
649 no disproved no possible number theory
650 no open no possible number theory
651 no disproved no possible geometry, convex
652 no open no N/A geometry, distances
653 no open no possible geometry, distances
654 no open no possible geometry, distances
655 no open no possible geometry, distances
656 no proved no N/A number theory, additive combinatorics
657 no open no possible geometry, distances
658 no proved no possible additive combinatorics
659 no open no possible geometry, distances
660 no open no possible geometry, distances, convex
661 $50 open no possible geometry, distances
662 no open no N/A geometry, distances ambiguous statement
663 no open no possible number theory
664 no disproved no N/A combinatorics
665 no open no N/A combinatorics
666 no disproved no possible graph theory
667 no open no N/A graph theory, ramsey theory
668 no open no possible geometry, distances
669 no open no A003035, A006065, A008997, possible geometry orchard problems
670 no open no N/A geometry, distances
671 $250 open no N/A analysis
672 no verifiable yes N/A number theory
673 no proved no N/A number theory, divisors
674 no proved no N/A number theory
675 no open no N/A number theory
676 no open no possible number theory
677 no open no possible number theory
678 no proved yes possible number theory
679 no open no N/A number theory
680 no open no N/A number theory, primes
681 no open no N/A number theory, primes
682 no proved no A386978 number theory, primes
683 no open no A006530, A074399, A121359, possible number theory, primes, binomial coefficients
684 no open no possible number theory, primes, binomial coefficients
685 no open no N/A number theory, primes, binomial coefficients
686 no open no N/A number theory
687 no open no A048670 number theory
688 no open no N/A number theory
689 no open yes N/A number theory
690 no open no possible number theory
691 no open no N/A number theory
692 no disproved no N/A number theory, divisors
693 no open no possible number theory, divisors
694 no open yes possible number theory
695 no open yes A061092 number theory
696 no open no possible number theory, divisors
697 no open no N/A number theory, divisors
698 no proved no possible number theory, binomial coefficients
699 no falsifiable no N/A number theory, binomial coefficients
700 no open no A091963, possible number theory, binomial coefficients
701 no open no N/A combinatorics, intersecting family
702 no proved no N/A combinatorics
703 $250 proved no possible combinatorics
704 no open no N/A graph theory, geometry, chromatic number
705 no open no N/A graph theory, chromatic number
706 no open no possible graph theory, chromatic number
707 $500 falsifiable yes N/A additive combinatorics, sidon sets
708 $100 open no possible number theory
709 no open no possible number theory
710 ₹2000 open no possible number theory
711 ₹1000 open no possible number theory
712 $500 open no possible graph theory, turan number, hypergraphs
713 $500 open no N/A graph theory, turan number
714 no open no possible graph theory, turan number
715 no proved no N/A graph theory
716 no proved no possible graph theory, hypergraphs Ruzsa-Szemerédi problem
717 no proved no N/A graph theory
718 no proved no N/A graph theory
719 no open no possible graph theory, hypergraphs
720 $100 proved no possible graph theory, ramsey theory
721 no solved no possible number theory, additive combinatorics, ramsey theory
722 no proved no N/A combinatorics
723 no falsifiable yes N/A combinatorics
724 no open no A001438 combinatorics
725 no open no A001009 combinatorics
726 no open no N/A number theory
727 no open yes A002503, A343507 number theory, factorials
728 no open no N/A number theory, factorials
729 no open no N/A number theory, factorials
730 no open yes A129515 number theory, binomial coefficients, base representations
731 no open no possible number theory, factorials
732 no proved no N/A combinatorics
733 no proved no possible combinatorics, geometry
734 no open no possible combinatorics
735 no solved no N/A geometry
736 no not provable no N/A graph theory, chromatic number
737 no proved no N/A graph theory, chromatic number
738 no open no N/A graph theory, chromatic number
739 no not provable no N/A graph theory, chromatic number
740 no open no N/A graph theory, chromatic number
741 no open no N/A additive combinatorics
742 no decidable no N/A graph theory
743 no falsifiable no N/A graph theory tree packing conjecture
744 no disproved no possible graph theory, chromatic number
745 no proved no N/A graph theory
746 no proved no N/A graph theory
747 no solved no N/A combinatorics, hypergraphs
748 no proved no A007865 number theory Cameron-Erdős conjecture
749 no open no N/A additive combinatorics
750 no open no N/A graph theory, chromatic number
751 no disproved no N/A graph theory, chromatic number
752 no proved no N/A graph theory, cycles
753 no disproved no N/A graph theory, chromatic number
754 no proved no possible geometry, distances
755 no proved no possible geometry
756 no proved no possible geometry, distances
757 no open no possible geometry, distances, sidon sets
758 no solved no possible graph theory, chromatic number
759 no solved no possible graph theory, chromatic number
760 no proved no N/A graph theory, chromatic number
761 no open no N/A graph theory, chromatic number
762 no disproved no N/A graph theory, chromatic number
763 no disproved no N/A number theory, additive combinatorics
764 no disproved no N/A number theory, additive combinatorics
765 no solved no possible graph theory, turan number
766 no open no possible graph theory, turan number
767 no proved no possible graph theory, turan number
768 no open no A001034, A352287 number theory
769 no open no possible number theory, geometry
770 no open no possible number theory
771 no proved no possible number theory
772 no proved no possible number theory, sidon sets, additive combinatorics
773 no open no possible number theory, sidon sets, squares
774 no open no N/A number theory
775 no open no possible graph theory, hypergraphs
776 no open no N/A combinatorics
777 no solved no N/A graph theory, combinatorics
778 no open no N/A graph theory
779 no falsifiable yes N/A number theory, primes
780 no proved no N/A combinatorics, hypergraphs, chromatic number
781 no disproved no possible additive combinatorics
782 no open no N/A number theory
783 no open no N/A number theory
784 no open no N/A number theory
785 no proved no N/A additive combinatorics exact additive complements
786 no open yes N/A number theory
787 no open no possible additive combinatorics
788 no open no possible additive combinatorics
789 no open no possible additive combinatorics
790 no open no possible additive combinatorics
791 no open no A066063 additive combinatorics
792 no open no possible additive combinatorics
793 no open no possible number theory
794 no disproved no N/A graph theory, hypergraphs, turan number
795 no proved no possible number theory
796 no open no possible number theory
797 no proved no possible graph theory, chromatic number
798 no proved no possible geometry
799 no proved no N/A graph theory, chromatic number
800 no proved no N/A graph theory, ramsey theory
801 no proved no N/A graph theory, ramsey theory
802 no open no N/A graph theory
803 no disproved no N/A graph theory
804 no disproved no possible graph theory
805 no open no possible graph theory
806 no proved no possible additive combinatorics
807 no disproved no N/A graph theory
808 no disproved no N/A additive combinatorics, graph theory
809 no open no possible graph theory, ramsey theory
810 no open no possible graph theory, ramsey theory
811 no open no possible graph theory, ramsey theory
812 no open no possible graph theory, ramsey theory
813 no open no possible graph theory
814 no proved no possible graph theory
815 no disproved no N/A graph theory
816 no proved no N/A graph theory
817 no open yes possible additive combinatorics
818 no proved no N/A additive combinatorics
819 no open no possible additive combinatorics
820 no open no A263647 number theory
821 no open no A014197 number theory
822 no open no A121048, A155085 number theory
823 no proved no N/A number theory
824 no open no possible number theory
825 $25 open yes A006037, A330244 number theory
826 no open yes N/A number theory
827 no open no possible geometry
828 no open yes N/A number theory
829 no open no possible number theory
830 no open yes A259180 number theory
831 no open no possible geometry
832 no disproved no N/A graph theory, hypergraphs, chromatic number
833 no proved no possible graph theory, hypergraphs, chromatic number
834 no verifiable no N/A graph theory, hypergraphs
835 no verifiable no N/A graph theory, hypergraphs
836 no open no N/A graph theory, hypergraphs, chromatic number
837 no open no N/A graph theory, hypergraphs
838 no open no possible geometry, convex
839 no open no N/A number theory
840 no open no N/A additive combinatorics, sidon sets
841 no solved no possible number theory
842 no proved no N/A graph theory, chromatic number
843 no proved no N/A number theory
844 no proved no N/A number theory, intersecting family
845 no open yes N/A number theory
846 no open yes N/A geometry
847 no open no N/A additive combinatorics
848 no falsifiable no N/A number theory
849 no open no A003016, A003015, A059233, A098565, A090162, A180058, A182237 number theory, binomial coefficients Singmaster's conjecture
850 no open no A343101 number theory, primes Erdős-Woods conjecture
851 no open yes N/A number theory
852 no open no possible number theory, primes
853 no open no A001223, possible number theory, primes
854 no open no possible number theory
855 no falsifiable no A023193 number theory, primes second Hardy-Littlewood conjecture
856 no open no possible number theory
857 no open no possible combinatorics
858 no open no N/A number theory, primitive sets
859 no open no N/A number theory, divisors
860 no open no possible number theory, primes
861 no solved no A143824, A227590, A003022, A143823 number theory, sidon sets
862 no open no possible number theory, sidon sets
863 no open no N/A number theory, sidon sets, additive combinatorics
864 no open no possible number theory, sidon sets, additive combinatorics
865 no open no possible number theory, additive combinatorics
866 no open no possible number theory, additive combinatorics
867 no disproved no possible additive combinatorics
868 no open yes N/A number theory, additive basis
869 no open no N/A number theory, additive basis
870 no open no N/A number theory, additive basis
871 no open no N/A number theory, additive basis
872 no open no possible number theory, primitive sets
873 no open yes N/A number theory
874 no proved no possible number theory, additive combinatorics
875 no open no N/A additive combinatorics
876 no open no N/A additive combinatorics
877 no proved no possible additive combinatorics
878 no open no possible number theory
879 no open no possible number theory
880 no proved no N/A number theory, additive basis
881 no open no N/A number theory, additive basis
882 no solved no possible number theory, primitive sets
883 no open no N/A number theory, graph theory
884 no open no N/A number theory, divisors
885 no open no N/A number theory, divisors
886 no open no N/A number theory, divisors
887 no open no N/A number theory, divisors
888 no open no A387584 number theory, squares
889 no open no possible number theory
890 no open no N/A number theory, primes
891 no open no N/A number theory
892 no open no N/A number theory, primitive sets
893 no open yes A046801, possible number theory, divisors
894 no proved no N/A number theory, ramsey theory
895 no proved no N/A additive combinatorics, graph theory
896 no open no possible number theory
897 no open yes N/A number theory
898 no proved no N/A geometry Erdős-Mordell inequality
899 no proved yes N/A additive combinatorics
900 no proved no N/A graph theory
901 no open no possible combinatorics, hypergraphs
902 no open no A362137 graph theory
903 no open no N/A combinatorics
904 no proved no N/A graph theory
905 no proved no N/A graph theory
906 no open no N/A analysis, iterated functions literature review sought
907 no proved no N/A analysis
908 no proved no N/A analysis
909 no proved no N/A analysis, topology
910 no disproved no N/A topology
911 no open no N/A graph theory, ramsey theory
912 no open no A071626 number theory, factorials
913 no open yes A359747 number theory
914 no proved no N/A graph theory
915 no falsifiable no N/A graph theory
916 no proved no N/A graph theory, cycles
917 no open no N/A graph theory, chromatic number
918 no open no N/A graph theory, chromatic number
919 no open no N/A graph theory, chromatic number
920 no open no possible graph theory, chromatic number
921 no proved no possible graph theory, chromatic number, cycles
922 no proved no N/A graph theory, chromatic number
923 no proved no N/A graph theory, chromatic number
924 no proved no N/A graph theory, ramsey theory
925 no disproved no possible graph theory, ramsey theory
926 no proved no possible graph theory
927 no disproved no possible graph theory
928 no open no A006530 number theory
929 no open no possible number theory
930 no open no N/A number theory
931 no open yes N/A number theory
932 no open yes possible number theory
933 no open no possible number theory
934 no open no possible graph theory
935 no open no A057521, A389244, possible number theory
936 no open yes A146968, possible number theory
937 no proved no possible number theory
938 no open yes possible number theory
939 no open yes possible number theory
940 no open yes possible number theory
941 no proved no N/A number theory
942 no open yes possible number theory
943 no open yes possible number theory
944 no open yes N/A graph theory, chromatic number
945 no open yes possible number theory, divisors
946 no proved yes A005237, A284783 number theory, divisors
947 no proved no N/A number theory, covering systems
948 no open no N/A number theory, ramsey theory
949 no open yes N/A ramsey theory
950 no open no N/A number theory, primes
951 no open no N/A number theory
952 no open no N/A number theory Gaussian moat problem
953 no open no N/A geometry, distances
954 no open no possible number theory
955 no open no possible number theory
956 no open no possible geometry, distances, convex
957 no proved no N/A geometry, distances
958 no disproved no N/A distances, geometry
959 no open no N/A geometry, distances
960 no open no possible geometry
961 no open no possible number theory
962 no open no possible number theory
963 no open no possible number theory
964 no proved no N/A number theory, divisors
965 no open no N/A ramsey theory
966 no proved no N/A number theory, additive combinatorics, ramsey theory
967 no open no N/A number theory, analysis
968 no open no A387591 number theory
969 no open no possible number theory
970 no open no possible number theory
971 no open no possible number theory
972 no open no N/A number theory
973 no open no N/A analysis literature revieww sought
974 no proved no N/A analysis
975 no open no A147807, possible number theory, divisors
976 no open no N/A number theory
977 no proved no A005420, A002583 number theory
978 no open no possible number theory
979 no open no A385316, possible number theory
980 no proved no A053760, A098990, possible number theory
981 no open no N/A number theory
982 no falsifiable no A004526 geometry, convex
983 no open no possible number theory
984 no proved no N/A arithmetic progressions, additive combinatorics
985 no open yes A002233, A219429, A103309, possible number theory
986 no open no A000791, A059442 graph theory, ramsey theory
987 no proved (Lean) no N/A analysis, discrepancy
988 no solved no possible discrepancy
989 no solved no possible discrepancy
990 no open no N/A analysis
991 no proved no N/A discrepancy literature review sought
992 no open no N/A discrepancy
993 no falsifiable no possible graph theory
994 no disproved no N/A analysis, discrepancy
995 no open no N/A analysis, discrepancy
996 no open no N/A analysis
997 no open no N/A analysis, discrepancy, primes
998 no proved no N/A analysis, diophantine approximation
999 no proved no N/A number theory, diophantine approximation Duffin-Schaeffer conjecture
1000 no open no N/A number theory, diophantine approximation
1001 no solved no N/A number theory, diophantine approximation
1002 no open no N/A analysis, diophantine approximation
1003 no open yes A001274 number theory
1004 no open no possible number theory
1005 no open no A386893 number theory
1006 no disproved no N/A graph theory, cycles
1007 no solved no N/A graph theory
1008 no proved no N/A graph theory literature review sought
1009 no open no N/A graph theory
1010 no proved no N/A graph theory
1011 no open no possible graph theory literature review sought
1012 no open no possible graph theory ambiguous statement
1013 no open no A292528 graph theory
1014 no open no possible graph theory
1015 no solved no possible graph theory, ramsey theory
1016 no open no A105206 graph theory, cycles literature review sought
1017 no open no possible graph theory
1018 no open no N/A graph theory, planar graphs
1019 no proved no N/A graph theory, planar graphs literature review sought
1020 no falsifiable no N/A graph theory, hypergraphs Erdős matching conjecture
1021 no open no N/A graph theory
1022 no open no possible combinatorics, hypergraphs
1023 no open no possible combinatorics
1024 no solved no possible graph theory, hypergraphs
1025 no solved no possible combinatorics
1026 no open no possible combinatorics ambiguous statement
1027 no proved no N/A combinatorics
1028 no solved no possible graph theory, discrepancy
1029 $100 open no possible graph theory, Ramsey theory
1030 no open no A000791, A059442 graph theory, Ramsey theory
1031 no proved no possible graph theory
1032 no open no possible graph theory, chromatic number
1034 no open no possible graph theory
1035 no open no possible graph theory
1035 no open no possible graph theory
1036 no proved no possible graph theory
1037 no disproved no N/A graph theory
1038 no open no N/A analysis
1039 no open no N/A analysis
1040 no open no N/A analysis
1041 no falsifiable no N/A analysis
1042 no proved no N/A analysis
1043 no falsifiable no N/A analysis
1044 no open no N/A analysis
1045 no falsifiable no N/A analysis
1046 no disproved no N/A analysis
1047 no disproved no N/A analysis
1048 no disproved no N/A analysis
1049 no open no N/A irrationality
1050 no proved no A331372 irrationality
1051 no open no N/A irrationality
1052 $10 open yes A002827 number theory unitary perfect numbers
1053 no open no A007539 number theory multiply perfect numbers
1054 no open no A167485 number theory, divisors
1055 no open no A005113 number theory, primes
1056 no open no A060427 number theory
1057 no open no A006931 number theory Carmichael numbers
1058 no proved no N/A number theory
1059 no open no A064152 number theory, primes
1060 no open no A327153 number theory
1061 no open no A110177, possible number theory
1062 no open no A038372 number theory
1063 no open no possible number theory
1064 no open no A051488, A051487 number theory
1065 no open no possible number theory
1066 no open no possible graph theory, planar graphs
1067 no disproved no N/A graph theory, set theory
1068 no open no N/A graph theory, set theory, chromatic number
1069 no solved no possible geometry
1070 no open no possible geometry
1071 no open no N/A geometry
1072 no open no A154554 number theory
1073 no open no A256519 number theory
1074 no open no A063980, A064164 number theory
1075 no open no N/A hypergraphs
1076 no open no possible hypergraphs
1077 no open no N/A graph theory
1078 no proved no N/A graph theory
1079 no open no N/A graph theory, turan number
1080 no open no possible graph theory

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