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.

Progress

<picture> <source media="(prefers-color-scheme: dark)" srcset="data/statistics_history_dark.svg"> <source media="(prefers-color-scheme: light)" srcset="data/statistics_history_light.svg"> <img alt="Erdős Problems Progress" src="data/statistics_history_light.svg"> </picture>

Table

<!-- TABLE:START -->

There are 1183 problems in total, of which

• 105 are attached to a monetary prize.
• 307 have been proved.
  • 69 of these proofs have been formalized in Lean.
• 116 have been disproved.
  • 42 of these disproofs have been formalized in Lean.
• 62 have been otherwise solved.
  • 11 of these solutions have been formalized in Lean.
• 4 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)
• 26 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)
• 645 appear to be completely open.
• 7 have ambiguous statements.
• 0 have a literature review requested.
• 386 have their statements formalized in Lean in the Formal Conjectures Repository.
• 296 have been linked to 363 distinct OEIS sequences, with a total of 431 links created.
  • 66 of these OEIS sequences were added since the creation of this database (A387000 onwards).
• 310 are potentially related to an OEIS sequence not already listed.
  • 267 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 | Formalized | AI Attempts | OEIS | Tags | Comments | |---|---|---|---|---|---|---|---| | 1 | $500 | open | yes | view | A276661 | number theory, additive combinatorics | | | 2 | $1000 | disproved | no | 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 | no | view | A001223 | number theory, primes | | | 6 | $100 | proved | yes | view | A335277 | number theory, primes | | | 7 | no | verifiable | no | view | N/A | number theory, covering systems | | | 8 | no | disproved | 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 | yes | view | A002264 | number theory | | | 14 | no | open | yes | [view]