The board / number theory / #219
Erdős Problem #219
Green-Tao theorem
PROVED LEANdatabase updated 2026-08-23
The statement as posed is true, and a proof exists. A solution has also been checked by machine, in Lean.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
The set of arithmetic progressions of primes
Are there arbitrarily long arithmetic progressions of primes? Solution: yes. Ref: Green, Ben and Tao, Terence, _The primes contain arbitrarily long arithmetic progressions_
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/219.Prizenone
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/219
Attempts
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