feat: add Green-Tao theorem eval problem#284
Open
kim-em wants to merge 1 commit into
Open
Conversation
This PR adds the Green-Tao theorem (§37 of Knill's "Some Fundamental Theorems in Mathematics") as a new eval problem: the set of primes contains arbitrarily long arithmetic progressions. Mathlib has Dirichlet's theorem and Roth's theorem on 3-APs but not Green-Tao, which has not yet been formalized in any major proof assistant. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
2 participants
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
This PR adds the Green–Tao theorem as a new lean-eval challenge problem — §37 of Oliver Knill's Some Fundamental Theorems in Mathematics.
The set of primes contains arbitrarily long arithmetic progressions: for every
kthere exista ≥ 0andb ≥ 1such thata + b·jis prime for everyj < k.mathlib has Dirichlet's theorem (
Nat.infinite_setOf_prime_and_modEq) and Roth's theorem on 3-APs (roth_3ap_theorem_nat) — but not Green–Tao. As of 2026 the theorem has not been formalized in any major proof assistant, making it a long-standing open formalization target.🤖 Prepared with Claude Code