feat: add Green-Tao theorem eval problem#284
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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>
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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