Source labels openChecked July 26, 2026

Ben Green's Open Problem 66

Is there always a sum of two squares between $X - \frac{1}{10}X^{1/4}$ and $X$ ? We formalize this as an eventual statement for sufficiently large real $X$ .

Number theory AMS 11

Mathematical statement

Is there always a sum of two squares between $X - \frac{1}{10}X^{1/4}$ and $X$ ? We formalize this as an eventual statement for sufficiently large real $X$ .

Statement source: Green's Open Problems statement material

Statement terms: Source-specific

Source-specific terms. Therefore does not assert reuse rights beyond attributed display.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

green_66

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem green_66 :    answer(sorry) ↔      ∀ᶠ X : ℝ in atTop,        ∃ n : ℕ, IsSumOfTwoSquares n ∧          (n : ℝ) ∈ Set.Icc (X - (1 / 10 : ℝ) * X ^ (1 / 4 : ℝ)) X := by  sorry

Statement source: Formal Conjectures
Lean version: v4.27.0
Placeholder: Present; no proof artifact
Source evidence: Pinned source index
Fidelity review: Community formulation

References

Pinned Formal Conjectures sourceformalization Ben Green's Open Problem 66background