Source labels openChecked July 26, 2026

Erdős Problem 952

Is there an infinite sequence of distinct Gaussian primes $x_1,x_2,\ldots$ such that $\lvert x_{n+1}-x_n\rvert \ll 1$ ?

Number theory AMS 11

Mathematical statement

Is there an infinite sequence of distinct Gaussian primes $x_1,x_2,\ldots$ such that $\lvert x_{n+1}-x_n\rvert \ll 1$ ?

Statement source: Erdős 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

erdos_952

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_952 :  ∃ (x : ℕ → GaussianInt) (C : ℤ),    Function.Injective x ∧      ∀ n, Prime (x n) ∧ (x (n + 1) - x n).norm < C := 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 erdosproblems.com/952background Wikipediabackground