Open problemChecked July 24, 2026

Normality of π

The question of whether the digits of π are uniformly distributed in every finite block.

Number theory Normal numbers Probability

Mathematical statement

The number $\pi$ is normal in base $10$ , so every block of $k$ decimal digits has limiting frequency $10^{-k}$ .

Statement source: Therefore editorial statement

Statement terms: Source-specific

Editorial wording by Therefore. No statement reuse license is granted.

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

NormalNumber.pi_normal_base_ten

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem pi_normal_base_ten :    IsNormalInBase 10 π := 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

Normal number overviewbackground