Source labels openChecked July 26, 2026

Artin's conjecture on primitive roots

Artin's Conjecture on Primitive Roots*, first half. Let $a$ be an integer that is not a square number and not $−1$ . Then the set $S(a)$ of primes $p$ such that $a$ is a primitive root modulo $p$ has a positive asymptotic density inside the set of primes. ...

Number theory AMS 11

Mathematical statement

Statement source: Wikipedia statement material

Statement terms: CC-BY-SA-4.0

Attributed source material. Reuse must follow the linked attribution and share-alike terms.

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

artin_primitive_roots.parts.i

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem artin_primitive_roots.parts.i (a : ℤ) (ha : ¬IsSquare a) (ha' : a ≠ -1) :    ∃ x > 0, (S a).HasDensity x {p | p.Prime} := 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 Wikipediabackground A85397background LMS14background