Source labels openChecked July 26, 2026

Erdős Problem 1074: Iii

Similarly, if $P$ is the set of all primes $p$ such that there exists an $m$ with $p\not\equiv 1\pmod{m}$ such that $m! + 1 \equiv 0\pmod{p}$ , then does $\lim\frac{|P\cap[1, x]|}{\pi(x)}$ exist?

Number theory AMS 11

Mathematical statement

Similarly, if $P$ is the set of all primes $p$ such that there exists an $m$ with $p\not\equiv 1\pmod{m}$ such that $m! + 1 \equiv 0\pmod{p}$ , then does

\lim\frac{|P\cap[1, x]|}{\pi(x)}

exist?

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_1074.parts.iii

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_1074.parts.iii : answer(sorry) ↔ ∃ c, PillaiPrimes.HasDensity c {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 erdosproblems.com/1074background