Source labels openChecked July 26, 2026

Erdős Problem 1055

A prime $p$ is in class $1$ if the only prime divisors of $p+1$ are $2$ or $3$ . In general, a prime $p$ is in class $r$ if every prime factor of $p+1$ is in some class $\leq r-1$ , with equality for at least one prime factor. Are there infinitely many primes...

Number theory AMS 11

Mathematical statement

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_1055

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_1055 (r) : {p | p.Prime ∧ IsOfClass r p}.Infinite := 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/1055background