Erdős Problem 218: Infinite Equal Prime Gap
There are infintely many indices such that the prime gap at is equal to the prime gap at . This is equivalent to the existence of infinitely many arithmetic progressions of length , see erdos_141.variants.infinite_three.
Mathematical statement
There are infintely many indices such that the prime gap at is equal to the prime gap
at . This is equivalent to the existence of infinitely many arithmetic progressions of
length , see erdos_141.variants.infinite_three.
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_218.variants.infinite_equal_prime_gap
theorem erdos_218.variants.infinite_equal_prime_gap : {n | primeGap n = primeGap (n + 1)}.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