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Source labels openChecked July 26, 2026

Erdős ProblemsNumber theory

Erdős Problem 913: Infinite Many 8p Sq Add One Primes

It is likely that there are infinitely many primes pp such that 8p218p^2 - 1 is also prime.

Mathematical statement

It is likely that there are infinitely many primes pp such that 8p218p^2 - 1 is also prime.

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_913.variants.infinite_many_8p_sq_add_one_primes

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem erdos_913.variants.infinite_many_8p_sq_add_one_primes :    { p | p.Prime  (8 * p ^ 2 - 1).Prime }.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