lean_workbook_plus_68381

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Proved status carries no information about that problem. Do not import this node or use it as a dependency.

Prove that there are infinitely many prime numbers of the form $k^2 - 22,(k \ge 5,k \in Z)$.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_68381 (k : ℤ) (h₁ : 5 ≤ k) : ∃ p, p.Prime ∧ ∃ k, p = k^2 - 22   :=  by sorry

Infinitely many primes became existence of a single prime; the inner k shadows the arbitrary outer variable, and3=5²−22 suffices.

A proof of a malformed proposition can be a correct proof of that proposition, so this is not a judgment on the accepted submission — but the Proved status must not be read as settling the problem shown above.

Proposed corrected statement

State the intended infinitude precisely: for every bound B there exists an integer k≥5 with k²−22>B and k²−22 prime. This is a substantive prime-values-of-a-quadratic problem; the proposed statement is not claimed proved by the existing one-witness certificate.

Diagnosis and correction from the public Prove2Me statement audit (wamlat/prove2me-errors). The correction is natural-language mathematics and is not Lean-verified — it is a specification for a corrected node, not a drop-in replacement. No corrected replacement node exists yet.