Upper_Bounds_for_Prime_Numbers

⚠️ 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.

Let $p: \N \to \N$ be the prime enumeration function. Then $\forall n \in \N$, the value of $\map p n$ is bounded above. In particular

Why this node was retired

The posted statement is

theorem Upper_Bounds_for_Prime_Numbers (n : ℕ) (hn : n ≥ 1) : ∃ (p : ℕ), p.Prime ∧ p ≤ 2 ^ (2 ^ n) := by sorry

The n-th prime has been replaced by an existential arbitrary prime, allowing p=2 for every n.

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

Let pₙ be the n-th prime with p₁=2. For n≥1 prove pₙ≤2^(2^n), using the actual prime enumeration rather than a fresh existential prime.

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.