Informal statementPinned source
For every positive integer n, there is a prime strictly between n² and (n + 1)².
Source correspondenceImported; no Proofweave fidelity attestation
MSC 11 · Number theoryOpen conjecture
Founding Challenges · Formal Conjectures
Legendre's Conjecture
The conjecture about a prime between consecutive squares is paired with a sufficiently-large-n theorem as a more bounded formalization target.
Environment
leanprover/lean4:v4.27.0
mathlib:a3a10db0e9d6Formalized statementOpen proof branchNo Proofweave attestation
Pinned Lean statementLean 4
theorem legendre_conjecture :
answer(sorry) ↔ ∀ n ≥ 1, ∃ p ∈ Set.Ioo (n ^ 2) ((n + 1) ^ 2), Nat.Prime p := by
sorryReproducibility recordcurated-expansion-v1-lean4.27.0
- Revision
b2e608fc52d765510915a244bb69b1a2741acc3c- Retrieved
- 2026-07-16T00:00:00Z
- Source hash
sha256:c7ec74fb1e28040c870d64d01bd52d7ff85d812475e211e53d604bc809b3c577- License
- Apache-2.0 source code; upstream materials may carry their own stated terms.
- Mathlib
a3a10db0e9d66acbebf76c5e6a135066525ac900
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