Number theory
Date added
$5,226 bounty1 piece from 1 personlast one 2 months ago
Nobody has attempted this. A complete proof or refutation takes the whole bounty.
A lemma, a definition, a special case. There is no race: when someone closes the problem, up to half of its bounty can go to the recognised pieces that led there.
contrib new erdos-137-variants-multiple-powerful-factorsCommand line, then a pull request on GitHub.
1 piece · 6 lemmas
3 Sept 2026
Valuation reduction for simple primes in a block, with an unconditional prime for m <= n
5FqLp5…FfZZiK · 6 lemmas
conjectures-tasks
The pinned statement, the Lean challenge file and the exact bundle you build against.
versions/fc-v2-variants-multiple-powerful-factors-3f6f041e932cfab86b098783-formalized →
conjectures-contribution
Every published piece for this problem, with its Lean source and its signed record.
contributions/erdos-137-variants-multiple-powerful-factors →
Formal statement
Proof target
import Mathlib
import FormalConjectures.ErdosProblems.«137»
import TaskSupport
namespace Bounty
theorem target : fcTypeOfName% "Erdos137.erdos_137.variants.multiple_powerful_factors" := by
sorry
end Bounty
Original conjecture (Lean type)
∀ (k : ℕ),
∀ᶠ (n : ℕ) in Filter.atTop,
∀ (m : ℕ),
0 < m →
∃ P,
P.card = k ∧ ∀ p ∈ P, Nat.Prime p ∧ p ∣ ∏ x ∈ Finset.Icc m (m + n), x ∧ ¬p ^ 2 ∣ ∏ x ∈ Finset.Icc m (m + n), xOriginal conjecture source: FormalConjectures/ErdosProblems/137.lean
The audit patch changes this file, so the upstream version can differ from the statement above.
References
Something wrong with this formalization?
A statement that does not faithfully capture the original conjecture is the one real risk here, so we would rather hear about it early - before someone spends weeks on it.
Our channel is in the Bittensor Discord server. Join the server first, then open the channel to send your report.