Every problem here was open when it entered the pool.
Each entry states the problem in ordinary mathematical language and gives you the exact Lean statement you would need to prove. Nothing is paraphrased, so what you read is what gets checked.
Erdős problem 137 - multiple powerful factors · Conjectures.io
Number theory
Erdős problem 137 - multiple powerful factors
Erdős [Er82c] conjectures that, if k is fixed, then for all n sufficiently large and all
positive integers m, there must be at least k distinct primes p such that
p∣m(m+1)⋯(m+n) and yet p2 does not divide the right hand side.
[Er82c] Erdős, Paul, "Miscellaneous problems in number theory". Congr. Numer. (1982), 25-45.,
0 α bounty·1 piece from 1 person·last one last month
week of 11 Oct 2025 · nothing publishedweek of 18 Oct 2025 · nothing publishedweek of 25 Oct 2025 · nothing publishedweek of 1 Nov 2025 · nothing publishedweek of 8 Nov 2025 · nothing publishedweek of 15 Nov 2025 · nothing published
Solve it
A complete proof or refutation in Lean. The first one the validator accepts takes the whole bounty.
∀ (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), x
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.