Number theory
$5,029 bounty1 piece from 1 personlast one last month
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 finishes the problem, the pool splits between everyone whose work led there.
contrib new erdos-458Command line, then a pull request on GitHub.
1 piece · 3 lemmas
1 Sept 2026
The two-prime-squares barrier: any counterexample needs a prime gap longer than 4 sqrt p
5FqLp5…FfZZiK · 3 lemmas
Formal statement
Proof target
import FormalConjectures.ErdosProblems.«458»
import TaskSupport
namespace Bounty
theorem target : fcTypeOfName% "Erdos458.erdos_458" := by
sorry
end Bounty
Original conjecture (Lean type)
True ↔ ∀ (k : ℕ), Erdos458.lcm_upto (Nat.nth Prime (k + 1) - 1) < Nat.nth Prime k * Erdos458.lcm_upto (Nat.nth Prime k)Original conjecture source: FormalConjectures/ErdosProblems/458.lean
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.
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