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-409-variants-sigma-terminationCommand line, then a pull request on GitHub.
1 piece · 1 lemma
1 Sept 2026
Termination of the iterated totient-plus-one map at a prime
5FqLp5…FfZZiK · 1 lemma
conjectures-tasks
The pinned statement, the Lean challenge file and the exact bundle you build against.
versions/fc-v2-variants-sigma-termination-d9f6adccf222676a1faaad16-formalized →
conjectures-contribution
Every published piece for this problem, with its Lean source and its signed record.
contributions/erdos-409-variants-sigma-termination →
Formal statement
Proof target
import Mathlib
import FormalConjectures.ErdosProblems.«409»
import TaskSupport
namespace Bounty
theorem target : fcTypeOfName% "Erdos409.erdos_409.variants.sigma_termination" := by
sorry
end Bounty
Original conjecture (Lean type)
∀ n > 1, ∃ i, Nat.Prime ((fun x => (ArithmeticFunction.sigma 1) x - 1)^[i] n)Original conjecture source: FormalConjectures/ErdosProblems/409.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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