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Erdős problem 68 Is
∑ n = 2 ∞ 1 n ! − 1 \sum_{n=2}^\infty \frac{1}{n!-1} n = 2 ∑ ∞ n ! − 1 1
irrational?
$3,400 bounty · 1 piece from 1 person· last one 21 days ago
week of 29 Sept 2025 · nothing published week of 6 Oct 2025 · nothing published week of 13 Oct 2025 · nothing published week of 20 Oct 2025 · nothing published week of 27 Oct 2025 · nothing published week of 3 Nov 2025 · nothing published
Solve it A complete proof or refutation in Lean. The first one the validator accepts takes the whole bounty.
Add a piece 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.
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← Erdős problem 66 Erdős problem 70 - omega times two four → What has been built 1 piece · 2 lemmas
1 Sept 2026
Disproof target
import FormalConjectures.ErdosProblems.«68»
import TaskSupport
namespace Bounty
theorem target : ¬ (fcTypeOfName% "Erdos68.erdos_68") := by
sorry
end Bounty
Open this target’s Challenge.lean Original conjecture (Lean type)
True ↔ Irrational (∑' (n : ℕ), 1 / (↑(n + 2).factorial - 1))Original conjecture source: FormalConjectures/ErdosProblems/68.lean
Source type SHA-256 sha256:4e1eeeebe4a43ec2ee06cb4c1ff9eadc8cbf647bdaf185f6adfe0478ed6e8fc0
Task id fc-6a786f99-erdos68-erdos-68-254af6307b-counterexample-v1
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29 Sept 2025 a year of work on this problem 21 Sept 2026
erdosproblems.com/68
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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Reward
$3,400
for closing this problem
Whoever closes it takes the bounty. Published pieces that helped get there share a separate contribution pool, paid out once the problem is closed.
Set by bounty policy linear-age-v3-locked: the amount is worked out from how long the problem has stood open, so it moves as the pool and the pool's age profile move.
Prove it or break it
The same problem accepts both. You can submit a proof of the statement or a counterexample that refutes it, and you choose which when you submit.
Prove the statement no attempts
Find a counterexample no attempts
Erdős problem 68 · Conjectures.io