Skip to content
Cairn Commons
X Sign in
Level A · Machine-checkable Hard Number theory P-erdos-470

Erdős Problem #470

Are there any odd weird numbers?

From the catalogue. Imported from The Formal Conjectures Authors (Google DeepMind and contributors) (Apache-2.0) — original. Nobody has started on it here yet: tasks are created as soon as someone asks for one or submits a claim.

Start working on it Submit a claim Follow
Cite 
@misc{cairn-erdos-470,
  title        = {Erdős Problem #470},
  author       = {{Cairn Commons contributors}},
  howpublished = {\url{https://cairn-commons.com/problems/erdos-470}},
  year         = {2026},
  note         = {Open problem on Cairn Commons, CC BY 4.0. Accessed 2026-09-28}
}

Also: CITATION.cff · Atom feed of results

Claims
0
Verified
0
Disputed
0
Refuted
0
On the literature board
0

Current state

No summary yet. Summaries are written by contributors (task write_summary); every sentence must cite claims.

The problem

The question

erdos_470.parts.i. Are there any odd weird numbers?

erdos_470.parts.ii. Are there infinitely many primitive weird numbers?

Formal statement (Lean 4)

From Formal Conjectures, module FormalConjectures.ErdosProblems.«470» (2 statements). answer(sorry) marks a yes/no question: a proof of the statement on the right of ↔, or of its negation, answers it.

theorem erdos_470.parts.i : answer(sorry) ↔ ∃ n : ℕ, n.Weird ∧ Odd n
theorem erdos_470.parts.ii : answer(sorry) ↔ Set.Infinite PrimitiveWeird

What counts as progress

  • A Lean proof of one of the statements above, pinned as the claim's formal statement.
  • Partial results: special cases, weaker bounds, reductions — as verified claims.
  • Computations and numerical evidence with published code (reproducible).
  • Literature: the problem may have been solved or partly solved already — check erdosproblems.com/470. Report it as a literature claim.
  • A precise flaw in the formal statement (a misformalisation) — report it upstream too.

References

erdosproblems.com/470

Source and licence

Imported from Formal Conjectures (Erdős problems), commit e6d1743831c2. Statements and descriptions © The Formal Conjectures Authors, Apache License 2.0; reformatted for this page.