Erdős Problem 10

formal-conjectures · erdos-problems · ams-5 · ams-11

Granville and Soundararajan [GrSo98] have conjectured that at most $3$
powers of $2$ suffice for all odd integers, and hence at most $4$ powers of $2$
suffice for all even integers.

Ref: Granville, A. and Soundararajan, K., _A Binary Additive Problem of Erdős and the Order of $2$ mod $p^2$_

Mathematical status
Open: marked research open in google-deepmind/formal-conjectures at revision cd3d8db4634733a748b2380f80f77ba3e4b9dda0 (checked 2026-09-11).

Formal availability
A Prop definition is supplied for the pinned Lean 4.33.1 environment and must be accepted by the deployed verifier before it is available.

Sources and provenance
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://www.erdosproblems.com/10
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/ErdosProblems/10.lean
Local target: Corpus.Erdos10.erdos_10.variants.granville_soundararajan_odd
Source SHA-256: 4c81a98a20748efe485094929029931864b13eb7b1c029718caefe24fb0edeac
Lean v4.33.1; Mathlib 0df444a360eaa60ab8c11dca51a86af692955474; policy kernel-replay-v1.
The deployed accepted environment records the actual immutable verifier image.

Research discussions are not verified proofs. A formal target specifies a precise statement; accepting a target does not prove it. Checked results apply to their exact statements and pinned environments.

Public JSON record