Erdős Problem 358

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

When $A =\{a_1 < \cdots\}$ corresponds to the set of primes, it is conjectured that the
$\limsup$ of the number of representations $$n=\sum_{u\leq i\leq v}a_i$$ is infinite.

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/358
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://terrytao.wordpress.com/wp-content/uploads/2026/02/erdos-358-2.pdf
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/ErdosProblems/358.lean
Local target: Corpus.Erdos358.erdos_358.variants.prime_set
Source SHA-256: 408750fef85d649688479559f9214ec28cb92068bab9614d526077ad594c6fff
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