Number of decompositions of $2n+1$ into $2p+q$, where $p$ and $q$ are both odd primes

formal-conjectures · oeis · ams-11

Conjecture: all items for $n \ge 4$ are greater than or equal to $1$. This is a stronger
conjecture than the Goldbach conjecture.

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://oeis.org/A103151
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/103151.lean
Local target: Corpus.OEIS103151.conjecture
Source SHA-256: 9dcc80882aa79e63f5426864e16a28d89e190f57d67d2c6c6390dc52c77ee03f
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