Number of prime powers strictly between $n$-th prime and $(n+1)$-th prime

formal-conjectures · oeis · ams-11

The sequence $a(n)$ is the number of prime powers $k$ strictly between the $n$-th prime $p_n$
and the $(n+1)$-th prime $p_{n+1}$: $p_n < k < p_{n+1}$.

It is conjectured that $a(n) \le 2$ for all $n$.

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/A080101
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/80101.lean
Local target: Corpus.OEIS80101.conjecture
Source SHA-256: a96157cc49af3d19497a355af136ac1a60470dfffb65cd22f4911d2b2698b314
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.

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