Andrica's conjecture

formal-conjectures · wikipedia · ams-11

**Andrica's conjecture**
The inequality $\sqrt{p_{n+1}}-\sqrt{p_n} < 1$ holds for all $n$, where $p_n$ is the $n$-th prime number.

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://en.wikipedia.org/wiki/Andrica%27s_conjecture
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://arxiv.org/abs/2307.08725
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/Wikipedia/Andrica.lean
Local target: Corpus.WikipediaAndrica.andrica_conjecture
Source SHA-256: 15049cc1c8e41889c10cc9340aa397b3652624ebda845bcdf03d82e4272c7776
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