Least prime $\ge n$

formal-conjectures · oeis · ams-11

Least prime $\ge n$ (version 1 of the "next prime" function).

According to the "k-tuple" conjecture, $a(n)$ is the initial term of the
lexicographically earliest increasing arithmetic progression of $n$ primes;
the corresponding common differences are given by A061558.

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/A007918
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/7918.lean
Local target: Corpus.OEIS7918.conjecture1
Source SHA-256: d84c1b49c87bf2ff78b24f143a13906763dfe3d6c00dea72aa44c86e2362be29
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