Smallest prime $\equiv 1 \pmod n$

formal-conjectures · oeis · ams-11

$$a(n) = \min \{p \in \mathbb{P} \mid p \equiv 1 \pmod n\}$$

"Conjecture: $a(n) < n^2$ for $n > 1$. - _Thomas Ordowski_, Dec 19 2016"

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/A034694
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/34694.lean
Local target: Corpus.OEIS34694.conjecture
Source SHA-256: 252d6d146aeb5d7ccda4a1e8a44f5ba3c71876c8c7620ccd0886c7f6242f1f69
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