Lesser of twin primes

formal-conjectures · oeis · ams-11

Primes $p$ such that $p+2$ is also prime.

Primes $p_k$ such that $p_k! \equiv 1 \pmod{p_{k+1}}$ with the exception of $p_{991} = 7841$ and
other unknown primes $p_k$ for which $(p_k+1)(p_k+2)\cdots(p_{k+1}-2) \equiv 1 \pmod{p_{k+1}}$
where $p_{k+1} - p_k > 2$.

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/A001359
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/1359.lean
Local target: Corpus.OEIS1359.conjecture
Source SHA-256: 1c320b6e084bd1db2329152c4406ff884991279cdde0b0a27d7cc288b3980024
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