Determinants of 2 X 2 matrices of non-overlapping blocks of 4 consecutive primes

formal-conjectures · oeis · ams-11

$a(n) = p_{4n-3}p_{4n} - p_{4n-2}p_{4n-1}$ where $p_k$ is the k-th prime number (1-indexed).

This suggests the ratio is approaching a limit close to 0.87.

Formalized as: The sequence of ratios $P(N)/Neg(N)$ converges to a limit L,
and L is in the interval (0.8, 0.9).

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/A117027
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/117027.lean
Local target: Corpus.OEIS117027.conjecture
Source SHA-256: 0a27384ad53ad7600759317318b879891422dfa91efe5bd0644b3cfed338e8ad
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