Determinant of Hankel matrix of the first $2n-1$ prime numbers

formal-conjectures · oeis · ams-11 · ams-15

The determinant of the $n \times n$ Hankel matrix whose entries are the first $2n-1$ prime numbers.
The matrix $M$ has entries $M_{i, j} = p_{i+j}$ for $i, j \in \{0, \dots, n-1\}$,
where $p_k = \mathrm{Nat.nth\;Nat.Prime} (k)$ is the $k$-th prime starting at $p_0=2$.
$a(0)=1$ by convention.

"I conjecture that $a(4)$ is the only zero. - _Jon Perry_, Mar 22 2004"

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/A024356
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/24356.lean
Local target: Corpus.OEIS24356.conjecture
Source SHA-256: e938a507294ee2e5c8d3037ffb693b7a290368405447393110f66dbeea29f9e7
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.

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