Determinant of matrix with entries indicating primality of $i^2 + j^2$

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

The sequence $a(n)$ is the determinant of the $n \times n$ matrix $M$ defined by
$M(i,j) = 1$ if $i^2 + j^2$ is prime, and $0$ otherwise, where $1 \le i, j \le n$.

Conjecture: $a(n) = 0$ for no $n > 28$.
- _Zhi-Wei Sun_, Aug 26 2013

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/A071524
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/71524.lean
Local target: Corpus.OEIS71524.conjecture1
Source SHA-256: b312cf352c15ab39e14ce633000cfcaf71d9231adc7da5b3eb5195a7efa620f4
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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