Square root of the absolute value of the determinant of the prime sum indicator matrix

We conjecture that a(n) > 0 for all n > 15.

From the catalogue. Imported from The Formal Conjectures Authors (Google DeepMind and contributors) (Apache-2.0) — original. Nobody has started on it here yet: tasks are created as soon as someone asks for one or submits a claim. A Lean proof is checked against the statement below by the Lean kernel; a curator confirms before the problem counts as resolved.

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Cite

@misc{cairn-oeis-228552,
  title        = {Square root of the absolute value of the determinant of the prime sum indicator matrix},
  author       = {{Cairn Commons contributors}},
  howpublished = {\url{https://cairn-commons.com/problems/oeis-228552}},
  year         = {2026},
  note         = {Open problem on Cairn Commons, CC BY 4.0. Accessed 2026-11-11}
}

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What a result looks like: C-16, a newcomer working with an AI model found C(85,24,3) ≤ 76 (previous best 77), and a computer verified it within minutes. A documented dead end counts too.

The problem

The question

We conjecture that $a (n) > 0$ for all $n > 15$ .

Square root of the absolute value of $det (M_{n})$ , where $M_{n}$ is the $n \times n$ matrix with $(i, j)$ -entry ( $1 \leq i, j \leq n$ ) equal to $1$ if $i + j$ is prime, and $0$ otherwise.

Formal statement (Lean 4)

From Formal Conjectures, module FormalConjectures.OEIS.«228552».

theorem conjecture (n : ℕ) (hn : n > 15) : a n > 0

What counts as progress

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A precise flaw in the formal statement (a misformalisation) — report it upstream too.

References

A228552

Source and licence

Imported from Formal Conjectures (OEIS), commit 2f91d251c07f. Statements and descriptions © The Formal Conjectures Authors, Apache License 2.0; reformatted for this page.