Zhi-Wei Sun's prime-difference matrix determinant conjecture

TheoremDB P11160 · number theory

Inferred from the community field; finer classification has not been reviewed.

Source catalogue assessmentAs of 2026-09-08Source & evidence ↓

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Problem statement

For each positive integer $n$ , let $M_n=(m_{ij})_{1\le i,j\le n}$ be the $n\times n$ matrix with integer entries defined by

m_{ij}=\begin{cases}1,&\text{if }|i-j|\text{ is prime},\\0,&\text{otherwise}.\end{cases}

Prove that $\det(M_n)\ne 0$ for every integer $n>3$ , or give an integer $n>3$ for which $\det(M_n)=0$ .

Lean 4

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Background

Additional formulation recorded by the source

$\forall n\in\mathbb{Z}_{>3},\;\det([\mathbf{1}_{\mathbb{P}}(|i-j|)]_{1\le i,j\le n})\ne 0.$

Progress & source assessment

Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.

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References

[1]TheoremDB P11160 link

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