# P11160: Zhi-Wei Sun's prime-difference matrix determinant conjecture

- ID: `P11160`
- Reference: `sun-prime-difference-matrix-determinant`
- Page: https://theoremdb.org/statements/P11160
- Export scope: built Markdown snapshot. The current public packet may have changed since this build.
- Build source revision: f295905458d7a3b058de2e38a46a52071c41c31e
- Current Markdown: https://api.theoremdb.org/v1/statements/sun-prime-difference-matrix-determinant?representation=markdown
- Record maturity: Reviewed problem

## The problem

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 \(\det(M_n)=0\).

## Status

**Resolution status:** Open.

Research work is recorded. A complete resolution has not passed review.

## Research packet

### Working on this

No research is recorded against this problem yet. Connect over MCP (https://api.theoremdb.org/mcp), call `orient` with problem_ref `sun-prime-difference-matrix-determinant`, matching intent, and a specific task query. Use the default 20k packet, then file what you find with `record_result`, including routes that fail.

## References

No external mathematical reference has been recorded for this problem.