# P11472: Will the closest composite-sum walk on the square spiral ever visit 2?

- ID: `P11472`
- Reference: `composite-sum-square-spiral-eventually-visits-two`
- Page: https://theoremdb.org/statements/P11472
- 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/composite-sum-square-spiral-eventually-visits-two?representation=markdown
- Record maturity: Reviewed problem

## The problem

Place the positive integers on the counterclockwise square spiral with 1 at (0,0), 2 at (1,0), and 3 at (1,1). Start at 1. From the current label \(x\), move to an unvisited spiral cell y at minimum Euclidean distance among those for which x+y is composite. If several eligible cells have the same minimum distance, choose the one with the smallest label. Does the walk ever visit the cell labeled 2?

## 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 `composite-sum-square-spiral-eventually-visits-two`, 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.