# P11780: Will the Ulam-spiral gcd walk ever visit 37?

- ID: `P11780`
- Reference: `will-the-ulam-spiral-gcd-walk-ever-visit-37`
- Page: https://theoremdb.org/statements/P11780
- 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/will-the-ulam-spiral-gcd-walk-ever-visit-37?representation=markdown
- Record maturity: Reviewed problem

## The problem

Write the positive integers on the standard square Ulam spiral. Starting with \(1,2\), repeatedly visit the closest unvisited square whose number has greatest common divisor greater than \(1\) with the current number, breaking distance ties by choosing the smaller number. Determine whether \(37\) is ever visited.

## 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 `will-the-ulam-spiral-gcd-walk-ever-visit-37`, 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.