# P11686: Aligned hundred-integer blocks containing exactly 22 or 23 primes

- ID: `P11686`
- Reference: `aligned-hundred-integer-blocks-containing-exactly-22-or-23-primes`
- Page: https://theoremdb.org/statements/P11686
- 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/aligned-hundred-integer-blocks-containing-exactly-22-or-23-primes?representation=markdown
- Record maturity: Reviewed problem

## The problem

For \(r\in\{22,23\}\), determine the least nonnegative integer \(k\) such that the inclusive interval \([100k,100k+99]\) contains exactly \(r\) primes. In particular, prove that each least \(k\) exists and is minimal, or prove that one of the two requested block counts never occurs.

## 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 `aligned-hundred-integer-blocks-containing-exactly-22-or-23-primes`, 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.