# P11698: A non-overlap victory for a consecutive-prime divisibility run

- ID: `P11698`
- Reference: `a-non-overlap-victory-for-a-consecutive-prime-divisibility-run`
- Page: https://theoremdb.org/statements/P11698
- Export scope: built Markdown snapshot. The current public packet may have changed since this build.
- Build source revision: b5a83bd9bdbf7dfdc7134c15b7360f889389e7bc
- Current Markdown: https://api.theoremdb.org/v1/statements/a-non-overlap-victory-for-a-consecutive-prime-divisibility-run?representation=markdown
- Record maturity: Reviewed problem

## The problem

For \(r,n\ge 1\), let \(E(r,n)\) be the earliest positive start of \(n\) consecutive integers divisible, in increasing or decreasing order, by the consecutive primes \(p_r,\ldots,p_{r+n-1}\). Does some \(n\) satisfy \(E(2,n)<E(1,n)\) in a nontrivial way, where the occurrence is excluded when one decreasing run of length \(n+1\) supplies both starts and gives \(E(2,n)=a(n+1)=a(n)-1\)?

## Status

The reviewed record remains open.

## 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 `a-non-overlap-victory-for-a-consecutive-prime-divisibility-run`, 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.