# P11382: When is sigma(sigma(2p - 1)) prime?

- ID: `P11382`
- Reference: `double-divisor-sum-prime-output-classification`
- Page: https://theoremdb.org/statements/P11382
- 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/double-divisor-sum-prime-output-classification?representation=markdown
- Record maturity: Reviewed problem

## The problem

Let \(sigma(k)\) be the sum of the positive divisors of the positive integer k. Classify all primes p for which q=sigma(sigma(2p-1)) is prime. Determine whether every such output q is a Mersenne prime, meaning q=2^r-1 for some prime r.

## 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 `double-divisor-sum-prime-output-classification`, 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.