# Additive prime decomposition limitation reference

Family 013: Ostmann’s inverse Goldbach conjecture. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Additive-combinatorics researchers can flag a proposed exact sumset representation of a finite modification of the primes.

## Applicability and commercial boundary

Infinite set indecomposability does not rule out approximate finite decompositions or create a fast prime generator.

## Initial business decision

Research infrastructure or conditional engineering until a computable implementation, effective bounds and a recurring buyer need are demonstrated. No commercial novelty or profitability is established.

## Next verification action

Construct a clear finite illustration and preserve the infinite quantifiers.

## Evidence scope

The catalog statement was individually reviewed. Manuscript proof and selected formal scope comparison remain queued. No independent Lean verification was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

[The additive indecomposability of the primes](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/the-additive-indecomposability-of-the-primes-September-24-2026/paper.pdf).