# Prime-gap distribution reference

Family 026: Positive lower density of large prime gaps. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Number-theory researchers can compare large normalized prime gaps to the stated positive lower density.

## Applicability and commercial boundary

The proportion depends on C and sufficient size; no explicit finite guarantee or faster prime generator is supplied.

## 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

Inspect effective constants and finite sample bias.

## 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).

[Positive lower density of large prime gaps](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Positive-lower-density-of-large-prime-gaps-September-25-2026/main.pdf).