# Consecutive integer factor statistics benchmark

Family 012: Independent largest prime factors of consecutive integers. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Arithmetic researchers can review joint largest-prime-factor independence and the density-one-half ordering conclusion.

## Applicability and commercial boundary

Asymptotic natural density is not finite sample independence, an efficient factoring algorithm or a security guarantee.

## 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

Extract effective convergence and compare exact small-integer factors.

## 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 joint Dickman law for consecutive integers](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-joint-Dickman-law-for-consecutive-integers-September-24-2026/paper.pdf).