Prime-minus-one factor statistics reference

Family 011: Prime-factor statistics of $p-1$. First application triage, 9 October 2026 Australia/Brisbane.

Problem and potential new use

Number-theory researchers can compare normalized ordered prime-factor logarithms with the Poisson–Dirichlet law.

Applicability and commercial boundary

An asymptotic distribution over primes does not guarantee a particular prime has desired factor structure or accelerate factoring. Totient multiplicity is a different consequence.

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 finite error rates and test a seeded arithmetic sample without security claims.

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.

Weighted dilation graphs, smooth shifted primes and totient fibers.