On this page
Coprime search interval budget research
Family 021: A quadratic bound for Jacobsthal’s function. First application triage, 9 October 2026 Australia/Brisbane.
Problem and potential new use
Arithmetic library teams could use a uniform Jacobsthal interval bound after extracting a numerical constant and prime-factor-count evidence.
Applicability and commercial boundary
The strengthened bound contains an existential absolute constant and depends on distinct prime factors, not integer bit length alone. It does not automatically shorten a practical search.
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
Read explicit constants and compare a gcd scan against existing coprime selection methods.
Evidence scope
The catalog statement was individually reviewed. Main-paper abstracts and available selected formal scope notes were also inspected. No independent Lean verification was run. Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. See source metadata.