prime_sixhundredfiftynine
plain-language theorem explainer
659 is a prime number. Number theorists anchoring arithmetic functions such as the Möbius function would cite this result to confirm small prime inputs. The proof proceeds by direct computational evaluation of the primality predicate.
Claim. $659$ is a prime number.
background
The module supplies lightweight wrappers around Mathlib's arithmetic function library, beginning with the Möbius function μ. The local theoretical setting keeps statements minimal before layering Dirichlet algebra and inversion. Prime is the repo-local transparent alias for the standard Nat.Prime predicate on natural numbers. Upstream results supply the basic alias definition of this predicate.
proof idea
The proof is a one-line wrapper that applies a computational decision procedure to discharge the primality statement directly.
why it matters
This supplies a concrete small prime inside the ArithmeticFunctions module to support sibling results on the Möbius function and squarefree checks. It fills a basic number-theoretic fact without advancing the forcing chain, phi-ladder, or Recognition Science constants. No open questions are touched.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.