prime_sixhundredthirtyone
plain-language theorem explainer
631 is established as a prime natural number. Number theorists using arithmetic functions such as the Möbius function for squarefree checks or inversion formulas in the Recognition Science setting would cite this fact. The proof is a one-line computational verification via native_decide that confirms no proper divisors exist.
Claim. $631$ is a prime number.
background
The module supplies lightweight wrappers around Mathlib arithmetic functions, starting with the Möbius function μ. Prime is the local transparent alias for Nat.Prime. The surrounding context is basic number-theoretic scaffolding for Dirichlet algebra and inversion once the interfaces stabilize.
proof idea
The proof is a one-line wrapper that applies the native_decide tactic to decide primality by direct computation.
why it matters
This supplies a concrete prime fact inside the ArithmeticFunctions module that supports Möbius-based constructions. It fills a basic number-theory slot in the Recognition framework without direct downstream uses listed. No link to the forcing chain or phi-ladder appears here.
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