prime_fourhundredsixtyone
plain-language theorem explainer
461 is asserted to be a prime natural number. Number theorists applying the Möbius function or squarefree checks within Recognition Science arithmetic would reference this fact for concrete verification. The proof is a direct computational discharge via the native_decide tactic with no manual steps.
Claim. The natural number $461$ is prime.
background
The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function μ. Prime is the repo-local alias for the standard Nat.Prime predicate on natural numbers. Upstream results supply the transparent abbrev Prime (n : ℕ) : Prop := Nat.Prime n together with several 'is' structures from foundation modules that certify collision-free or algebraic properties used in the broader context.
proof idea
The proof is a one-line term-mode wrapper that invokes the native_decide tactic to computationally confirm primality of 461.
why it matters
The declaration supplies a basic primality fact inside the arithmetic-functions module that supports later Möbius and big-Omega calculations. It fills a concrete number-theoretic placeholder for the Recognition framework without linking to the forcing chain, RCL, or phi-ladder. No downstream uses are recorded yet.
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