prime_fourhundredsixtythree
plain-language theorem explainer
463 is established as a prime natural number. Number theorists building arithmetic functions such as the Möbius function in the Recognition Science module would cite this fact for squarefree checks and inversion formulas. The proof is a one-line term that invokes Lean's native_decide tactic on the primality predicate.
Claim. $463$ is a prime number.
background
The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function μ. Prime is the transparent alias for the standard primality predicate on natural numbers. Upstream results supply basic class and structure definitions from foundation and game-theory modules that stabilize the surrounding interfaces, though the local primality check stands alone.
proof idea
The proof is a one-line wrapper that applies native_decide to discharge the primality goal for 463.
why it matters
The declaration supplies a concrete prime required for Möbius evaluations and squarefree tests inside the arithmetic-functions module. It fills a basic number-theoretic slot that later Dirichlet-algebra layers can reference. No direct link to the forcing chain or phi-ladder appears, yet the fact supports the lightweight interface described in the module header.
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