prime_fourhundredfiftyseven
plain-language theorem explainer
457 is a prime natural number. Researchers applying arithmetic functions such as the Möbius function within the Recognition Science number theory module reference this fact to validate prime inputs. The proof consists of a direct term-level native_decide call that delegates the primality check to the computational kernel.
Claim. The natural number $457$ is prime.
background
The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function. Statements remain minimal to allow later addition of Dirichlet inversion once interfaces stabilize. Prime is the transparent alias, defined in the Basic sibling module, for the standard Nat.Prime predicate on natural numbers.
proof idea
The proof is a one-line term proof that applies the native_decide tactic to discharge the primality goal by direct computation.
why it matters
The declaration supplies a verified concrete prime inside the arithmetic functions module, supporting subsequent use of the Möbius function at prime arguments. It forms part of the number theory layer in the Recognition Science framework. No downstream citations are recorded.
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