prime_fivehundredseventyseven
plain-language theorem explainer
577 is a prime natural number. Number theorists working with arithmetic functions in the Recognition Science setting would cite this when verifying small primes for Möbius or related calculations. The proof is a direct term-mode reduction via the native_decide tactic that evaluates the primality predicate by native computation.
Claim. The natural number 577 is prime.
background
The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function as the initial foothold. Prime is defined as a transparent abbrev for Nat.Prime. The local setting keeps statements minimal so that Dirichlet inversion and deeper algebra can be added once interfaces stabilize. Upstream results include the Prime alias from the Basic submodule together with structural is declarations from foundation modules that record collision-free or tautological properties.
proof idea
The proof is a one-line term that applies native_decide to decide the primality predicate for 577 outright.
why it matters
This supplies a verified primality instance that supports arithmetic-function scaffolding in the NumberTheory.Primes module. It fills a concrete fact needed for prime-based calculations, though it records no downstream uses. The result aligns with the framework's reliance on small integers in phi-ladder constructions and eight-tick arithmetic.
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