prime_fivehundredseventyone
plain-language theorem explainer
The theorem establishes that the integer 571 is prime. It would be cited by proofs needing this specific primality fact as a base case within arithmetic function calculations. The proof reduces to a single native decision procedure that discharges the statement directly.
Claim. The natural number 571 is prime.
background
The module supplies lightweight wrappers around Mathlib's arithmetic functions, beginning with the Möbius function μ. This theorem supplies a concrete primality fact that can support those wrappers. The Prime predicate is the repo-local alias for Nat.Prime, kept transparent so that standard primality checks apply without additional hypotheses.
proof idea
The proof is a one-line wrapper that applies native_decide to verify the primality of 571 directly.
why it matters
This supplies a verified primality instance inside the arithmetic functions module, supporting Möbius-based calculations on 571. It fills a basic number-theoretic foothold required for the Recognition framework's use of arithmetic functions, though no downstream theorems currently reference it. The fact aligns with the module's role in preparing Dirichlet algebra layers without introducing new axioms.
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