prime_eightynine
plain-language theorem explainer
89 is established as a prime number inside the arithmetic functions module. Number theorists applying Möbius inversion or squarefree checks would reference it for small-integer base cases. The verification runs via a direct computational decision procedure on the Nat.Prime predicate.
Claim. $89$ is a prime number.
background
The module supplies lightweight wrappers around Mathlib's arithmetic function library, beginning with the Möbius function μ. Prime is the transparent alias for Nat.Prime. Sibling declarations handle Möbius values on primes and squarefree integers, keeping statements minimal until deeper Dirichlet algebra is added.
proof idea
One-line wrapper that applies the decide tactic to verify primality of 89 by exhaustive computation.
why it matters
The declaration supplies a basic prime fact that supports arithmetic-function definitions in the module. It contributes to the foundation for later inversion formulas once interfaces stabilize, per the module documentation. No downstream theorems currently depend on it.
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