pith. sign in
theorem

prime_onehundredninetyseven

proved
show as:
module
IndisputableMonolith.NumberTheory.Primes.ArithmeticFunctions
domain
NumberTheory
line
971 · github
papers citing
none yet

plain-language theorem explainer

The theorem asserts that 197 is prime. Number theorists using arithmetic functions on small primes would cite this fact when verifying inputs for Möbius or related computations. The proof is a direct native_decide tactic that reduces the claim to an immediate computational check.

Claim. $197$ is a prime number.

background

The module supplies lightweight wrappers around Mathlib's arithmetic function library, beginning with the Möbius function. Prime is the repo-local alias for Nat.Prime. The local setting keeps statements minimal so that deeper Dirichlet algebra can be added later once basic interfaces stabilize.

proof idea

The proof is a one-line wrapper that applies the native_decide tactic to perform a direct computational verification of primality.

why it matters

This supplies a concrete primality fact needed for arithmetic-function calculations on small primes. No downstream uses are recorded yet, so it functions as a basic building block rather than a link in a larger chain. It supports the module's goal of providing stable interfaces before layering inversion formulas.

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