prime_sixhundredseventythree
plain-language theorem explainer
673 is established as a prime number by direct computational verification. Number theorists applying arithmetic functions such as the Möbius function to small integers would cite this fact when checking squarefreeness or inversion formulas. The proof is a one-line native decision procedure that evaluates the primality predicate by exhaustive search.
Claim. The natural number $673$ is prime, i.e., it satisfies the predicate that it has no positive divisors other than $1$ and itself.
background
The module supplies lightweight wrappers around Mathlib's arithmetic function library, beginning with the Möbius function. The local theoretical setting is preparation for Dirichlet algebra and inversion once the basic interfaces stabilize. Prime is the repo-local transparent alias for the standard natural-number primality predicate.
proof idea
The proof is a one-line wrapper that applies the native_decide tactic. This reduces the statement to a decidable computation and confirms primality of the small integer 673 by direct evaluation.
why it matters
This supplies a verified primality fact inside the arithmetic functions module, supporting later use of the Möbius function and related inversion tools. It contributes to the NumberTheory.Primes collection that underpins squarefree checks and arithmetic-function identities. No downstream uses are recorded yet, leaving the fact available for composition with Recognition Science constructions such as the phi-ladder or Recognition Composition Law.
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