prime_twohundredfiftyone
plain-language theorem explainer
251 is established as prime in the natural numbers. Number theorists applying arithmetic functions such as the Möbius function would cite this fact when checking squarefreeness or inversion formulas involving 251. The verification is a direct native decision procedure that evaluates the primality predicate without manual factorization.
Claim. The natural number 251 satisfies the primality predicate, i.e., it is prime.
background
The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function μ. These wrappers presuppose basic facts about primes and squarefree numbers to support Dirichlet inversion and related identities. The local setting is therefore a collection of small, stable interfaces that later layers can extend with full Dirichlet algebra.
proof idea
The proof is a one-line wrapper that invokes the native_decide tactic to evaluate the primality predicate at compile time.
why it matters
The result supplies a concrete prime fact required by the arithmetic-function layer. It sits beneath any later use of Möbius or big-Omega on 251 and therefore supports the module's role as a foothold for number-theoretic constructions inside Recognition Science. No downstream citations are recorded yet.
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