prime_fourhundredtwentyone
plain-language theorem explainer
421 is established as a prime natural number. Number theorists applying Möbius inversion or arithmetic functions in this module would cite the fact when handling factorizations that include 421. The verification is a direct native decision procedure that computationally confirms the primality predicate.
Claim. The natural number 421 is prime.
background
The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function μ and its basic properties for primes and squarefree integers. Prime is the repo-local transparent alias for the standard primality predicate on natural numbers, defined as an abbreviation for Nat.Prime. The local theoretical setting keeps statements minimal to stabilize interfaces before adding Dirichlet algebra and inversion results.
proof idea
The proof is a one-line wrapper that applies the native_decide tactic to discharge the primality goal for 421.
why it matters
This supplies a concrete primality instance that anchors arithmetic function calculations in the module, supporting Möbius applications to numbers involving 421. It fills a basic fact in the primes submodule without reference to the forcing chain or physical constants. No downstream uses are recorded yet.
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