prime_fivehundredtwentythree
plain-language theorem explainer
523 is established as a prime number within the arithmetic functions module. Number theorists working with Möbius inversion or squarefree checks would cite this fact when verifying small primes in explicit computations. The verification proceeds via a single native decision procedure that evaluates the primality predicate directly.
Claim. $523$ is a prime number.
background
The module supplies lightweight wrappers around Mathlib's arithmetic function library, beginning with the Möbius function μ. Prime is introduced as a transparent alias for the standard natural-number primality predicate. Upstream results include the basic Prime abbreviation together with foundational structures such as collision-free classes and simplicial ledger constructions, though the immediate dependency for this declaration is the primality definition itself.
proof idea
The proof is a one-line wrapper that invokes native_decide to confirm the primality of 523 by direct computational evaluation.
why it matters
This declaration supplies a concrete prime fact that supports downstream arithmetic function definitions such as Möbius applications within the same module. It contributes to the number theory scaffolding in Recognition Science without direct ties to the T0-T8 forcing chain, the Recognition Composition Law, or the phi-ladder. No parent theorems appear in the used-by graph.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.