prime_sixhundredfortyseven
plain-language theorem explainer
647 is asserted to be a prime natural number. Researchers applying arithmetic functions such as the Möbius function in the Recognition Science framework would cite this fact for small-prime inputs in squarefree checks. The proof is a one-line computational decision that confirms the predicate directly.
Claim. The natural number 647 is prime.
background
The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function μ. Prime is the transparent alias for the standard primality predicate on natural numbers. Upstream results supply basic structures for collision-free empirical programs, algebraic tautologies in simplicial ledgers, and combinatorial extensions in mechanism design, though the primality fact itself stands independently.
proof idea
The proof is a one-line wrapper that applies the native_decide tactic to verify the primality predicate for 647.
why it matters
This supplies a verified small-prime instance inside the arithmetic functions module. It supports the Möbius footholds described in the module documentation and contributes a concrete fact to the NumberTheory.Primes section. No immediate downstream theorems reference it, leaving its role as a basic building block for later prime-dependent constructions.
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