primeCounting_thousand
plain-language theorem explainer
π(1000) equals 168. Number theorists verifying explicit arithmetic values inside the Recognition Science module would cite this result. The proof is a one-line wrapper that invokes native_decide on the definition of primeCounting.
Claim. $π(1000) = 168$, where $π(n)$ counts the primes ≤ n.
background
The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function μ. The prime counting function is introduced as π(n) := Nat.primeCounting n, which simply tallies primes not exceeding n. The local theoretical setting keeps statements minimal so that Dirichlet inversion and deeper algebra can be added once the basic interfaces stabilize.
proof idea
One-line wrapper that applies native_decide to evaluate the equality directly from the definition of primeCounting.
why it matters
This supplies a concrete numerical checkpoint for arithmetic functions in the Recognition Science number theory layer. It can anchor later calculations involving prime distributions or constants on the phi-ladder, though no parent theorem or downstream use is recorded. The result fills a computational slot before the module proceeds to Ω and ω definitions for RS constants.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.