pith. sign in
theorem

prime_twohundredtwentynine

proved
show as:
module
IndisputableMonolith.NumberTheory.Primes.ArithmeticFunctions
domain
NumberTheory
line
1944 · github
papers citing
none yet

plain-language theorem explainer

229 is asserted to be prime. Researchers applying Möbius inversion or Dirichlet series within the Recognition Science arithmetic-functions layer would cite this fact when handling the specific prime 229. The verification relies on native_decide for direct computational confirmation of the absence of nontrivial divisors.

Claim. $229$ is a prime number.

background

The module supplies lightweight wrappers around Mathlib's arithmetic-function library, beginning with the Möbius function μ. Prime is a transparent alias for the standard predicate Nat.Prime on natural numbers. Upstream results include the definition of Prime together with interface structures from foundation modules that enforce collision-free and algebraic consistency across the framework.

proof idea

The proof is a one-line wrapper that applies the native_decide tactic to perform exhaustive computational checking that 229 has no divisors other than 1 and itself.

why it matters

This supplies a concrete prime inside the arithmetic-functions module for potential use with Möbius or squarefree predicates. It fills a basic number-theoretic prerequisite in the Recognition Science framework where primes support the phi-ladder and mass formulas. No downstream uses are recorded yet, leaving the result as foundational scaffolding for later Dirichlet-algebra layers.

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