pith. sign in
theorem

prime_onehundredeightyone

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

plain-language theorem explainer

The declaration establishes that 181 is a prime number. Number theorists working with arithmetic functions in the Recognition Science context would reference this fact when verifying properties of the Möbius function or square-free integers involving 181. The proof proceeds via a direct computational decision procedure that confirms primality without manual factorization steps.

Claim. The natural number $181$ satisfies the primality predicate.

background

The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function. The primality predicate is the repo-local alias for the standard natural-number primality check. This result depends on the basic definition of primality imported from the primes module.

proof idea

The proof is a one-line wrapper that invokes the native_decide tactic to computationally verify the primality of 181.

why it matters

This fact supplies a concrete prime instance needed for arithmetic-function statements such as Möbius evaluations on square-free inputs. It occupies a basic slot in the number-theory layer of the Recognition Science foundations, though no downstream theorems yet cite it.

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