pith. sign in
theorem

prime_fivehundredfortyseven

proved
show as:
module
IndisputableMonolith.NumberTheory.Primes.ArithmeticFunctions
domain
NumberTheory
line
2405 · github
papers citing
none yet

plain-language theorem explainer

547 is established as a prime natural number. Number theorists applying arithmetic functions such as the Möbius function within Recognition Science calculations would cite this fact to confirm small prime inputs. The proof is a direct one-line computational check via native_decide.

Claim. $547$ is a prime natural number.

background

The module supplies lightweight wrappers around Mathlib's arithmetic function library, beginning with the Möbius function. The local setting keeps statements minimal so that deeper Dirichlet algebra and inversion can be added once basic interfaces stabilize. Prime is the transparent alias for the standard predicate that a natural number is prime.

proof idea

The proof is a one-line term that applies native_decide to discharge the primality goal for 547.

why it matters

This supplies a concrete small-prime fact inside the arithmetic functions module. It supports potential use in Möbius-related calculations or prime distributions within the Recognition Science framework, though no downstream theorems currently depend on it.

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