pith. sign in
theorem

prime_fivehundredthree

proved
show as:
module
IndisputableMonolith.NumberTheory.Primes.ArithmeticFunctions
domain
NumberTheory
line
2390 · github
papers citing
none yet

plain-language theorem explainer

The declaration asserts that 503 is a prime natural number. Number theorists using arithmetic functions in the Recognition Science module would cite this fact when isolating prime cases inside Möbius sums or inversion identities. The proof reduces the claim to a direct computational decision via the native_decide tactic.

Claim. $503$ is a prime number.

background

The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function μ. Prime is the transparent alias for Nat.Prime supplied by the Basic submodule. Upstream results include the is interfaces from OptionAEmpiricalProgram, SimplicialLedger, MechanismDesignFromSigma, and MockThetaPhantom, which function as collision-free or tautological placeholders, together with the Prime abbrev itself.

proof idea

The proof is a one-line wrapper that applies the native_decide tactic to discharge the primality statement by direct computation.

why it matters

The result supplies a concrete prime fact inside the arithmetic-functions module that supports Möbius footholds. It sits among the number-theoretic primitives that feed the Recognition Science forcing chain and phi-ladder constructions, although no downstream uses are recorded at present.

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