pith. sign in
theorem

prime_fourhundredthirtyone

proved
show as:
module
IndisputableMonolith.NumberTheory.Primes.ArithmeticFunctions
domain
NumberTheory
line
2178 · github
papers citing
none yet

plain-language theorem explainer

431 is a prime natural number. Number theorists working with arithmetic functions in the Recognition Science framework cite this when handling prime inputs for Möbius or related calculations. The proof is a one-line computational check via native_decide.

Claim. $431$ is a prime number.

background

The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function. The local setting keeps statements basic before layering Dirichlet algebra. Prime is the transparent alias for the standard Nat.Prime predicate on natural numbers.

proof idea

The proof is a one-line wrapper that applies the native_decide tactic to verify primality of 431.

why it matters

This supplies a concrete prime fact inside the arithmetic functions module. It supports the number theory toolkit needed for Recognition Science derivations such as the phi-ladder and constants in the T0-T8 chain. No parent theorems appear in the used_by edges.

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