pith. sign in
theorem

prime_threehundredfortyseven

proved
show as:
module
IndisputableMonolith.NumberTheory.Primes.ArithmeticFunctions
domain
NumberTheory
line
2003 · github
papers citing
none yet

plain-language theorem explainer

347 is established as a prime integer. Number theorists applying Möbius inversion or arithmetic functions would cite this for small-prime verifications inside the Recognition Science number-theory layer. The proof is a one-line term that invokes native_decide to resolve the primality predicate computationally.

Claim. $347$ 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. The local setting keeps statements minimal so that Dirichlet inversion and related algebra can be added once the basic interfaces stabilize.

proof idea

The proof is a one-line term that applies native_decide to the primality statement.

why it matters

This supplies a verified small-prime fact that can serve as input for Möbius-function calculations in the arithmetic-functions module. It does not touch the forcing chain, RCL, or phi-ladder constructions.

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