pith. sign in
theorem

prime_threehundredthirtyone

proved
show as:
module
IndisputableMonolith.NumberTheory.Primes.ArithmeticFunctions
domain
NumberTheory
line
1997 · github
papers citing
none yet

plain-language theorem explainer

331 is established as a prime natural number. Number theorists working with arithmetic functions and Möbius properties in this module would cite the fact for small-prime verification in computations. The proof is a direct computational check via native decision procedure.

Claim. $331$ 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 the standard Nat.Prime predicate on natural numbers. Upstream results include structural definitions such as collision-free classes and algebraic tautologies from foundation modules, though the present declaration remains self-contained.

proof idea

The proof is a one-line term that invokes native_decide to confirm primality of 331 by direct computation.

why it matters

This supplies a concrete prime instance supporting the arithmetic functions module and its Möbius footholds. It fills a basic need in the NumberTheory.Primes section without advancing the core Recognition Science forcing chain (T5 J-uniqueness through T8 D=3) or constants such as phi and alpha. No downstream uses are recorded.

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