prime_threehundredseven
plain-language theorem explainer
307 is a prime natural number. Researchers applying arithmetic functions such as the Möbius function to small integers would cite this fact when verifying inputs for inversion formulas. The proof is a direct computational verification that evaluates the primality predicate in one step.
Claim. The natural number $307$ is prime.
background
The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function μ. Prime is the repository-local alias for the standard primality predicate on natural numbers. Upstream results include foundational class and structure declarations from option programs, simplicial ledgers, mechanism design, and Ramanujan bridges, with the immediate dependency being the transparent Prime abbreviation.
proof idea
The proof is a one-line wrapper that applies native_decide to confirm primality of 307 by direct computation.
why it matters
This supplies a verified small prime for Möbius function evaluations and related arithmetic in the NumberTheory section. It supports preparation for Dirichlet algebra and inversion that may later connect to the phi-ladder or forcing chain steps, though no downstream citations are recorded. The module context keeps statements lightweight pending stabilization of deeper interfaces.
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