prime_fiftynine
plain-language theorem explainer
59 is established as a prime natural number. Researchers applying arithmetic functions such as the Möbius function to small primes would cite this concrete fact. The verification executes via a direct computational decision procedure that checks for the absence of nontrivial divisors.
Claim. The integer $59$ is prime, i.e., its only positive divisors are $1$ and $59$.
background
The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function μ. Prime is the repo-local alias for the standard primality predicate on natural numbers. The local setting is the arithmetic-functions layer that prepares Möbius footholds before deeper Dirichlet algebra is added.
proof idea
One-line wrapper that applies the decide tactic to perform exhaustive computational verification of primality for the constant 59.
why it matters
The declaration supplies a verified small prime for use inside the arithmetic-functions module. No downstream theorems are recorded, and the result does not connect to Recognition Science landmarks such as the phi-ladder, J-cost, or the forcing chain T0-T8. It closes a basic instance without raising open questions.
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