prime_sixtyseven
plain-language theorem explainer
67 is a prime number. Number theorists applying arithmetic functions such as the Möbius function to small primes would reference this fact for direct verification in calculations. The proof is a one-line decision tactic that checks the primality predicate for this fixed integer.
Claim. $67$ is a prime number.
background
The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function μ. Prime is the module-local alias for the standard predicate Nat.Prime on natural numbers. This supplies a concrete prime instance inside the primes submodule.
proof idea
The proof is a one-line wrapper that applies the decide tactic to the primality predicate.
why it matters
The declaration supplies a verified small prime for arithmetic-function work in the module. It supports later statements such as mobius_prime that rely on explicit prime instances, though no downstream uses are recorded. It fills a basic number-theoretic need without touching the Recognition Science forcing chain or constants.
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