prime_twohundredseventyseven
plain-language theorem explainer
277 is a prime number. Number theorists working with small primes inside arithmetic-function calculations would cite this fact for reference. The proof is a one-line computational check that applies native decision to the constant.
Claim. The natural number 277 is prime: it has no positive divisors other than 1 and itself.
background
The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function μ. Local notation defines Prime as a transparent alias for the standard primality predicate on natural numbers. The upstream Prime abbreviation is imported directly from the Basic primes module and carries no additional hypotheses.
proof idea
The proof is a one-line wrapper that applies native_decide to verify the primality predicate on the literal 277.
why it matters
This theorem supplies a concrete primality instance inside the arithmetic-functions file. It contributes to the number-theoretic scaffolding that precedes deeper Dirichlet algebra and Möbius inversion, as described in the module documentation. No downstream uses are recorded yet.
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