prime_sixhundredseventeen
plain-language theorem explainer
617 is established as a prime integer. Researchers building tables of small primes or applying arithmetic functions such as the Möbius function would cite this result to confirm the status of 617. The proof proceeds via a single native_decide invocation that reduces the primality check to a decidable computation.
Claim. $617$ is a prime number.
background
The module supplies lightweight wrappers around Mathlib's arithmetic functions, beginning with the Möbius function μ. Prime is defined locally as an alias for Nat.Prime. Upstream results include the definition of Prime and various is structures from foundation modules that ensure collision-free or tautological properties.
proof idea
The proof is a term-mode application of the native_decide tactic, which performs a direct computational check of primality for the constant 617.
why it matters
This fact populates the list of verified small primes in the arithmetic functions module. It supports downstream applications of the Möbius function and related inversion formulas, though no immediate dependents are recorded. It aligns with the need for concrete prime data in number-theoretic constructions within the Recognition framework.
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