prime_fivehundredsixtythree
plain-language theorem explainer
563 is established as a prime number inside the arithmetic functions module. Researchers computing Möbius values or small-prime sums in Dirichlet series would cite the fact for verification. The proof applies a single native_decide tactic that reduces the predicate to an internal decidable computation.
Claim. $563$ is a prime number.
background
The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function μ. Statements remain minimal so that Dirichlet inversion and related algebra can be added once interfaces stabilize. Prime is the transparent alias for Nat.Prime, the standard predicate on natural numbers.
proof idea
The proof is a one-line wrapper that invokes the native_decide tactic on the primality predicate for 563.
why it matters
The result supplies a concrete small-prime fact inside the arithmetic-functions section. It supports later Möbius-based calculations that may feed into Recognition Science number-theoretic constructions, though no downstream uses are recorded. The placement aligns with the need for verified primes when building ladders or inversion formulas.
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