isolated_prime_eightythree
plain-language theorem explainer
83 is prime while 81 and 85 are composite, confirming an isolated prime at this location. Number theorists verifying concrete cases inside the Recognition Science arithmetic-function layer would cite the result for explicit checks on the phi-ladder. The proof is a one-line native_decide term that evaluates the three primality predicates directly.
Claim. $83$ is prime while $81=3^4$ and $85=5×17$ are composite.
background
The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function μ. The Prime predicate is the transparent alias for Nat.Prime. Upstream results supply collision-free structures and structural verifications from foundation and game-theory modules, but the present statement rests only on the basic primality definition.
proof idea
The proof is a one-line wrapper that applies native_decide to the conjunction of the three primality statements.
why it matters
The declaration supplies a concrete prime-isolation datum inside the NumberTheory.Primes.ArithmeticFunctions module. It supports downstream arithmetic-function constructions that may later invoke the Möbius function or big-Omega counts, though no direct parent theorem is recorded. It touches the eight-tick octave pattern through explicit prime-gap verification.
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