pith. sign in
theorem

isolated_prime_seventynine

proved
show as:
module
IndisputableMonolith.NumberTheory.Primes.ArithmeticFunctions
domain
NumberTheory
line
2850 · github
papers citing
none yet

plain-language theorem explainer

79 is prime while 77 = 7 × 11 and 81 = 3^4 are composite. Number theorists checking explicit cases inside the Recognition Science arithmetic functions layer would cite this verification. The proof is a one-line native_decide evaluation of the primality predicates.

Claim. $79$ is prime, $77 = 7 × 11$ is composite, and $81 = 3^4$ is composite.

background

The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function μ. Prime is the transparent alias for Nat.Prime. The local setting keeps statements minimal so that Dirichlet inversion and related algebra can be added once the basic interfaces stabilize.

proof idea

The proof is a one-line wrapper that applies native_decide to the conjunction of the three primality statements.

why it matters

This supplies a concrete isolated-prime check inside the arithmetic-functions file. It has no listed downstream uses and does not feed any parent theorem in the supplied graph. The result remains a leaf verification with no direct tie to the forcing chain or RS constants.

Switch to Lean above to see the machine-checked source, dependencies, and usage graph.