prime_onehundredsixtythree
plain-language theorem explainer
163 is established as a prime integer. Number theorists working with arithmetic functions such as the Möbius function on small prime arguments would cite this fact for verification. The proof proceeds by direct computational evaluation of the primality predicate.
Claim. $163$ is a prime number.
background
The module supplies lightweight wrappers around Mathlib's arithmetic functions, beginning with the Möbius function. Prime is the repo-local alias for the standard primality predicate on natural numbers. This theorem provides a concrete instance among basic prime checks that can support later statements involving squarefree integers and Möbius values.
proof idea
The proof is a one-line wrapper that invokes the native_decide tactic to evaluate the primality condition computationally.
why it matters
This supplies a verified small-prime fact inside the arithmetic-functions module. It fills a basic number-theoretic slot that can feed into prime-dependent arithmetic statements, though no direct downstream uses are recorded. It remains separate from Recognition Science landmarks such as the forcing chain or phi-ladder.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.