pith. sign in
theorem

prime_sixtyseven

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

plain-language theorem explainer

67 is a prime number. Number theorists applying arithmetic functions such as the Möbius function to small primes would reference this fact for direct verification in calculations. The proof is a one-line decision tactic that checks the primality predicate for this fixed integer.

Claim. $67$ is a prime number.

background

The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function μ. Prime is the module-local alias for the standard predicate Nat.Prime on natural numbers. This supplies a concrete prime instance inside the primes submodule.

proof idea

The proof is a one-line wrapper that applies the decide tactic to the primality predicate.

why it matters

The declaration supplies a verified small prime for arithmetic-function work in the module. It supports later statements such as mobius_prime that rely on explicit prime instances, though no downstream uses are recorded. It fills a basic number-theoretic need without touching the Recognition Science forcing chain or constants.

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