pith. sign in
theorem

emirp_seventyone

proved
show as:
module
IndisputableMonolith.NumberTheory.Primes.ArithmeticFunctions
domain
NumberTheory
line
2333 · github
papers citing
none yet

plain-language theorem explainer

71 reversed is the distinct prime 17. Researchers cataloging small emirps or verifying explicit prime pairs cite this instance. The proof executes as a single native_decide call that computes the primality predicates and inequality directly.

Claim. $71$ is prime, $17$ is prime, and $71 ≠ 17$.

background

The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function μ and basic squarefree checks. The local setting keeps statements minimal until Dirichlet inversion layers stabilize. Prime is the transparent alias for Nat.Prime, permitting direct use of standard primality without additional hypotheses.

proof idea

The proof is a one-line wrapper that applies native_decide to evaluate the conjunction of the two primality statements and the inequality.

why it matters

This supplies a concrete verified emirp instance inside the arithmetic functions module. It supports the number theory scaffolding that may feed later prime constructions, though the dependency graph records no downstream uses. The placement aligns with the emphasis on explicit small-case checks before deeper algebraic development.

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