pith. sign in
theorem

emirp_ninetyseven

proved
show as:
module
IndisputableMonolith.NumberTheory.Primes.ArithmeticFunctions
domain
NumberTheory
line
2342 · github
papers citing
none yet

plain-language theorem explainer

97 and its digit reversal 79 are both prime numbers and distinct. Researchers cataloging emirps or verifying small prime reversals would cite this explicit check. The proof is a direct native_decide invocation that reduces the statement to kernel-level evaluation of primality predicates.

Claim. $97$ is prime, $79$ is prime, and $97$ is not equal to $79$.

background

The module supplies lightweight wrappers for Mathlib arithmetic functions, beginning with the Möbius function. The local setting focuses on basic interfaces for Dirichlet algebra before deeper inversion results. The Prime predicate is the repository alias for the standard natural-number primality predicate from Mathlib.

proof idea

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

why it matters

This supplies a concrete verified instance of an emirp within the number-theory layer. It supports downstream checks on prime-related arithmetic functions such as the Möbius function applied to emirps. No direct parent theorem is listed, and it touches the broader question of enumerating special primes in the Recognition framework's arithmetic scaffolding.

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