palindromic_prime_threehundredthirteen
plain-language theorem explainer
313 is a prime number that reads identically forwards and backwards. Number theorists working with specific prime instances in arithmetic function contexts would cite this fact. The proof is a direct one-line computational verification via native decision.
Claim. The positive integer $313$ is prime.
background
The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function μ and keeping statements minimal until Dirichlet algebra stabilizes. Primality is the repo-local transparent alias for the standard predicate on natural numbers. Upstream results supply collision-free class properties, algebraic tautology discharge, and structure definitions from foundation and game-theory modules that feed into the number-theory layer.
proof idea
The proof is a one-line wrapper that applies the native_decide tactic to confirm primality of 313 by direct computation.
why it matters
This supplies a concrete prime instance inside the arithmetic-functions component. It sits downstream of the basic Prime alias and supports potential Möbius or big-Omega calculations on palindromic numbers, though no downstream uses are recorded. It fills a basic fact slot in the primes submodule without touching the eight-tick octave or Recognition Composition Law.
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