sophie_germain_twentynine
plain-language theorem explainer
29 qualifies as a Sophie Germain prime because both 29 and 59 are prime. Number theorists working inside Recognition Science number-theory modules cite this for small-case primality checks that feed arithmetic-function wrappers. The proof reduces the conjunction directly to a native decision procedure that evaluates the two primality predicates by computation.
Claim. Both $29$ and $59$ are prime numbers.
background
The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function. Prime is the transparent alias for the standard natural-number primality predicate. The listed upstream results supply only the basic primality definition and several unrelated structural hypotheses from other modules.
proof idea
The proof is a one-line term that applies the native_decide tactic to resolve the conjunction of the two primality statements by direct evaluation.
why it matters
This supplies a concrete small-prime fact inside the primes section of the arithmetic-functions module. No downstream theorems are listed, so it functions as a verified constant rather than a lemma feeding larger results. It sits alongside the Möbius definitions without invoking the forcing chain or Recognition Composition Law.
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