repunit_five_composite
plain-language theorem explainer
Repunit R_5 equals 11111 and factors as 41 times 271, establishing compositeness. Number theorists verifying small repunit cases for primality patterns would cite the explicit factorization. The proof reduces to a single native_decide call that evaluates both the equality and the negated primality predicate directly.
Claim. $11111 = 41 × 271 ∧ ¬Prime(11111)$
background
The module supplies lightweight wrappers around Mathlib arithmetic functions, starting with the Möbius function μ. This theorem records a concrete numerical fact about repunits inside the primes section. The predicate Prime is the transparent alias for Nat.Prime supplied by the Basic sibling module.
proof idea
The proof is a one-line term wrapper that invokes native_decide on the conjunction of the factorization equality and the negated primality statement.
why it matters
The declaration supplies a verified small-integer fact that can support Möbius-function calculations on composite inputs, though no downstream theorems currently depend on it. It fills a basic check in the arithmetic-functions scaffolding without reference to the forcing chain, phi-ladder, or Recognition Science constants.
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