pith. sign in
theorem

repunit_three_composite

proved
show as:
module
IndisputableMonolith.NumberTheory.Primes.ArithmeticFunctions
domain
NumberTheory
line
2368 · github
papers citing
none yet

plain-language theorem explainer

111 factors as 3 times 37 and is therefore composite. Number theorists verifying small repunit cases in Recognition Science arithmetic contexts would cite this result. The proof is a direct computational check via native_decide.

Claim. $¬ Prime(111) ∧ 111 = 3 × 37$, where Prime is the standard predicate for natural-number primality.

background

The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function μ. The local setting keeps statements minimal to support later Dirichlet algebra. Prime is the repository alias for Nat.Prime.

proof idea

One-line term proof that invokes native_decide to confirm the factorization and non-primality.

why it matters

It records the explicit factorization of the third repunit, flagged as RS-relevant through the factor 37. The result sits in the primes arithmetic functions section with no downstream uses recorded.

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