pith. sign in
theorem

palindromic_prime_sevenhundredtwentyseven

proved
show as:
module
IndisputableMonolith.NumberTheory.Primes.ArithmeticFunctions
domain
NumberTheory
line
2525 · github
papers citing
none yet

plain-language theorem explainer

727 is established as a prime number. Number theorists referencing explicit palindromic primes or building arithmetic function examples in the Recognition Science setting would cite this fact. The proof is a one-line wrapper that applies native_decide to confirm primality by direct computation.

Claim. $727$ is a prime number.

background

The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function μ. Prime is the transparent alias for the standard Nat.Prime predicate on natural numbers. Upstream results supply the Prime abbreviation together with structural definitions from OptionAEmpiricalProgram, SimplicialLedger, MechanismDesignFromSigma, and MockThetaPhantom that supply the surrounding empirical and combinatorial context.

proof idea

The proof is a one-line wrapper that applies native_decide to verify the primality predicate on 727.

why it matters

The declaration supplies a concrete verified instance of a palindromic prime inside the arithmetic-functions module. It fills a specific numerical fact that can support later applications of Möbius or big-Omega functions, though no downstream uses are recorded. It touches the Recognition Science interest in explicit constants without linking directly to the phi-ladder or T0-T8 chain.

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