pith. sign in
theorem

prime_threehundredthirtyseven

proved
show as:
module
IndisputableMonolith.NumberTheory.Primes.ArithmeticFunctions
domain
NumberTheory
line
2000 · github
papers citing
none yet

plain-language theorem explainer

337 is a prime natural number. Number theorists applying Möbius or other arithmetic functions in the Recognition Science primes module cite this fact to anchor small-prime inputs. The proof is a direct computational verification via native_decide.

Claim. $337$ is prime, i.e., its only positive divisors are $1$ and itself.

background

The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function μ. Prime is the repo-local alias for Nat.Prime. Upstream results include collision-free and algebraic-tautology structures from OptionAEmpiricalProgram, SimplicialLedger, MechanismDesignFromSigma, and MockThetaPhantom, plus the transparent Prime abbreviation.

proof idea

One-line wrapper that applies native_decide to evaluate the primality predicate by exhaustive divisor search.

why it matters

Supplies a verified small prime for sibling results such as mobius_prime and mobius_apply_of_squarefree in the same module. It anchors basic number-theoretic facts required for later Dirichlet inversion layers, without reference to the forcing chain, RCL, or phi-ladder.

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