pith. sign in
theorem

prime_sixhundredone

proved
show as:
module
IndisputableMonolith.NumberTheory.Primes.ArithmeticFunctions
domain
NumberTheory
line
2627 · github
papers citing
none yet

plain-language theorem explainer

601 is established as prime in the natural numbers. Number theorists building arithmetic tools inside the Recognition Science codebase cite this when checking specific integers for Möbius or prime-ladder calculations. The proof is a direct computational verification via native decision.

Claim. The natural number 601 is prime.

background

The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function μ. Prime is the transparent alias for Nat.Prime. The local setting keeps statements minimal so that Dirichlet inversion and deeper algebra can be added once the basic interfaces stabilize.

proof idea

The proof is a one-line term that invokes native_decide to confirm primality of 601.

why it matters

This supplies a verified concrete prime fact inside the arithmetic-functions library. No immediate parent theorems or downstream uses are recorded, so it functions as a leaf building block for later number-theoretic work. It supports the prime-related infrastructure needed for constants and ladders in the Recognition framework.

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