pith. sign in
theorem

fermat_zero

proved
show as:
module
IndisputableMonolith.NumberTheory.Primes.ArithmeticFunctions
domain
NumberTheory
line
1256 · github
papers citing
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plain-language theorem explainer

fermat_zero asserts that the zeroth Fermat number equals 3 and is prime. Number theorists building base cases for Fermat sequences or arithmetic foundations in Recognition Science would cite this explicit verification. The proof is a one-line term that invokes native_decide to evaluate the expression and confirm primality.

Claim. The integer $2^{2^0} + 1$ is prime.

background

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

proof idea

The proof is a one-line term that applies native_decide to the concrete value 2^(2^0)+1 and returns the primality judgment.

why it matters

It supplies the base verified Fermat prime inside the arithmetic-functions section of the primes development. No downstream uses are recorded. The fact sits among other explicit prime constructions that support the number-theory layer of the Recognition Science framework.

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