pith. sign in
theorem

mod6_seventythree_prime

proved
show as:
module
IndisputableMonolith.NumberTheory.Primes.ArithmeticFunctions
domain
NumberTheory
line
1882 · github
papers citing
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plain-language theorem explainer

73 is a prime congruent to 1 modulo 6. Number theorists applying arithmetic functions such as the Möbius function would cite this to anchor small-prime checks in residue class 1 mod 6. The proof is a one-line wrapper that applies the native_decide tactic to evaluate the conjunction directly.

Claim. 73 is a prime number and $73 ≡ 1 mod 6$.

background

The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function μ. This theorem supplies a concrete prime fact for use in that setting. Prime is the module-local alias for the standard Nat.Prime predicate.

proof idea

The proof is a one-line wrapper that invokes native_decide to evaluate the primality predicate and the modular condition by direct computation.

why it matters

The result supplies a verified small-prime datum in the arithmetic-functions module. It supports later work on squarefree numbers and Möbius inversion by confirming 73 lies in the required residue class. No downstream invocations are recorded.

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