pith. sign in
theorem

mod6_onehundredthree_prime

proved
show as:
module
IndisputableMonolith.NumberTheory.Primes.ArithmeticFunctions
domain
NumberTheory
line
1891 · github
papers citing
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plain-language theorem explainer

103 is prime and congruent to 1 modulo 6. Number theorists checking small-prime residues for arithmetic-function identities would cite the result as a verified instance. The proof is a one-line native_decide wrapper that evaluates both conjuncts by direct computation.

Claim. $103$ is prime and $103 ≡ 1 mod 6$.

background

The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function μ. The local setting is the preparation of basic number-theoretic tools for later Dirichlet-algebra layers. The sole upstream dependency is the transparent alias Prime for Nat.Prime.

proof idea

The proof is a one-line wrapper that applies native_decide to the conjunction of primality and the residue condition.

why it matters

The declaration supplies a concrete modular fact marked RS-relevant for 103. It sits among the arithmetic-function footholds but has no recorded downstream uses in the current graph. The result therefore functions as a ready-to-hand instance rather than a lemma feeding a larger theorem.

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