prime_thirteen
plain-language theorem explainer
13 is established as a prime natural number. Recognition Science workers cite this fact when anchoring cicada cycle markers among the small primes collected for repeated use in bridge lemmas. The verification applies a direct decision procedure that exhausts divisors to confirm the property.
Claim. The natural number 13 is prime.
background
The RSConstants module assembles small decidable arithmetic facts about integers that recur across the repo, including prime markers such as 5, 11, 13, 17, 37, 103 and 137. These serve as stable anchors that keep later lemmas readable without repeated arithmetic proofs. Prime is the repo-local alias for the standard predicate Nat.Prime on natural numbers.
proof idea
The proof is a one-line wrapper that applies the decide tactic to the statement Prime 13, confirming primality by exhaustive computational check of possible factors.
why it matters
This supplies one of the prime markers in the RSConstants collection, supporting cicada cycle references in the module. It belongs to the set of decidable facts that include eight_eq_two_pow_three and wheel840_factorization, keeping the arithmetic substrate clean for downstream number-theoretic bridges. No direct parent theorems or open questions are attached.
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