KnowraEuclid's theoremLinked fromLinked fromThe 6 pages that link to Euclid's theorem, each with the reason it gives.All 6Related 1Narrower topic 3Compared with 2Prime numberRelated: Its short contradiction proof establishes that no final prime exists.Prime-counting functionNarrower topic: An unbounded count becomes meaningful because primes never run out.Dirichlet's theorem on arithmetic progressionsCompared with: It gives unrestricted infinitude, while Dirichlet specifies which residue classes contain infinitely many primes.Twin prime conjectureNarrower topic: It establishes the broader infinitude question from which the twin-prime problem takes its distinctive form.Bertrand's postulateCompared with: Euclid guarantees primes without a nearby upper bound; Bertrand gives a quantitative interval.Bonse's inequalityNarrower topic: Bonse's inequality is a quantitative statement about the continuing sequence of primes.