Fast algorithm for finding prime numbers

U ovom radu su opisani i analizirani brzi algoritmi za pronalazak prostih brojeva. Definirani su prosti brojevi i objašnjena njihova matematička svojstva. Rad opisuje osnovni algoritam pronalaska prostih brojeva zasnovan na osnovnim pravilima djeljivosti. Nadalje, navedene su četiri njegove nadogradnje koje uvode dodatna pravila i mehanizme u implementaciji, čime se ubrzava rad osnovnog algoritma. Također su opisana i tri sita: Eratostenovo, Sundramovo i Atkinovo te nadogradnje za Eratostenovo i Atkinovo sito. Svi algoritmi su implementirani u C++ programskom jeziku te su analizirane njihove performanse. Analiza je pokazala da je optimirano Atkinovo sito najbrže.This thesis describes and analyses fast algorithms for prime number detection. Prime numbers are defined and their mathematical properties described. Basic algorithm based on fundamental division principle is described. Furthermore, four augmentations are also described, they introduce additional rules and mechanisms which results in increased performance. Three sieves, Eratosten´s, Sundram´s, Atkin´s are also described as well as enhancements to Eratosten´s and Atkin´s sieves. All algorithms were implemented in C++ programming language and their performance analyzed. Enhanced Atkin´s sieve has shown to be the fastest