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master's thesis
Učinkovito generiranje prostih brojeva
Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing, 2022. urn:nbn:hr:168:193268
Harbaš, Miro
University of Zagreb
Faculty of Electrical Engineering and Computing

Institutional repository: FER Repository

Cite this document

Harbaš, M. (2022). Učinkovito generiranje prostih brojeva (Master's thesis). Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing. Retrieved from https://urn.nsk.hr/urn:nbn:hr:168:193268

Harbaš, Miro. "Učinkovito generiranje prostih brojeva." Master's thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, 2022. https://urn.nsk.hr/urn:nbn:hr:168:193268

Harbaš, Miro. "Učinkovito generiranje prostih brojeva." Master's thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, 2022. https://urn.nsk.hr/urn:nbn:hr:168:193268

Harbaš, M. (2022). 'Učinkovito generiranje prostih brojeva', Master's thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, accessed 21 December 2024, https://urn.nsk.hr/urn:nbn:hr:168:193268

Harbaš M. Učinkovito generiranje prostih brojeva [Master's thesis]. Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing; 2022 [cited 2024 December 21] Available at: https://urn.nsk.hr/urn:nbn:hr:168:193268

M. Harbaš, "Učinkovito generiranje prostih brojeva", Master's thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, Zagreb, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:168:193268

Metadata
TitleUčinkovito generiranje prostih brojeva
Title (english)Efficient Generation of Prime Numbers
AuthorMiro Harbaš
MentorJosipa Pina Milišić (mentor)
Committee memberJosipa Pina Milišić (predsjednik povjerenstva)
Committee memberAndrea Aglić Aljinović (član povjerenstva)
Committee memberMate Puljiz (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Electrical Engineering and Computing
Zagreb
Defense date and country2022-07-13, Croatia
Scientific / art field,
discipline and subdiscipline		TECHNICAL SCIENCES
Computing
Abstract
U radu se daje definicija prostog broja te pregled osnovnih svojstava. Zatim slijedi osvrt na aritmetičke operacije s binarnim brojevima kako bi se postiglo razumijevanje mogućih implementacijskih poteškoća prilikom rada s velikim binarnim brojevima. Zatim su opisani Eratostenovo sito, Sumadarovo sito i Atikinovo sito kao metode generiranja prostih brojeva, daje se uvid u njihove moguće optimizacije te se navodi usporedba njihove efikasnosti. Zatim se opisuju Miller-Rabin provjera prostosti, Pocklingtonova provjera prostosti i Baillie-PSW provjera prostosti. Za kraj se opisuje algoritam za generiranje prostih brojeva kojeg izlaže Maurer u 1995. godini, njegova implementacija u programskom jeziku C# te se prikazuju dobiveni rezultati.
Abstract (english)
In this thesis the definition of a prime number is given, along with its basic properties. Following that, an overview of binary number arithmetic is given to provide an understanding of possible issues that can arise while working with large binary numbers. Then the sieves of Eratosthenes, Sundaram and Atkin are presented along with their asymptotic time complexities, and possibilities for their further optimization are discussed. After, primality tests of Miller-Rabin, Pocklington and Atkin are presented. The thesis concludes with an overview of the Prime generation algorithm presented by Maurer in 1995, as well as the implementation details of the same algorithm written in C# and the results thereof.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:168:193268
Study programmeTitle: Computing
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra inženjer/inženjerka računarstva (magistar/magistra inženjer/inženjerka računarstva)
Type of resourceText
File originBorn digital
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Created on2023-01-14 20:33:09