<div class="csl-bib-body">
<div class="csl-entry">Steiner, T. (2018). <i>The complexity of prime number tests</i> [Diploma Thesis, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2018.50351</div>
</div>
-
dc.identifier.uri
https://doi.org/10.34726/hss.2018.50351
-
dc.identifier.uri
http://hdl.handle.net/20.500.12708/3434
-
dc.description
Abweichender Titel nach Übersetzung der Verfasserin/des Verfassers
-
dc.description.abstract
Prime numbers have been a significant focus of mathematics throughout the years. Although the study of prime numbers may seem at first quite simple, perhaps because every schoolchild knows what a prime number is, the search for all of the secrets of prime numbers is far from over. Even one of the most famous, thus far unsolved, problems in mathematical history is directly linked to prime numbers, namely the Riemann Hypothesis. Until 2002, it was simply assumed that prime numbers can be differentiated from composites in polynomial time with a great deal of certainty; however, there was no definite proof to say this problem can be solved in polynomial time. If the General Riemann Hypothesis is true, though, some algorithms would classify as deterministic polynomial. If a counterexample for such an algorithm can be found, the test would not longer be classified as deterministic but rather probabilistic. In 2002, though, three Indian mathematicians developed a deterministic algorithm that runs in polynomial time; it is totally independent not only from the Riemann Hypothesis but also all other conjectures - the first of its kind. This result is, of course, groundbreaking for not only the specific field of number theory but also all of mathematics. The development of such an algorithm proves that the prime number problem can be deterministically solved in polynomial time. Additionally, following this initial discovery, further optimizations have been made by other researchers.
en
dc.language
English
-
dc.language.iso
en
-
dc.rights.uri
http://rightsstatements.org/vocab/InC/1.0/
-
dc.subject
Primzahltest
de
dc.subject
Komplexität
de
dc.subject
Riemannsche Vermutung
de
dc.subject
primality test
en
dc.subject
complexity
en
dc.subject
Riemann hypothesis
en
dc.title
The complexity of prime number tests
en
dc.title.alternative
Die Komplexität von Primzahltests
de
dc.type
Thesis
en
dc.type
Hochschulschrift
de
dc.rights.license
In Copyright
en
dc.rights.license
Urheberrechtsschutz
de
dc.identifier.doi
10.34726/hss.2018.50351
-
dc.contributor.affiliation
TU Wien, Österreich
-
dc.rights.holder
Theres Steiner
-
dc.publisher.place
Wien
-
tuw.version
vor
-
tuw.thesisinformation
Technische Universität Wien
-
tuw.publication.orgunit
E104 - Institut für Diskrete Mathematik und Geometrie
-
dc.type.qualificationlevel
Diploma
-
dc.identifier.libraryid
AC15075126
-
dc.description.numberOfPages
87
-
dc.identifier.urn
urn:nbn:at:at-ubtuw:1-113099
-
dc.thesistype
Diplomarbeit
de
dc.thesistype
Diploma Thesis
en
dc.rights.identifier
In Copyright
en
dc.rights.identifier
Urheberrechtsschutz
de
tuw.advisor.staffStatus
staff
-
item.fulltext
with Fulltext
-
item.cerifentitytype
Publications
-
item.mimetype
application/pdf
-
item.openairecristype
http://purl.org/coar/resource_type/c_bdcc
-
item.languageiso639-1
en
-
item.openaccessfulltext
Open Access
-
item.openairetype
master thesis
-
item.grantfulltext
open
-
crisitem.author.dept
E101 - Institut für Analysis und Scientific Computing