References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt152",{id:"formSmash:upper:j_idt152",widgetVar:"widget_formSmash_upper_j_idt152",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt153_j_idt156",{id:"formSmash:upper:j_idt153:j_idt156",widgetVar:"widget_formSmash_upper_j_idt153_j_idt156",target:"formSmash:upper:j_idt153:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

The Goldston-Pintz-Yildirim sieveand some applicationsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2013 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
##### Abstract [en]

##### Place, publisher, year, edition, pages

2013. , 50 p.
##### Series

TRITA-MAT-E, 2013:16
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:kth:diva-122011OAI: oai:DiVA.org:kth-122011DiVA: diva2:620680
##### Subject / course

Mathematics
##### Educational program

Master of Science - Mathematics
##### Uppsok

Physics, Chemistry, Mathematics

#####

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##### Supervisors

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt461",{id:"formSmash:j_idt461",widgetVar:"widget_formSmash_j_idt461",multiple:true});
##### Examiners

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt467",{id:"formSmash:j_idt467",widgetVar:"widget_formSmash_j_idt467",multiple:true});
Available from: 2013-05-10 Created: 2013-05-07 Last updated: 2013-05-10Bibliographically approved

The twin prime conjecture - that there exist infinitely many pairs of "twin primes" p, p + 2 - is among the most famous problems in number theory. In 2005, Goldston, Pintz and Yildirim (GPY) made a major and unexpected breakthrough in this direction using a simple variant of the Selberg sieve. Namely, they proved that the gap between consecutive primes is infinitely often arbitrarily smaller than average.

In this master’s thesis we discuss some of the key concepts and ideas behind the GPY method and results on primes in tuples and prime gaps in general. In particular, we discuss the notion of the level of distribution of the primes, and in connection with this the celebrated Bombieri-Vinogradov theorem, which gives a result of the strength of the Generalized Riemann Hypothesis in an average sense.

As an application of the GPY method, we present a new result related to conjecture of Erdos-Mirsky concerning the divisor function at consecutive integers. This result is an improvement of Hildebrand’s previous work.

.

References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1196",{id:"formSmash:lower:j_idt1196",widgetVar:"widget_formSmash_lower_j_idt1196",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1197_j_idt1199",{id:"formSmash:lower:j_idt1197:j_idt1199",widgetVar:"widget_formSmash_lower_j_idt1197_j_idt1199",target:"formSmash:lower:j_idt1197:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});