English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In 2015, Abatzoglou, Silverberg, Sutherland, and Wong presented a frameworkfor primality proving algorithms for special sequences of integers using anelliptic curve with complex multiplication. They applied their framework toobtain algorithms for elliptic curves with complex multiplication by imaginaryquadratic field of class numbers one and two, but, they were not able to obtainprimality proving algorithms in cases of higher class number. In this paper, wepresent a method to apply their framework to imaginary quadratic fields ofclass number three. In particular, our method provides a more efficientprimality proving algorithm for special sequences of integers than the existingalgorithms by using an imaginary quadratic field of class number three in which2 splits. As an application, we give two special sequences of integers derivedfrom $\Q(\sqrt{-23})$ and $\Q(\sqrt{-31})$, which are all the imaginaryquadratic fields of class number three in which 2 splits. Finally, we give acomputational result for the primality of these sequences.

Primality proving using elliptic curves with complex multiplication by imaginary quadratic fields of class number three