Extending the generalized Fermat prime search beyond one million digits

Iain Bethune, Michael Goetz

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Great strides have been made in recent years in the search for ever larger prime Generalized Fermat Numbers (GFN). We briefly review the history of the GFN prime search, and describe new implementations of the ‘Genefer’ software (now available as open source) using CUDA and optimised CPU assembler which have underpinned this unprecedented progress. The results of the ongoing search are used to extend Gallot and Dubner’s published tables comparing the theoretical predictions with actual distributions of primes, and we report on recent discoveries of GFN primes with over one million digits.
Original languageEnglish
Title of host publication10th International Conference, PPAM 2013, Warsaw, Poland, September 8-11, 2013, Revised Selected Papers, Part I
EditorsRoman Wyrzykowski, Jack Dongarra, Konrad Karczewski, Jerzy Waśniewski
PublisherSpringer Berlin Heidelberg
Pages106-113
Number of pages20
ISBN (Electronic)978-3-642-55224-3
ISBN (Print)978-3-642-55223-6
DOIs
Publication statusPublished - 6 May 2014
Event10th International Conference on Parallel Processing and Applied Mathematics (PPAM 2013) - Warsaw, Poland
Duration: 8 Sep 201311 Sep 2013

Publication series

NameLecture Notes in Computer Science
PublisherSpringer Berlin Heidelberg
Volume8384
ISSN (Print)0302-9743

Conference

Conference10th International Conference on Parallel Processing and Applied Mathematics (PPAM 2013)
CountryPoland
CityWarsaw
Period8/09/1311/09/13

Keywords

  • Generalized Fermat Numbers
  • Primality Testing
  • Volunteer Computing
  • Computational Mathematics
  • GPU computing
  • CUDA

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