Extending the generalized Fermat prime search beyond one million digits

Iain Bethune; Michael Goetz

doi:10.1007/978-3-642-55224-3_11

Extending the generalized Fermat prime search beyond one million digits

Iain Bethune, Michael Goetz

School of Physics and Astronomy

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English
Title of host publication	10th International Conference, PPAM 2013, Warsaw, Poland, September 8-11, 2013, Revised Selected Papers, Part I
Editors	Roman Wyrzykowski, Jack Dongarra, Konrad Karczewski, Jerzy Waśniewski
Publisher	Springer
Pages	106-113
Number of pages	20
ISBN (Electronic)	978-3-642-55224-3
ISBN (Print)	978-3-642-55223-6
DOIs	https://doi.org/10.1007/978-3-642-55224-3_11
Publication status	Published - 6 May 2014
Event	10th International Conference on Parallel Processing and Applied Mathematics (PPAM 2013) - Warsaw, Poland Duration: 8 Sept 2013 → 11 Sept 2013

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer Berlin Heidelberg
Volume	8384
ISSN (Print)	0302-9743

Conference

Conference	10th International Conference on Parallel Processing and Applied Mathematics (PPAM 2013)
Country/Territory	Poland
City	Warsaw
Period	8/09/13 → 11/09/13

Keywords / Materials (for Non-textual outputs)

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

Access to Document

10.1007/978-3-642-55224-3_11

Cite this

Bethune, I., & Goetz, M. (2014). Extending the generalized Fermat prime search beyond one million digits. In R. Wyrzykowski, J. Dongarra, K. Karczewski, & J. Waśniewski (Eds.), 10th International Conference, PPAM 2013, Warsaw, Poland, September 8-11, 2013, Revised Selected Papers, Part I (pp. 106-113). (Lecture Notes in Computer Science; Vol. 8384). Springer. https://doi.org/10.1007/978-3-642-55224-3_11

@inproceedings{5c35a34c0ac04e638309cb7bd2bc14f1,

title = "Extending the generalized Fermat prime search beyond one million digits",

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 {\textquoteleft}Genefer{\textquoteright} 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{\textquoteright}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.",

keywords = "Generalized Fermat Numbers, Primality Testing, Volunteer Computing, Computational Mathematics, GPU computing, CUDA",

author = "Iain Bethune and Michael Goetz",

year = "2014",

month = may,

day = "6",

doi = "10.1007/978-3-642-55224-3\_11",

language = "English",

isbn = "978-3-642-55223-6",

series = "Lecture Notes in Computer Science",

publisher = "Springer",

pages = "106--113",

editor = "Roman Wyrzykowski and Jack Dongarra and Konrad Karczewski and Jerzy Wa{\'s}niewski",

booktitle = "10th International Conference, PPAM 2013, Warsaw, Poland, September 8-11, 2013, Revised Selected Papers, Part I",

address = "United Kingdom",

note = "10th International Conference on Parallel Processing and Applied Mathematics (PPAM 2013) ; Conference date: 08-09-2013 Through 11-09-2013",

}

Bethune, I & Goetz, M 2014, Extending the generalized Fermat prime search beyond one million digits. in R Wyrzykowski, J Dongarra, K Karczewski & J Waśniewski (eds), 10th International Conference, PPAM 2013, Warsaw, Poland, September 8-11, 2013, Revised Selected Papers, Part I. Lecture Notes in Computer Science, vol. 8384, Springer, pp. 106-113, 10th International Conference on Parallel Processing and Applied Mathematics (PPAM 2013), Warsaw, Poland, 8/09/13. https://doi.org/10.1007/978-3-642-55224-3_11

Extending the generalized Fermat prime search beyond one million digits. / Bethune, Iain; Goetz, Michael.
10th International Conference, PPAM 2013, Warsaw, Poland, September 8-11, 2013, Revised Selected Papers, Part I. ed. / Roman Wyrzykowski; Jack Dongarra; Konrad Karczewski; Jerzy Waśniewski. Springer, 2014. p. 106-113 (Lecture Notes in Computer Science; Vol. 8384).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Extending the generalized Fermat prime search beyond one million digits

AU - Bethune, Iain

AU - Goetz, Michael

PY - 2014/5/6

Y1 - 2014/5/6

N2 - 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.

AB - 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.

KW - Generalized Fermat Numbers

KW - Primality Testing

KW - Volunteer Computing

KW - Computational Mathematics

KW - GPU computing

KW - CUDA

UR - https://www.scopus.com/pages/publications/84901287913

U2 - 10.1007/978-3-642-55224-3_11

DO - 10.1007/978-3-642-55224-3_11

M3 - Conference contribution

SN - 978-3-642-55223-6

T3 - Lecture Notes in Computer Science

SP - 106

EP - 113

BT - 10th International Conference, PPAM 2013, Warsaw, Poland, September 8-11, 2013, Revised Selected Papers, Part I

A2 - Wyrzykowski, Roman

A2 - Dongarra, Jack

A2 - Karczewski, Konrad

A2 - Waśniewski, Jerzy

PB - Springer

T2 - 10th International Conference on Parallel Processing and Applied Mathematics (PPAM 2013)

Y2 - 8 September 2013 through 11 September 2013

ER -

Bethune I, Goetz M. Extending the generalized Fermat prime search beyond one million digits. In Wyrzykowski R, Dongarra J, Karczewski K, Waśniewski J, editors, 10th International Conference, PPAM 2013, Warsaw, Poland, September 8-11, 2013, Revised Selected Papers, Part I. Springer. 2014. p. 106-113. (Lecture Notes in Computer Science). doi: 10.1007/978-3-642-55224-3_11

Extending the generalized Fermat prime search beyond one million digits

Abstract

Publication series

Conference

Keywords / Materials (for Non-textual outputs)

Access to Document

Other files and links

Fingerprint

Science and Innovation: Numerical Algorithms and Intelligent Software for the Evolving HPC Platform

Cite this

Extending the generalized Fermat prime search beyond one million digits

Abstract

Publication series

Conference

Keywords / Materials (for Non-textual outputs)

Access to Document

Other files and links

Fingerprint

Projects

Science and Innovation: Numerical Algorithms and Intelligent Software for the Evolving HPC Platform

Cite this