Factorization of the tenth and eleventh Fermat numbers
Description
We describe the complete factorization of the tenth and eleventh Fermat numbers. The tenth Fermat number is a product of four prime factors with 8, 10, 40 and 252 decimal digits. The eleventh Fermat number is a product of five prime factors with 6, 6, 21, 22 and 564 decimal digits. We also note a new 27-decimal digit factor of the thirteenth Fermat number. This number has four known prime factors and a 2391-decimal digit composite factor. All the new factors reported here were found by the...[Show more]
dc.contributor.author | Brent, Richard P | |
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dc.date.accessioned | 2003-07-08 | |
dc.date.accessioned | 2004-05-19T12:44:46Z | |
dc.date.accessioned | 2011-01-05T08:37:41Z | |
dc.date.available | 2004-05-19T12:44:46Z | |
dc.date.available | 2011-01-05T08:37:41Z | |
dc.date.created | 1996 | |
dc.identifier.uri | http://hdl.handle.net/1885/40767 | |
dc.identifier.uri | http://digitalcollections.anu.edu.au/handle/1885/40767 | |
dc.description.abstract | We describe the complete factorization of the tenth and eleventh Fermat numbers. The tenth Fermat number is a product of four prime factors with 8, 10, 40 and 252 decimal digits. The eleventh Fermat number is a product of five prime factors with 6, 6, 21, 22 and 564 decimal digits. We also note a new 27-decimal digit factor of the thirteenth Fermat number. This number has four known prime factors and a 2391-decimal digit composite factor. All the new factors reported here were found by the elliptic curve method (ECM). The 40-digit factor of the tenth Fermat number was found after about 140 Mop-years of computation. We discuss aspects of the practical implementation of ECM, including the use of special-purpose hardware, and note several other large factors found recently by ECM. | |
dc.format.extent | 380293 bytes | |
dc.format.extent | 356 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | application/octet-stream | |
dc.language.iso | en_AU | |
dc.subject | Fermat numbers | |
dc.subject | factorization | |
dc.subject | elliptic curve method | |
dc.subject | primality proofs | |
dc.title | Factorization of the tenth and eleventh Fermat numbers | |
dc.type | Working/Technical Paper | |
local.description.refereed | no | |
local.identifier.citationmonth | feb | |
local.identifier.citationyear | 1996 | |
local.identifier.eprintid | 1603 | |
local.rights.ispublished | yes | |
dc.date.issued | 1996 | |
local.contributor.affiliation | ANU | |
local.contributor.affiliation | Department of Computer Science, FEIT | |
local.citation | TR-CS-96-02 | |
Collections | ANU Research Publications |
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TR-CS-96-02.pdf | 371.38 kB | Adobe PDF |
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