A Report on Integer Factorization by Elliptic Curve Method ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ I would like to report that I found the following integer factorization on 2001.10.06 using GMP-ECM 4c, by P. Zimmermann[ECM-NET]. The 55-digit factor below is the largest factor known to have been found by ECM[Brent]. Input number (629^59 - 1)/(628 * 36537729662842124950382971 * 13274814114538692574828847) (112 digits) prime factor of 55 digits 7230880127526821693925059508972082952702133004552346281 prime cofactor 599055788512257114593036852972837566170071937294830361923 57 digits B1=45000000 sigma=267937500 trial : about 28000 curves Machine : PentiumIII 800MHz 256MB TurboLinux Thanks go to Professor Paul Zimmermann who computed the following data. Group order = 7230880127526821693925059512516755420711283207114558464 = 2^10*3*13*103*151*1123*12619*15649*26249*404197*4742809*25268183*41286269351 P = 7230880127526821693925059508972082952702133004552346281 Distance = 3544672468009150202562212183 P-1 = 2^3*3*5*7^2*11*59*12451*54469849267*382541885447633*7303478218762241179 P+1 = 2*123661*5865679*4984368234991696091660199134866334322464839 Remark: The input number is a cyclotomic number noticed in [MISHIMA] "what's new / history / errata (August 19, 2001) (59 629 (13274814114538692574828847) (C 138))By Masaki Ukai (August 03, 2001)" [Brent] ftp://ftp.comlab.ox.ac.uk/pub/Documents/techpapers/Richard.Brent/champs.txt [ECM-NET] http://www.loria.fr/~zimmerma/records/ecmnet.html [MISHIMA] http://www.asahi-net.or.jp/~KC2H-MSM/cn/index.htm Best regards, Izumi Miyamoto Yamanashi University, Japan izumi@esi.yamanashi.ac.jp