A factorization method, abbreviated ECM, which computes a large multiple of a point on a random elliptic curve modulo the number to be factored N. It tends to be faster than the Pollard rho factorization and Pollard p-1 factorization methods.
Zimmermann maintains a table of the largest factors found using the ECM. As of March 2005, the largest prime factor found using the ECM had 59 decimal digits and was found was found by B. Dodson on Feb. 20, 2005 (Zimmerman 2005).
Atkin-Goldwasser-Kilian-Morain Certificate, Elliptic Curve Primality Proving, Elliptic Pseudoprime, Prime Factorization, Prime Factorization Algorithms
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Zimmermann, P. "New ECM Record (59 Digits) and GMP-ECM Release (6.0)." NMBRTHRY@listserv.nodak.edu mailing list. 4 Mar 2005. http://listserv.nodak.edu/cgi-bin/wa.exe?A2=ind0503&L=nmbrthry&F=&S=&P=192.