The previous record was RSA200 (200 digits), which was factored on May 9, 2005 by Bahr, Boehm, Franke and Kleinjung.
The previous record was 11^{281}+1 (176 digits), which was factored on May 2nd, 2005 by Aoki, Kida, Shimoyama and Ueda.
The previous record was RSA-576 (174 digits), which was factored on December 3rd, 2003 into two 87-digit factors using GNFS by Franke, Kleinjung, Montgomery, te Riele, Bahr, Leclair, Leyland, Wackerbarth.
[previous records and graphical representation].
ECM. The largest factor found by the Elliptic Curve method has 83 digits, found by Ryan Propper on September 8, 2013.
The previous record had 79 digits, found by Sam Wagstaff on August 12, 2012.
The previous record had 75 digits, found by Sam Wagstaff on August 2, 2012.
The previous record had 73 digits, found by J. Bos, T. Kleinjung, A. Lenstra, P. Montgomery on March 6, 2010.
The previous record had 68 digits, found by yoyo@home/M. Thompson on December 28, 2009.
The previous record had 67 digits, found by B. Dodson on August 24, 2006.
[previous records and graphical representation].
Using Hardware. The very first GNFS factorization using hardware is that of 7^{352}+1 c128 done by a Fujitsu LTD group headed by Shimoyama Takeshi.
Special Numbers. With the special number field sieve, the record is 320 digits, with 2^{1061}-1, factored by NFS@home on August 4, 2012 (report). The previous record was 313 digits, with 2^{1039}-1, factored by Aoki, Franke, Kleinjung, Lenstra and Osvik on May 21, 2007 (report). The previous record was 274 digits, with (6^{353}-1)/5 factored by Aoki/Kida/Shimoyama/Ueda on January 23, 2006. [previous records]
Free implementations. Jens Franke has an implementation of PPMPQS. Another implementation for the discrete logarithm problem is due to Chris Studholme. Jason Papadopoulos's MSIEVE is claimed to be "faster than any other code implementing any other algorithm [...] for completely factoring general inputs between 40 and 100 digits", but Ben Buhrow's YAFU is a new challenger. For NFS, the following implementations exist:
Test Numbers: try your favorite factoring algorithm or implementation on these numbers.