Editing RSA numbers (section)

==RSA-140==
RSA-140 has 140 decimal digits (463 bits), and was factored on February 2, 1999, by a team led by [[Herman te Riele]] and composed of [[Stefania Cavallar]], Bruce Dodson, [[Arjen Lenstra|Arjen K. Lenstra]], Paul Leyland, [[Walter Lioen]], Peter L. Montgomery, [[Brian Murphy (mathematician)|Brian Murphy]] and [[Paul Zimmermann (mathematician)|Paul Zimmermann]].<ref>{{Cite mailing list |url=http://listserv.nodak.edu/scripts/wa.exe?A2=ind9902&L=nmbrthry&P=302 |title=Factorization of RSA-140 using the Number Field Sieve |date=4 Feb 1999 |mailing-list=Number Theory List <NMBRTHRY@LISTSERV.NODAK.EDU> |last=Riele |first=Herman te |url-status=dead |archive-url=https://web.archive.org/web/20041208075604/http://listserv.nodak.edu/scripts/wa.exe?A2=ind9902&L=nmbrthry&P=302 |archive-date=2004-12-08 |orig-date=February 3, 1999 |first2=Stefania |last2=Cavallar |first3=Bruce |last3=Dodson |first4=Arjen |last4=Lenstra |first5=Paul |last5=Leyland |first6=Walter |last6=Lioen |first7=Peter |last7=Montgomery |first8=Brian |last8=Murphy |first9=Paul |last9=Zimmermann |author-link=Herman te Riele |access-date=2008-03-10 |publisher=North Dakota University System}}</ref><ref>{{Cite web |title=RSA-140 is factored! |url=http://www.rsasecurity.com/rsalabs/node.asp?id=2099 |url-status=dead |archive-url=https://web.archive.org/web/20061230233737/http://www.rsasecurity.com/rsalabs/node.asp?id=2099 |archive-date=2006-12-30 |access-date=2008-03-10 |website=RSA Laboratories |publisher=RSA Security |department=Other Activities: Cryptographic Challenges: The RSA Factoring Challenge}}</ref>

The value and factorization are as follows:

 RSA-140 = 21290246318258757547497882016271517497806703963277216278233383215381949984056495911366573853021918316783107387995317230889569230873441936471

 RSA-140 = 3398717423028438554530123627613875835633986495969597423490929302771479
         × 6264200187401285096151654948264442219302037178623509019111660653946049

The factorization was found using the [[Number Field Sieve]] algorithm and an estimated 2000 [[MIPS-year]]s of computing time.

The matrix had 4671181 rows and 4704451 columns and weight 151141999 (32.36 nonzeros per row)<ref name="RSA Honor Roll" />