Editing RSA numbers (section)

==RSA-768==
RSA-768 has 232 decimal digits (768&nbsp;bits), and was factored on December 12, 2009, over the span of two years, by Thorsten Kleinjung, Kazumaro Aoki, Jens Franke, [[Arjen Lenstra|Arjen K. Lenstra]], Emmanuel Thomé, Pierrick Gaudry, Alexander Kruppa, [[Peter Montgomery (mathematician)|Peter Montgomery]], Joppe W. Bos, Dag Arne Osvik, Herman te Riele, Andrey Timofeev, and [[Paul Zimmermann (mathematician)|Paul Zimmermann]].<ref name="rsa768">{{Citation |last1=Kleinjung |first1=Thorsten |title=Factorization of a 768-bit RSA modulus |date=2010 |url=https://eprint.iacr.org/2010/006 |access-date=2024-02-10 |last2=Aoki |first2=Kazumaro |last3=Franke |first3=Jens |last4=Lenstra |first4=Arjen |last5=Thomé |first5=Emmanuel |last6=Bos |first6=Joppe |last7=Gaudry |first7=Pierrick |last8=Kruppa |first8=Alexander |last9=Montgomery |first9=Peter}}</ref>

 RSA-768 = 1230186684530117755130494958384962720772853569595334792197322452151726400507
           2636575187452021997864693899564749427740638459251925573263034537315482685079
           1702612214291346167042921431160222124047927473779408066535141959745985690214
           3413

 RSA-768 = 3347807169895689878604416984821269081770479498371376856891243138898288379387
           8002287614711652531743087737814467999489
         × 3674604366679959042824463379962795263227915816434308764267603228381573966651
           1279233373417143396810270092798736308917

The CPU time spent on finding these factors by a collection of parallel computers amounted approximately to the equivalent of almost 2000 years of computing on a single-core 2.2&nbsp;GHz AMD Opteron-based computer.<ref name=rsa768/>