Editing RSA numbers (section)

==RSA-130==
RSA-130 has 130 decimal digits (430 bits), and was factored on April 10, 1996, by a team led by [[Arjen Lenstra|Arjen K. Lenstra]] and composed of [[Jim Cowie]], [[Marije Elkenbracht-Huizing]], [[Wojtek Furmanski]], [[Peter Montgomery (mathematician)|Peter L. Montgomery]], [[Damian Weber]] and [[Joerg Zayer]].<ref>{{Cite mailing list |url=https://t5k.org/notes/rsa130.html |title=Factorization of RSA-130 |date=12 Apr 1996 |mailing-list=NMBRTHRY |last=Lenstra |first=Arjen K. |orig-date=April 11, 1996 |first2=Jim |last2=Cowie |first3=Marije |last3=Elkenbracht-Huizing |first4=Wojtek |last4=Furmanski |first5=Peter L. |last5=Montgomery |first6=Damian |last6=Weber |first7=Joerg |last7=Zayer |access-date=2008-03-10 |author-link=Arjen Lenstra |website= |publisher=PrimePages: prime number research records and results |editor-first=Chris |editor-last=Caldwell |via=Notes, Proofs and other Comments |url-status=live |archive-url=https://web.archive.org/web/20230902110041/https://t5k.org/notes/rsa130.html |archive-date=2023-09-02}}</ref>

The factorization was found in the third trial.<ref name="RSA Honor Roll" />

The value and factorization are as follows:

 RSA-130 = 1807082088687404805951656164405905566278102516769401349170127021450056662540244048387341127590812303371781887966563182013214880557

 RSA-130 = 39685999459597454290161126162883786067576449112810064832555157243
         × 45534498646735972188403686897274408864356301263205069600999044599

The factorization was found using the [[Number Field Sieve]] algorithm and the [[polynomial]]

    5748302248738405200 x<sup>5</sup> +  9882261917482286102 x<sup>4</sup>
 - 13392499389128176685 x<sup>3</sup> + 16875252458877684989 x<sup>2</sup>
 +  3759900174855208738 x<sup>1</sup> - 46769930553931905995

which has a root of 12574411168418005980468 modulo RSA-130.