Editing Quadratic sieve (section)

==Factoring records==
Until the discovery of the [[general number field sieve|number field sieve]] (NFS), QS was the asymptotically fastest known general-purpose factoring algorithm. Now, [[Lenstra elliptic curve factorization]] has the same asymptotic running time as QS (in the case where ''n'' has exactly two prime factors of equal size), but in practice, QS is faster since it uses [[single-precision]] operations instead of the [[multi-precision]] operations used by the elliptic curve method.

On April 2, 1994, the factorization of [[RSA-129]] was completed using QS. It was a 129-digit number, the product of two large primes, one of 64 digits and the other of 65 digits. The factor base for this factorization contained 524339 primes. The data collection phase took 5000 [[MIPS-year]]s, done in distributed fashion over the Internet. The data collected totaled 2[[gigabyte|GB]]. The data processing phase took 45 hours on [[Bellcore]]'s (now [[Telcordia Technologies]]) [[MasPar]] (massively parallel) supercomputer. This was the largest published factorization by a general-purpose algorithm, until NFS was used to factor [[RSA-130]], completed April 10, 1996. All [[RSA number]]s factored since then have been factored using NFS.

The current QS factorization record is the 140-digit (463-bit) RSA-140, which was factored by Patrick Konsor in June 2020 using approximately 6,000 core hours over 6 days.<ref>{{Cite web|title=Useless Accomplishment: RSA-140 Factorization with Quadratic Sieve - mersenneforum.org|url=https://www.mersenneforum.org/showthread.php?t=25676|access-date=2020-07-07|website=www.mersenneforum.org}}</ref>