factoring large integers

[Pfoertner, Hugo]

-----Ursprüngliche Nachricht-----
Von: Thomas Baruchel [mailto:thomas.baruchel at laposte.net]
Gesendet am: 29 March, 2004 05:55
An: seqfan at ext.jussieu.fr
Betreff: Re: factoring large integers

On Sun, Mar 28, 2004 at 04:13:59PM -0800, David Wasserman wrote:
> Dear SeqFans,
>      Anyone know where I can find state-of-the-art software for 
> factoring large numbers?

I posted to NG sci.math:

<<
"Re: Pollard-Strassen and other factorization algorithms"
Date: 2003-07-08 23:39:17 PST

Try S. Tomabechi's PPSIQS and PPMPQS:
http://www.asahi-net.or.jp/~KC2H-MSM/cn/
PPSIQS has been reported to be capable of factoring a 105 digit
composite in 10 days CPU time on a 2.5 GHz PC, see
http://euclide.euclide.free.fr/partition/top10ppsiqs.htm

I found a 49-digit factor of the 100 digit number
(41!)^2+1 with Yuji Kida's multiple polynomial quadratic
sieve UBASIC PPMPQS v3.5 in 13 days CPU time on an Intel PIII 550 Mhz.
UBASIC Home (Japanese): http://www.rkmath.rikkyo.ac.jp/~kida/ubasic.htm

Dario Alperns ECM Java applet works pretty well for factors
up to ~35..40 digits: http://www.alpertron.com.ar/ECM.HTM
>>

and read "A tale of Two Sieves" by Carl Pomerance
http://www.ams.org/notices/199612/pomerance.pdf

See also:
http://mathworld.wolfram.com/PrimeFactorizationAlgorithms.html

Hugo Pfoertner