Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

Topic: Prime factorization
Replies: 17   Last Post: Nov 16, 2013 9:40 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Pubkeybreaker

Posts: 1,412
Registered: 2/12/07
Re: Prime factorization
Posted: Nov 12, 2013 7:54 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Monday, November 11, 2013 11:03:00 PM UTC-5, Kermit Rose wrote:
> On Monday, November 4, 2013 12:49:47 PM UTC-5, Michael F. Stemper wrote: > On 11/04/2013 11:35 AM, me wrote: > > > tell me what you think? > > > http://www.davesinvoice.com/papers/factorization2.pdf > > > > Interesting idea. How about using it to factor 130642890110987? >>> Factor(130642890110987) [58789, 2222233583, 134, 'Pollard Rho, x^2 + 1, First factor check'] Pollard Rho is a very efficient means to factor numbers of this size.

No, it is NOT. Please tell us how long the computation took you.

(1) It requires double length arithmetic. i.e. multi-precision arithmetic
that is twice the length of the number being factored.
(2) It is more efficient than trial division but still runs in exponential
time. O(N^1/4)
(3) Both SQUFOF and ECM are more efficient (i.e. faster on average)
for numbers this size.
(4) If you know in advance that it is the product of two large primes, MPQS
will be even more efficient.

My NFS code factors number this size (and slightly larger/smaller) by the billions.
I tried Pollard Rho in the past. It is slow. I first run ECM, then if it
fails, MPQS.



>>It factored 130642890110987 almost instantly

Specify: "almost instantly". Exactly how long?







Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.