Asp Forum - Re: Calculating very large exponents in python

geremy condra

3/8/2010 7:06:00 PM

On Mon, Mar 8, 2010 at 2:15 AM, Fahad Ahmad <miraclesoul@hotmail.com> wrote:
> Thanks Geremy,
>
> That has been an absolute bump........... GOD i cant sit on my chair, it has
> worked even on 512 bit number and with no time..........
> superb i would say.
>
> lastly, i am using the code below to calculate Largest Prime factor of a
> number:
>
> print
> ('''==============================================================================='''
>        '''              CALCULATE HIGHEST PRIME
> FACTOR                                  '''
>
> '''===============================================================================''')
>
> #!/usr/bin/env python
> def highest_prime_factor(n):
>    if isprime(n):
>       return n
>    for x in xrange(2,n ** 0.5 + 1):
>       if not n % x:
>          return highest_prime_factor(n/x)
> def isprime(n):
>    for x in xrange(2,n ** 0.5 + 1):
>       if not n % x:
>          return False
>    return True
> if __name__ == "__main__":
>    import time
>    start = time.time()
>    print highest_prime_factor(1238162376372637826)
>    print time.time() - start
>
> the code works with a bit of delay on the number : "1238162376372637826" but
> extending it to
> (109026109913291424366305511581086089650628117463925776754560048454991130443047109026109913291424366305511581086089650628117463925776754560048454991130443047)
> makes python go crazy. Is there any way just like above, i can have it
> calculated it in no time.
>
>
> thanks for the support.

If you're just looking for the largest prime factor I would suggest using
a fermat factorization attack. In the example you gave, it returns
nearly immediately.

Geremy Condra

4 Answers

casevh

3/9/2010 6:40:00 AM

[also replying to Geremy since the OP's message doesn't appear...]

On Mar 8, 11:05 am, geremy condra <debat...@gmail.com> wrote:
> On Mon, Mar 8, 2010 at 2:15 AM, Fahad Ahmad <miracles...@hotmail.com> wrote:
> > Thanks Geremy,
>
> > That has been an absolute bump........... GOD i cant sit on my chair, it has
> > worked even on 512 bit number and with no time..........
> > superb i would say.
>
> > lastly, i am using the code below to calculate Largest Prime factor of a
> > number:
>
> > print
> > ('''==============================================================================='''
> >        '''              CALCULATE HIGHEST PRIME
> > FACTOR                                  '''
>
> > '''===============================================================================''')
>
> > #!/usr/bin/env python
> > def highest_prime_factor(n):
> >    if isprime(n):
> >       return n
> >    for x in xrange(2,n ** 0.5 + 1):
> >       if not n % x:
> >          return highest_prime_factor(n/x)
> > def isprime(n):
> >    for x in xrange(2,n ** 0.5 + 1):
> >       if not n % x:
> >          return False
> >    return True
> > if __name__ == "__main__":
> >    import time
> >    start = time.time()
> >    print highest_prime_factor(1238162376372637826)
> >    print time.time() - start
>
> > the code works with a bit of delay on the number : "1238162376372637826" but
> > extending it to
> > (109026109913291424366305511581086089650628117463925776754560048454991130443047109026109913291424366305511581086089650628117463925776754560048454991130443047)
> > makes python go crazy. Is there any way just like above, i can have it
> > calculated it in no time.
>
> > thanks for the support.
>
> If you're just looking for the largest prime factor I would suggest using
> a fermat factorization attack. In the example you gave, it returns
> nearly immediately.
>
> Geremy Condra- Hide quoted text -
>
> - Show quoted text -

For a Python-based solution, you might want to look at pyecm (http://
sourceforge.net/projects/pyecm/)

On a system with gmpy installed also, pyecm found the following
factors:

101, 521, 3121, 9901, 36479, 300623, 53397071018461,
1900381976777332243781

There still is a 98 digit unfactored composite:

60252507174568243758911151187828438446814447653986842279796823262165159406500174226172705680274911

Factoring this remaining composite using ECM may not be practical.

casevh

casevh

3/9/2010 1:54:00 PM

On Mar 8, 10:39 pm, casevh <cas...@gmail.com> wrote:
> [also replying to Geremy since the OP's message doesn't appear...]
>
> On Mar 8, 11:05 am, geremy condra <debat...@gmail.com> wrote:
>
>
>
>
>
> > On Mon, Mar 8, 2010 at 2:15 AM, Fahad Ahmad <miracles...@hotmail.com> wrote:
> > > Thanks Geremy,
>
> > > That has been an absolute bump........... GOD i cant sit on my chair, it has
> > > worked even on 512 bit number and with no time..........
> > > superb i would say.
>
> > > lastly, i am using the code below to calculate Largest Prime factor of a
> > > number:
>
> > > print
> > > ('''==============================================================================='''
> > >        '''              CALCULATE HIGHEST PRIME
> > > FACTOR                                  '''
>
> > > '''===============================================================================''')
>
> > > #!/usr/bin/env python
> > > def highest_prime_factor(n):
> > >    if isprime(n):
> > >       return n
> > >    for x in xrange(2,n ** 0.5 + 1):
> > >       if not n % x:
> > >          return highest_prime_factor(n/x)
> > > def isprime(n):
> > >    for x in xrange(2,n ** 0.5 + 1):
> > >       if not n % x:
> > >          return False
> > >    return True
> > > if __name__ == "__main__":
> > >    import time
> > >    start = time.time()
> > >    print highest_prime_factor(1238162376372637826)
> > >    print time.time() - start
>
> > > the code works with a bit of delay on the number : "1238162376372637826" but
> > > extending it to
> > > (109026109913291424366305511581086089650628117463925776754560048454991130443047109026109913291424366305511581086089650628117463925776754560048454991130443047)
> > > makes python go crazy. Is there any way just like above, i can have it
> > > calculated it in no time.
>
> > > thanks for the support.
>
> > If you're just looking for the largest prime factor I would suggest using
> > a fermat factorization attack. In the example you gave, it returns
> > nearly immediately.
>
> > Geremy Condra- Hide quoted text -
>
> > - Show quoted text -
>
> For a Python-based solution, you might want to look at pyecm (http://
> sourceforge.net/projects/pyecm/)
>
> On a system with gmpy installed also, pyecm found the following
> factors:
>
> 101, 521, 3121, 9901, 36479, 300623, 53397071018461,
> 1900381976777332243781
>
> There still is a 98 digit unfactored composite:
>
> 60252507174568243758911151187828438446814447653986842279796823262165159406500174226172705680274911
>
> Factoring this remaining composite using ECM may not be practical.
>
> casevh- Hide quoted text -
>
> - Show quoted text -

After a few hours, the remaining factors are

6060517860310398033985611921721

and

9941808367425935774306988776021629111399536914790551022447994642391

casevh

Mark Dickinson

3/10/2010 5:47:00 PM

On Mar 9, 6:39 am, casevh <cas...@gmail.com> wrote:
> [also replying to Geremy since the OP's message doesn't appear...]
>
> On Mar 8, 11:05 am, geremy condra <debat...@gmail.com> wrote:
>
>
>
>
>
> > On Mon, Mar 8, 2010 at 2:15 AM, Fahad Ahmad <miracles...@hotmail.com> wrote:
> > > Thanks Geremy,
>
> > > That has been an absolute bump........... GOD i cant sit on my chair, it has
> > > worked even on 512 bit number and with no time..........
> > > superb i would say.
>
> > > lastly, i am using the code below to calculate Largest Prime factor of a
> > > number:
>
> > > print
> > > ('''======================================================================= ========'''
> > >        '''              CALCULATE HIGHEST PRIME
> > > FACTOR                                  '''
>
> > > '''======================================================================== =======''')
>
> > > #!/usr/bin/env python
> > > def highest_prime_factor(n):
> > >    if isprime(n):
> > >       return n
> > >    for x in xrange(2,n ** 0.5 + 1):
> > >       if not n % x:
> > >          return highest_prime_factor(n/x)
> > > def isprime(n):
> > >    for x in xrange(2,n ** 0.5 + 1):
> > >       if not n % x:
> > >          return False
> > >    return True
> > > if __name__ == "__main__":
> > >    import time
> > >    start = time.time()
> > >    print highest_prime_factor(1238162376372637826)
> > >    print time.time() - start
>
> > > the code works with a bit of delay on the number : "1238162376372637826" but
> > > extending it to
> > > (10902610991329142436630551158108608965062811746392577675456004845499113044 30471090261099132914243663055115810860896506281174639257767545600484549911 30443047)
> > > makes python go crazy. Is there any way just like above, i can have it
> > > calculated it in no time.
>
> > > thanks for the support.
>
> > If you're just looking for the largest prime factor I would suggest using
> > a fermat factorization attack. In the example you gave, it returns
> > nearly immediately.
>
> > Geremy Condra- Hide quoted text -
>
> > - Show quoted text -
>
> For a Python-based solution, you might want to look at pyecm (http://
> sourceforge.net/projects/pyecm/)
>
> On a system with gmpy installed also, pyecm found the following
> factors:
>
> 101, 521, 3121, 9901, 36479, 300623, 53397071018461,
> 1900381976777332243781
>
> There still is a 98 digit unfactored composite:
>
> 602525071745682437589111511878284384468144476539868422797968232621651594065 00174226172705680274911
>
> Factoring this remaining composite using ECM may not be practical.
>
> casevh

The complete factorization is: 101 x 521 x 3121 x 9901 x 36479 x
300623 x 53397071018461 x 1900381976777332243781 x
6060517860310398033985611921721 x
9941808367425935774306988776021629111399536914790551022447994642391

It helps if you notice that the digits of the original 156-digit
number come from concatenating a 78-digit string to itself, giving an
immediate factor of 10**78 + 1. (Oops. Perhaps this was supposed to
be a secret back door to the OP's crypto scheme. I've given it away
now. :))

--
Mark

Mark Dickinson

3/10/2010 5:51:00 PM

On Mar 9, 1:54 pm, casevh <cas...@gmail.com> wrote:
> After a few hours, the remaining factors are
>
> 6060517860310398033985611921721
>
> and
>
> 9941808367425935774306988776021629111399536914790551022447994642391
>
> casevh

Whoops---I missed this. I'm too slow! But at least my answers agree
with yours. (Factoring 10**78+1 took around 7 seconds using GP/Pari
on a 2.5 GHz MacBook; factoring the remaining quotient n / (10**78+1)
was much quicker.)

--
Mark

comp.lang.python

Re: Calculating very large exponents in python

geremy condra

casevh

casevh

Mark Dickinson

Mark Dickinson

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