Groups | Search | Server Info | Keyboard shortcuts | Login | Register [http] [https] [nntp] [nntps]

Groups > comp.lang.python > #77692

Re: Prime testing [was Re: My backwards logic]

Show key headers only | View raw

On Sun, Sep 7, 2014 at 11:53 AM, Peter Pearson
<pkpearson@nowhere.invalid> wrote:
> On Sat, 6 Sep 2014 12:53:16 +0200, Manolo Martínez wrote:
>> On 09/06/14 at 08:38pm, Steven D'Aprano wrote:
>>> But even that's not how the specialists do it. If you want to check whether
>>> (say) 2**3000+1 is prime, you don't want to use trial division at all...
>>
>> When I was interested in these things, specialists would use the [number
>> field sieve](https://en.wikipedia.org/wiki/General_number_field_sieve).
>
> No, one uses the number field sieve to *factor* large numbers.  To
> test for primality, one uses simple tests like Fermat's test (x**(n-1)%n == 1,
> for many different x) or the slightly more complex Miller-Rabin test.

Usually you'd preceed a Miller-Rabin test with trial division by some
small primes, as division by small primes identifies a lot of
composites more quickly than Miller-Rabin.

> These probabilistic primality tests can prove that a number is composite,
> but they can't actually *prove* that a number is prime.  For that, you
> need a more complex test that is beyond my ken as a cryptologist.

Actually, smallish numbers are always correctly identified as prime or
composite by Miller-Rabin.  It's the big ones that aren't.

For a deterministic primality test that works on large numbers, check
out the AKS algorithm.

Back to comp.lang.python | Previous | Next — Previous in thread | Next in thread | Find similar | Unroll thread

Thread

My backwards logic Seymore4Head <Seymore4Head@Hotmail.invalid> - 2014-09-05 12:48 -0400
  Re: My backwards logic MRAB <python@mrabarnett.plus.com> - 2014-09-05 17:57 +0100
  Re: My backwards logic Bob Gailer <bgailer@gmail.com> - 2014-09-05 13:04 -0400
  Re: My backwards logic John Gordon <gordon@panix.com> - 2014-09-05 17:08 +0000
  Re: My backwards logic Ethan Furman <ethan@stoneleaf.us> - 2014-09-05 10:08 -0700
    Re: My backwards logic Seymore4Head <Seymore4Head@Hotmail.invalid> - 2014-09-05 13:44 -0400
      Re: My backwards logic Chris Kaynor <ckaynor@zindagigames.com> - 2014-09-05 11:17 -0700
      Re: My backwards logic Ian Kelly <ian.g.kelly@gmail.com> - 2014-09-05 15:04 -0600
      Re: My backwards logic Chris Angelico <rosuav@gmail.com> - 2014-09-06 09:44 +1000
  Re: My backwards logic Chris Kaynor <ckaynor@zindagigames.com> - 2014-09-05 10:09 -0700
  Re:My backwards logic Dave Angel <davea@davea.name> - 2014-09-05 13:15 -0400
  Re: My backwards logic Ian Kelly <ian.g.kelly@gmail.com> - 2014-09-05 11:17 -0600
  Re: My backwards logic Juan Christian <juan0christian@gmail.com> - 2014-09-05 14:35 -0300
  Re: My backwards logic Ethan Furman <ethan@stoneleaf.us> - 2014-09-05 11:41 -0700
  Re: My backwards logic MRAB <python@mrabarnett.plus.com> - 2014-09-05 19:48 +0100
  Re: My backwards logic Juan Christian <juan0christian@gmail.com> - 2014-09-05 16:34 -0300
    Re: My backwards logic Paul Rubin <no.email@nospam.invalid> - 2014-09-05 13:07 -0700
      Re: My backwards logic Rustom Mody <rustompmody@gmail.com> - 2014-09-05 18:24 -0700
  Re: My backwards logic Mark Lawrence <breamoreboy@yahoo.co.uk> - 2014-09-05 20:54 +0100
  Re: My backwards logic Seymore4Head <Seymore4Head@Hotmail.invalid> - 2014-09-05 17:49 -0400
    Re: My backwards logic Chris Kaynor <ckaynor@zindagigames.com> - 2014-09-05 15:14 -0700
      Re: My backwards logic Seymore4Head <Seymore4Head@Hotmail.invalid> - 2014-09-05 18:36 -0400
    Re: My backwards logic Ian Kelly <ian.g.kelly@gmail.com> - 2014-09-05 16:35 -0600
      Re: My backwards logic Seymore4Head <Seymore4Head@Hotmail.invalid> - 2014-09-05 19:05 -0400
    Re: My backwards logic Dave Angel <davea@davea.name> - 2014-09-05 23:10 -0400
  Re: My backwards logic Juan Christian <juan0christian@gmail.com> - 2014-09-05 22:54 -0300
    Re: My backwards logic Rustom Mody <rustompmody@gmail.com> - 2014-09-05 18:58 -0700
  Posting style: interleaved responses (was: My backwards logic) Ben Finney <ben+python@benfinney.id.au> - 2014-09-06 12:37 +1000
  Re: Posting style: interleaved responses (was: My backwards logic) Juan Christian <juan0christian@gmail.com> - 2014-09-06 00:06 -0300
  Re: Posting style: interleaved responses (was: My backwards logic) Zachary Ware <zachary.ware+pylist@gmail.com> - 2014-09-05 23:04 -0500
  Re: My backwards logic Mark Lawrence <breamoreboy@yahoo.co.uk> - 2014-09-06 08:45 +0100
  Re: My backwards logic Denis McMahon <denismfmcmahon@gmail.com> - 2014-09-06 07:49 +0000
    Prime testing [was Re: My backwards logic] Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-09-06 20:38 +1000
      Re: Prime testing [was Re: My backwards logic] Chris Angelico <rosuav@gmail.com> - 2014-09-06 20:42 +1000
      Re: Prime testing [was Re: My backwards logic] Manolo Martínez <manolo@austrohungaro.com> - 2014-09-06 12:53 +0200
        Re: Prime testing [was Re: My backwards logic] Peter Pearson <pkpearson@nowhere.invalid> - 2014-09-07 18:53 +0000
          Re: Prime testing [was Re: My backwards logic] Manolo Martínez <manolo@austrohungaro.com> - 2014-09-07 21:09 +0200
          Re: Prime testing [was Re: My backwards logic] Dan Stromberg <drsalists@gmail.com> - 2014-09-07 20:23 -0700
  Re: Posting style: interleaved responses Mark Lawrence <breamoreboy@yahoo.co.uk> - 2014-09-06 08:46 +0100

csiph-web