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Re: My backwards logic

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On Fri, Sep 5, 2014 at 2:49 PM, Seymore4Head <Seymore4Head@hotmail.invalid>
wrote:

> On Fri, 05 Sep 2014 12:48:56 -0400, Seymore4Head
> <Seymore4Head@Hotmail.invalid> wrote:
>
> >I'm still doing practice problems.  I haven't heard from the library
> >on any of the books I have requested.
> >
> >
> http://www.practicepython.org/exercise/2014/04/16/11-check-primality-functions.html
> >
> >This is not a hard problem, but it got me to thinking a little.  A
> >prime number will divide by one and itself.  When setting up this
> >loop, if I start at 2 instead of 1, that automatically excludes one of
> >the factors.  Then, by default, Python goes "to" the chosen count and
> >not "through" the count, so just the syntax causes Python to rule out
> >the other factor (the number itself).
> >
> >So this works:
> >while True:
> >    a=random.randrange(1,8)
> >    print (a)
> >    for x in range(2,a):
> >        if a%x==0:
> >            print ("Number is not prime")
> >            break
> >    wait = input (" "*40  + "Wait")
> >
> >But, what this instructions want printed is "This is a prime number"
> >So how to I use this code logic NOT print (not prime) and have the
> >logic print "This number is prime"
>
> I am sure this has already been done, but after it was pointed out
> that you don't need to test for any number that multiplies by 2 it
> made me think again.
>
> If you start with the list [3,5,7] and step through the list of all
> remaining odd numbers (step 2), and start appending numbers that won't
> divide by numbers already appended in the list, that would seem like a
> pretty efficient way to find all prime numbers.
>

To be correct, you only need to check for n being divisible by primes less
than sqrt(n). For example, the following code will produce a list of primes
from 2 to 1000 (the result will be in the "primes" list):

import math
primes = [2]
for i in range(3, 1000):
    end = math.sqrt(i)
    for x in primes:
        if x > end: # Once x is larger than the sqrt(i), we know it must be
prime, so we can early exit.
            #print(i, "is a prime number")
            primes.append(i)
            break
        if (i % x) == 0:
            #print(i, "is a composite number")
            break

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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

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