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Re: My backwards logic

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Juan Christian <juan0christian@gmail.com> writes:
>  I made this code just for fun and learning, it's working, but would
>  this be a good approach? Thanks. ...
>  ** ** for number in range(start, stop + 1):
>  ** ** ** ** divisors = [(number % x) for x in range(1, number + 1)]
>  ** ** ** ** ** ** print("{n} prime? {r}".format(n = number, r =
>  (divisors.count(0) == 2)))

1. Mathematically it's better to stop checking once you've gone past
the square root of the number, since if n = p*q and is composite,
then at least one of p,q will be <= sqrt(n).

2. As a program design matter, it's generally preferable for functions
like this to not print the answer.  They should just return a value, in
this case a bool indicating whether the number is prime.  That makes it
easier to re-use the function, to wrap it in a unit test framework, etc.
If you want to print the result, then call the function and have the
caller print the returned value.

3. As a simple optimization, once you have checked that the number is
not divisible by 2, you don't have to check for other even divisors.
So just check for 2, then the odd numbers 3,5,7...

This is a little bit fancy but I like to use itertools for these
sorts of problems:

  from itertools import chain, takewhile, count

  def is_prime(n):
      if n < 2: return False
      candidates = chain([2], count(3,2))
      return all(n%d!=0 for d in takewhile(lambda d: d*d<=n, candidates))

If you're not familiar with those functions, "chain" concatenates
two sequences, and "count(n,i)" gives an increasing sequence starting
with n and incrementing by i.  So chain([2], count(3,2)) gives
the unending sequence [2, 3, 5, 7, 9, ...] which is the numbers
you want to check against.  Then the takewhile expression chops
that sequence once it gets past sqrt(n), and "all" returns true iff
all of the candidate divisors fail to divide the number.

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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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