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Re: Primality sieve challenge

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Scott Sauyet wrote:

> Thomas 'PointedEars' Lahn wrote:
>> Ben Bacarisse wrote:
>>> but all those that have the form 6k + {0, 2, 3, 4} are clearly
>>> composite.
>> I can see why it is so for {0, 2, 4} (all multiples of 6 are divisible by
>> 2, so are the sums when added 2 or 4), but why also for the summand 3?
> 
> Because 6k + 3 is divisible by 3.

Why?  I can see that it follows for k = 1 (9), k = 2 (15), k = 3 (21), and 
for several greater k, but why for *all* k?

> And if it's greater than 5 it's clearly not equal to 3, so it's not prime.

I find that a specious argument at best.

>> Also, I do not see how your argument proves Gene's assertion.
> 
> His assertion was that
> 
> | [...]  All primes >= 5 are of the form 6k +/- 1 where k is a positive
> | integer.

Yes.
 
> Since all positive integers > 5 are (trivially) of one of forms `6k + 0`,
> `6k + 1`, `6k + 2`, `6k + 3`, `6k + 4`, or `6k + 5`, and we've easily
> demonstrated that all those of the form `6k + {0, 2, 3, 4}` are composite,

Yes.

> all primes must be of the form `6k + 1` or `6k + 5`.

Again, why?  If something is true for A and B, it does not follow that it is 
not true for C ∉ {A, B}: p(A) ∧ p(B) ↛ ¬p(C); here p(X) := “X is composite 
(not prime)”.  What relation I am missing here?
 
-- 
PointedEars
FAQ: <http://PointedEars.de/faq> | SVN: <http://PointedEars.de/wsvn/>
Twitter: @PointedEars2 | ES Matrix: <http://PointedEars.de/es-matrix>
Please do not cc me. / Bitte keine Kopien per E-Mail.

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Primality sieve challenge jonas.thornvall@gmail.com - 2016-01-17 01:40 -0800
  Re: Primality sieve challenge jonas.thornvall@gmail.com - 2016-01-17 02:20 -0800
  Re: Primality sieve challenge Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-01-17 16:24 +0000
    Re: Primality sieve challenge jonas.thornvall@gmail.com - 2016-01-17 09:03 -0800
      Re: Primality sieve challenge jonas.thornvall@gmail.com - 2016-01-17 09:17 -0800
        Re: Primality sieve challenge jonas.thornvall@gmail.com - 2016-01-17 09:22 -0800
          Re: Primality sieve challenge jonas.thornvall@gmail.com - 2016-01-17 11:32 -0800
          Re: Primality sieve challenge Stefan Weiss <krewecherl@gmail.com> - 2016-01-18 00:13 +0100
            Re: Primality sieve challenge jonas.thornvall@gmail.com - 2016-01-18 04:10 -0800
          Re: Primality sieve challenge Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-01-18 01:20 +0000
            Re: Primality sieve challenge "Evertjan." <exxjxw.hannivoort@inter.nl.net> - 2016-01-18 12:16 +0100
              Re: Primality sieve challenge Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-01-18 11:25 +0000
                Re: Primality sieve challenge "Evertjan." <exxjxw.hannivoort@inter.nl.net> - 2016-01-18 12:43 +0100
                Re: Primality sieve challenge jonas.thornvall@gmail.com - 2016-01-18 04:18 -0800
                Re: Primality sieve challenge jonas.thornvall@gmail.com - 2016-01-18 04:25 -0800
              Re: Primality sieve challenge Gene Wirchenko <genew@telus.net> - 2016-01-18 09:52 -0800
                Re: Primality sieve challenge "Evertjan." <exxjxw.hannivoort@inter.nl.net> - 2016-01-18 19:23 +0100
                Re: Primality sieve challenge "Michael Haufe (TNO)" <tno@thenewobjective.com> - 2016-01-18 10:48 -0800
                Re: Primality sieve challenge Gene Wirchenko <genew@telus.net> - 2016-01-18 13:09 -0800
                Re: Primality sieve challenge Scott Sauyet <scott.sauyet@gmail.com> - 2016-01-18 13:14 -0800
                Re: Primality sieve challenge "Evertjan." <exxjxw.hannivoort@inter.nl.net> - 2016-01-18 22:45 +0100
                Re: Primality sieve challenge jonas.thornvall@gmail.com - 2016-01-18 14:23 -0800
                Re: Primality sieve challenge Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-01-18 22:56 +0000
                Re: Primality sieve challenge jonas.thornvall@gmail.com - 2016-01-18 15:02 -0800
                Re: Primality sieve challenge jonas.thornvall@gmail.com - 2016-01-18 16:04 -0800
                Re: Primality sieve challenge Stefan Weiss <krewecherl@gmail.com> - 2016-01-19 02:42 +0100
                Re: Primality sieve challenge jonas.thornvall@gmail.com - 2016-01-18 23:34 -0800
                Re: Primality sieve challenge jonas.thornvall@gmail.com - 2016-01-19 01:34 -0800
                Re: Primality sieve challenge "Michael Haufe (TNO)" <tno@thenewobjective.com> - 2016-01-19 06:23 -0800
                Re: Primality sieve challenge jonas.thornvall@gmail.com - 2016-01-19 07:10 -0800
                Re: Primality sieve challenge jonas.thornvall@gmail.com - 2016-01-19 07:15 -0800
                Re: Primality sieve challenge jonas.thornvall@gmail.com - 2016-01-19 08:34 -0800
                Re: Primality sieve challenge Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-01-19 16:54 +0000
                Re: Primality sieve challenge "Michael Haufe (TNO)" <tno@thenewobjective.com> - 2016-01-19 08:57 -0800
                Re: Primality sieve challenge jonas.thornvall@gmail.com - 2016-01-19 10:18 -0800
                Re: Primality sieve challenge jonas.thornvall@gmail.com - 2016-01-19 10:59 -0800
                Re: Primality sieve challenge Stefan Weiss <krewecherl@gmail.com> - 2016-01-20 01:33 +0100
                Re: Primality sieve challenge jonas.thornvall@gmail.com - 2016-01-20 02:10 -0800
                Re: Primality sieve challenge jonas.thornvall@gmail.com - 2016-01-20 02:21 -0800
                Re: Primality sieve challenge Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-01-20 10:45 +0000
                Re: Primality sieve challenge "Michael Haufe (TNO)" <tno@thenewobjective.com> - 2016-01-20 06:43 -0800
                Re: Primality sieve challenge Scott Sauyet <scott.sauyet@gmail.com> - 2016-01-20 15:21 -0800
                Re: Primality sieve challenge Stefan Weiss <krewecherl@gmail.com> - 2016-01-21 03:18 +0100
                Re: Primality sieve challenge Jon Ribbens <jon+usenet@unequivocal.co.uk> - 2016-01-21 12:12 +0000
                Re: Primality sieve challenge Dr J R Stockton <reply1600@merlyn.demon.co.uk.invalid> - 2016-01-21 23:20 +0000
                Re: Primality sieve challenge Stefan Weiss <krewecherl@gmail.com> - 2016-01-22 19:44 +0100
                Re: Primality sieve challenge Dr J R Stockton <reply1600@merlyn.demon.co.uk.invalid> - 2016-01-23 21:50 +0000
                Re: Primality sieve challenge Stefan Weiss <krewecherl@gmail.com> - 2016-01-24 01:26 +0100
                Re: Primality sieve challenge "Michael Haufe (TNO)" <tno@thenewobjective.com> - 2016-01-23 17:54 -0800
                Re: Primality sieve challenge "Chris M. Thomasson" <nospam@no-spam.ws> - 2016-01-24 13:34 -0800
                Re: Primality sieve challenge Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-01-25 00:21 +0000
                Re: Primality sieve challenge Stefan Weiss <krewecherl@gmail.com> - 2016-01-25 03:08 +0100
                Re: Primality sieve challenge "Michael Haufe (TNO)" <tno@thenewobjective.com> - 2016-01-24 19:35 -0800
                Re: Primality sieve challenge jonas.thornvall@gmail.com - 2016-01-25 03:53 -0800
                Re: Primality sieve challenge Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-01-18 19:32 +0000
        Re: Primality sieve challenge Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-01-17 19:51 +0000
          Re: Primality sieve challenge jonas.thornvall@gmail.com - 2016-01-17 13:43 -0800
  Re: Primality sieve challenge "Chris M. Thomasson" <nospam@nospam.nospam> - 2016-01-17 12:46 -0800
    Re: Primality sieve challenge Gene Wirchenko <genew@telus.net> - 2016-01-18 09:50 -0800
      Re: Primality sieve challenge Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-01-18 20:09 +0100
        Re: Primality sieve challenge Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-01-18 19:28 +0000
          Re: Primality sieve challenge Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-01-18 21:37 +0100
            Re: Primality sieve challenge Scott Sauyet <scott.sauyet@gmail.com> - 2016-01-18 13:12 -0800
              Re: Primality sieve challenge jonas.thornvall@gmail.com - 2016-01-18 13:46 -0800
                Re: Primality sieve challenge jonas.thornvall@gmail.com - 2016-01-18 14:00 -0800
              Re: Primality sieve challenge Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-01-19 13:47 +0100
                Re: Primality sieve challenge Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-01-19 14:04 +0000
                Re: Primality sieve challenge Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-01-19 19:59 +0100
                Re: Primality sieve challenge Scott Sauyet <scott.sauyet@gmail.com> - 2016-01-19 10:55 -0800
                Re: Primality sieve challenge Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-01-19 20:04 +0100
                Re: Primality sieve challenge Scott Sauyet <scott.sauyet@gmail.com> - 2016-01-19 13:42 -0800
                Re: Primality sieve challenge Erwin Moller <erwinmollerusenet@xs4all.nl> - 2016-01-21 17:21 +0100
                Re: Primality sieve challenge Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-02-03 19:52 +0100
        Re: Primality sieve challenge Dr J R Stockton <reply1600@merlyn.demon.co.uk.invalid> - 2016-01-19 19:43 +0000

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