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Groups > comp.lang.javascript > #29355
| From | Thomas 'PointedEars' Lahn <PointedEars@web.de> |
|---|---|
| Newsgroups | comp.lang.javascript |
| Subject | Re: Primality sieve challenge |
| Date | 2016-01-19 19:59 +0100 |
| Organization | PointedEars Software (PES) |
| Message-ID | <40372295.ejPoVfOnFb@PointedEars.de> (permalink) |
| References | (4 earlier) <87ziw27kln.fsf@bsb.me.uk> <2865358.ifOrN9Bpor@PointedEars.de> <0f34c52b-ae45-49b0-8363-080d3d11d5fb@googlegroups.com> <3532030.noGN7VB15C@PointedEars.de> <87bn8h64yr.fsf@bsb.me.uk> |
Ben Bacarisse wrote:
> Thomas 'PointedEars' Lahn <PointedEars@web.de> writes:
>> 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?
>
> (6k + 3)/3 = 2k + 1 which is an integer. […]
It is obvious to me, now that you have put it *this* way :)
> The key is that every integer > 5 is in one of the six sets Rr = { 6k +
> r | k ∈ N } where r is one of 0, 1,... 5. All the primes are there
> somewhere in one or more of these sets. But all the numbers in R0, R2,
> R3 and R4 are composite. What options are left? There may be no
^^^^^^^^^^^^^^^
> primes, of course, but if there are any, they must in either R1 or R5.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
And integers n = 6k − 1 (in your original statement) are members of the same
equivalence class as integers m = 6k + 5. Thank you, I see it now. I
missed the marked part as I misunderstood Gene’s statement so that it would
mean that you can *find* primes that way.
--
PointedEars
FAQ: <http://PointedEars.de/faq> | SVN: <http://PointedEars.de/wsvn/>
Twitter: @PointedEars2 | ES Matrix: <http://PointedEars.de/es-matrix>
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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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