Path: csiph.com!weretis.net!feeder4.news.weretis.net!feeder1.news.weretis.net!news.solani.org!.POSTED!not-for-mail From: Thomas 'PointedEars' Lahn Newsgroups: comp.lang.javascript Subject: Re: Primality sieve challenge Date: Tue, 19 Jan 2016 13:47:58 +0100 Organization: PointedEars Software (PES) Lines: 44 Message-ID: <3532030.noGN7VB15C@PointedEars.de> References: <5b608a56-e16b-4467-a0ce-4e30f6796920@googlegroups.com> <37264925.IaaGi9xk8D@PointedEars.de> <87ziw27kln.fsf@bsb.me.uk> <2865358.ifOrN9Bpor@PointedEars.de> <0f34c52b-ae45-49b0-8363-080d3d11d5fb@googlegroups.com> Reply-To: Thomas 'PointedEars' Lahn Mime-Version: 1.0 Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: 8Bit X-Trace: solani.org 1453207680 14148 eJwFwYEBgDAIA7CXKFLAc8DZ/09YwieRX0Uyg6LQETDJX+vejnKDz/F/ZngQqgGGVu7MXV0DOxCF (19 Jan 2016 12:48:00 GMT) X-Complaints-To: abuse@news.solani.org NNTP-Posting-Date: Tue, 19 Jan 2016 12:48:00 +0000 (UTC) User-Agent: KNode/4.14.2 X-User-ID: eJwFwYEBwCAIA7CXFGmBcwba/09YgsPNCSfoENTWBl/M+8nYsmScernho3nXH3NyMEFVLGuO4rt3xVah8ANYbhW1 Cancel-Lock: sha1:nixOwhAosb6dt3JDUMcR23VRUnY= X-NNTP-Posting-Host: eJwFwYEBwDAEBMCVEP9hHKX2HyF3OFT2dYKOxcad//SxXPc701qCkFFRRJLGbdsUV5RE5fcAEH8Qcw== Xref: csiph.com comp.lang.javascript:29344 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: | SVN: Twitter: @PointedEars2 | ES Matrix: Please do not cc me. / Bitte keine Kopien per E-Mail.