Path: csiph.com!weretis.net!feeder6.news.weretis.net!nntp.club.cc.cmu.edu!micro-heart-of-gold.mit.edu!newsswitch.lcs.mit.edu!nntp.TheWorld.com!.POSTED!not-for-mail From: moroney@world.std.spaamtrap.com (Michael Moroney) Newsgroups: sci.math Subject: Re: AP's stupid conjecture Date: Fri, 5 Oct 2018 21:21:33 +0000 (UTC) Organization: The World : www.TheWorld.com : Since 1989 Lines: 28 Message-ID: References: <333afe82-575a-48f3-ae45-a180b494274f@googlegroups.com> <621eb0a3-9f8f-408e-8f7d-a7c4083ff84e@googlegroups.com> NNTP-Posting-Host: shell01.theworld.com X-Trace: pcls7.std.com 1538774493 1392 192.74.137.71 (5 Oct 2018 21:21:33 GMT) X-Complaints-To: abuse@TheWorld.com NNTP-Posting-Date: Fri, 5 Oct 2018 21:21:33 +0000 (UTC) User-Agent: nn/6.6.5 Xref: csiph.com sci.math:425030 eastside.erik@gmail.com writes: >On Friday, October 5, 2018 at 1:33:58 PM UTC-7, Archimedes Plutonium wrote: >> Alright, I have a brand new definition of Prime, that involves AP Columns. >> And it leaves a conjecture open. >Hey Archie! Look at your first column if P is prime: >P 0 >P-1 1 >P-2 2 >... >P-n n >... >Just for fun, divide both columns by anything, say m. You get >P/m - n/m n/m >Even is n/m is integer, P/m is NEVER integer. Your conjecture is TRIVIAL. >This whole "theory of New Era Primes" is not even wrong. Archie has stumbled across a variation of trial division to find primes. Instead of trying every number n from 2 to P/2 and seeing if n divides P evenly, he is trying every number n from 2 to P/2 and seeing if (P-n)/n divides evenly. However, whenever n divides P evenly, n divides (P-n) evenly, since (P-n)/n = P/n-n/n = P/n-1. The Sieve of Eratosthenes is more efficient as it only attempts division by already identified primes.