Path: csiph.com!x330-a1.tempe.blueboxinc.net!usenet.pasdenom.info!aioe.org!feeder.news-service.com!newsfeed.xs4all.nl!newsfeed6.news.xs4all.nl!xs4all!post.news.xs4all.nl!not-for-mail Return-Path: X-Original-To: python-list@python.org Delivered-To: python-list@mail.python.org X-Spam-Status: UNSURE 0.307 X-Spam-Level: *** X-Spam-Evidence: '*H*': 0.41; '*S*': 0.02; 'check.': 0.07; 'division,': 0.16; 'subject: \n ': 0.16; 'subject:was': 0.16; 'header:In-Reply-To:1': 0.21; 'seems': 0.21; 'received:209.85.220': 0.25; '(e.g.': 0.26; "i'm": 0.27; 'message- id:@mail.gmail.com': 0.28; 'bound': 0.29; 'subject:How': 0.30; 'to:addr:python-list': 0.33; 'however,': 0.34; 'there': 0.35; 'received:google.com': 0.37; 'received:209.85': 0.37; 'another': 0.37; 'page': 0.37; 'two': 0.37; 'could': 0.38; 'subject:can': 0.38; 'but': 0.38; 'smaller': 0.38; 'subject:: ': 0.38; 'some': 0.38; 'subject: (': 0.39; 'received:209': 0.39; 'to:addr:python.org': 0.39; 'more': 0.60; 'kind': 0.60; 'subject:, ': 0.60; 'john': 0.62; 'subject:. ': 0.65; 'square': 0.67; 'discovered': 0.69; 'prime': 0.73; 'trial': 0.76; 'subject:over': 0.84; 'factors': 0.91; 'unclear': 0.91; 'subject:much': 0.93 DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:mime-version:in-reply-to:references:date :message-id:subject:from:to:content-type; bh=U0d17qj4/2SRQ6Ueoow8ZuP8+eQe5EJ1Yr8mW2qdgAU=; b=IwcFCqLNeVCBS6bhLHfoHo6VcdNksrtVE/dQjGtnDzsjeNfOegsanzVPd3kNfN4KG8 zWS+6W2fQFZbV98Gxwc4SuZMvZRQyJUW0zuhbsVByYg0dj9Y5NnPubZKSNm0F8HayxPx nIPq/DixDc/XyRlOd+LLGbAVP7rBM8f7O71SI= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=mime-version:in-reply-to:references:date:message-id:subject:from:to :content-type; b=q31T4z0mNoY7Ol83Xi9P311p6YpchUg+QLUB53F+vPeLxD2f34AiHRE+4nU/Y8cuQl Ui0ipfNiNVYp1zKAG/UhHV0z3JMJw29XjaxR/ipbXceRgsJuSMaJQebF7G+mqj5Sl/xh jAslo3Dy7vs0j3P2kZ+zu9jfwk22i98dzIB2M= MIME-Version: 1.0 In-Reply-To: <8b8c4bc8-7b26-4113-b95b-7eccbbd0e901@q30g2000yqb.googlegroups.com> References: <4e00faa9$0$49180$e4fe514c@news.xs4all.nl> <4e00fd85$0$49038$e4fe514c@news.xs4all.nl> <8b8c4bc8-7b26-4113-b95b-7eccbbd0e901@q30g2000yqb.googlegroups.com> Date: Tue, 21 Jun 2011 23:33:33 +0200 Subject: Re: sorry, possibly too much info. was: Re: How can I speed up a script that iterates over a large range (600 billion)? From: Vlastimil Brom To: python-list@python.org Content-Type: text/plain; charset=ISO-8859-1 X-Mailman-Approved-At: Wed, 22 Jun 2011 01:51:59 +0200 X-BeenThere: python-list@python.org X-Mailman-Version: 2.1.12 Precedence: list List-Id: General discussion list for the Python programming language List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , Newsgroups: comp.lang.python Message-ID: Lines: 14 NNTP-Posting-Host: 82.94.164.166 X-Trace: 1308700322 news.xs4all.nl 49047 [::ffff:82.94.164.166]:49537 X-Complaints-To: abuse@xs4all.nl Xref: x330-a1.tempe.blueboxinc.net comp.lang.python:8146 2011/6/21 John Salerno : > However, even after reading the Wikipedia page about prime numbers and > trial division, I'm still a little unclear as to why the square root > of the number is the upper bound of the range you need to check. > -- There are likely be some more elaborated proofs, but it seems sufficiently evident, that with the factors being the square root you get some kind of "middle position"; with other factors (e.g. two for simplicity), one of them could be greater, while the another has to be smaller; this smaller one would have been discovered already, while searching continuously until the square root of the given number. vbr