## Message 6888 from Yahoo.Groups.Primeform

Return-Path: <jens.k.a@...> X-Sender: jens.k.a@... X-Apparently-To: primeform@yahoogroups.com Received: (qmail 59890 invoked from network); 2 Feb 2006 05:55:47 -0000 Received: from unknown (66.218.66.167) by m34.grp.scd.yahoo.com with QMQP; 2 Feb 2006 05:55:47 -0000 Received: from unknown (HELO swip.net) (212.247.154.65) by mta6.grp.scd.yahoo.com with SMTP; 2 Feb 2006 05:55:47 -0000 X-T2-Posting-ID: Wa9Z96h7eeSAJR1BSSbOog== X-Cloudmark-Score: 0.000000 [] Received: from [195.47.135.241] (HELO jensathlonxp) by mailfe03.swip.net (CommuniGate Pro SMTP 5.0.2) with SMTP id 113278088 for primeform@yahoogroups.com; Thu, 02 Feb 2006 06:32:13 +0100 Message-ID: <005801c627ba$071ab930$f1872fc3@jensathlonxp> To: <primeform@yahoogroups.com> References: <20060202005352.29039.qmail@...> Date: Thu, 2 Feb 2006 06:30:16 +0100 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2741.2600 X-MIMEOLE: Produced By Microsoft MimeOLE V6.00.2742.200 X-Originating-IP: 212.247.154.65 X-eGroups-Msg-Info: 1:12:0:0 From: "Jens Kruse Andersen" <jens.k.a@...> Subject: Re: [primeform] Prime versus composite X-Yahoo-Group-Post: member; u=125539524; y=oC3yh15fcXC_9pvMcINYNrAVlLyeff1r1RDIqZQACSQysg X-Yahoo-Profile: jkand71Joao Silva wrote: > All the "transformed Fermat numbers" are primes! So you say, but I'm sorry to say that I have limited trust in you by now. > I have devised a special-purpose factoring algorithm which > was recently expanded into a general purpose one... > Unfortunately, I do not plan to reveal it here. Let's just say > that if anyone is able to find a factor for any of the > "transformed Fermat numbers" I will gladly leave the group > and you will never here from me again. The numbers are prp's (probable primes). They are almost certainly prime but I don't believe you have proved primality of the largest. > After all, I vividly > remember my "naive mistake" with the 60229 decimal > digit PRP that I submitted some months ago... Actually, that was the 60239-digit composite repunit (10^60239-1)/9 you submitted to the Prime Pages. It has the small factor 4073791 so Chris didn't have to make a prp test. If you don't know the difference between a prp and a proven prime then look e.g. at http://primes.utm.edu/prove/proving.html > You are right, rule is not the right word! It is simply an > interesting mathematical observation.... Glad to see you admit "rule" was bad. We also disagree on "interesting" here, but that's more subjective. > F5 = 4294967297 = 641* 6700417 but > 4294969297 = 4294967297 + 2 *10^3 = 643 * 6679579 > which gives two factors of similar size and same order of > magnitude. Now you are changing a digit by more than 1 (and you may have tried with other numbers than F5). This gives so many possibilities that it is not very surprising you can find a small number with a similar factorization. If you find what you think is a remarkable property then you should really consider whether it would just be an unsurprising event for random numbers. It would be more impressive if you found a similar property for F7 = 59649589127497217 * 5704689200685129054721 The law of small numbers may be of interest: http://primes.utm.edu/glossary/page.php?sort=LawOfSmall > Finally, I did not understand what you meant by (probably > because everybody here writes in a very abbreviated manner?!): > > A better "rule" is: > There is an n-digit near-repdigit prime for each n>1. > Heuristic excercises: > Do you expect exceptions? > Would you search for them? This is only vaguely related to your posts and you can ignore it. A near-repdigit prime is a prime where all digits except one are the same, e.g. 3333373. I disliked your use of the word rule. My "rule" is about something else where it looks completely infeasible to find exceptions. However, I do expect very rare exceptions. I would even conjecture them. Andersen's near-repdigit conjectures: 1) There are infinitely many n without an n-digit near-repdigit prime. 2) No such n will ever be found. And congratulations to Harvey Dubner on retaking the palindromic prime record: http://primes.utm.edu/top20/page.php?id=53 -- Jens Kruse Andersen