October 2006 - mathfun@mailman.xmission.com

[math-fun] To Rich: Finding primes between multiples of a fixed number
by Daniel Asimov 10 Oct '06

10 Oct '06

Rich -- turns out Franklin calculated a few terms of the same sequence, about a year ago, which apparently is what led to its becoming A110835 of the OEIS! (At least I can contribute a bunch more terms, in case anyone's interested.) -------------------------- Note: The log_N(k) figure (k is largest registered N-tuple before the first one that's totally composite) seems it may be converging to something around e = 2.718... which seems too weird to be true. As with your 2^N +-3 prime observation, I'll wait till I see a lot more terms, but there's some kind of gestalt definitely emerging. --Dan

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[math-fun] Primes in 2^N +-3
by Schroeppel, Richard 09 Oct '06

09 Oct '06

A curiosity: There seem to be 1.5 times as many primes of the form 2^N-3 as there are of the form 2^N+3. 2^N+3 is prime for N = 1 2 3 4 6 7 12 15 16 18 28 30 55 67 84 228 390 784 while 2^N-3 is prime for N = 3 4 5 6 9 10 12 14 20 22 24 29 94 116 122 150 174 213 221 233 266 336 452 545 689 694 850 (up to N=1000). The former sequence is divisible by 7 when N = 2 mod 3, while the latter is never a multiple of 7. Small primes other than 7 seem to strike both sequences equally. The large gaps (390-784, and 29-94) and general bunchiness (213, 221, 233; 689, 694) makes it hard to draw any firm conclusions. Rich

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[math-fun] Off topic
by David Wilson 09 Oct '06

09 Oct '06

Sorry people. I can't tell you how many time computer job recruiters have contacted me, and the minute they hear I haven't worked since 2002 they disappear. I guess I'll just keep working my deli job till I get so fed up with it I shoot myself. Hurray for America, land of opportunity. God sucks. Now back to my regularly scheduled program. - Dave Wilson

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RE: [math-fun] Prime path
by Eric Angelini 09 Oct '06

09 Oct '06

Thanks, David -- those are my first steps into graphs and indeed, since I've posted my mail, I've discovered that those questions are quite difficult to answer. Thanks also for providing me the correct words « tree », « child », etc. Thanks to Gottfried Helms, too. Best, É. -----Message d'origine----- De : math-fun-bounces+eric.angelini=kntv.be(a)mailman.xmission.com [mailto:math-fun-bounces+eric.angelini=kntv.be@mailman.xmission.com] De la part de David Wilson Envoyé : lundi 9 octobre 2006 16:31 À : math-fun Objet : Re: [math-fun] Prime path Empirical evidence suggests that there is a prime on [(n^2-3n+8)/2, (n^2-n+4)/2] for every n >= 2, that is to say, every node of your tree has a prime child, so that there is an infinite path of increasing primes starting not only at 1 (counting 1 as prime), but at any node of your tree. On the other hand, Opperman's similar 1882 conjecture that there is a prime on [n^2, (n+1)^2] for every n >= 2 is also supported by empirical evidence, but resists proof to this day. This attests to the difficulty of such questions. Admittedly, your initial conjecture is weaker than the conjecture that every node of your tree has a prime child. We might be able to prove that most of the nodes of your tree have a prime child, and that we are able to choose a path that avoids those few nodes that do not have prime children. Still, such a proof would be very involved, well beyond my capabilities. _______________________________________________ math-fun mailing list math-fun(a)mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

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[math-fun] Prime path
by Eric Angelini 09 Oct '06

09 Oct '06

Hello Math-Fun and SeqFan, I have the feeling this is (very) old hat... Anyway: http://www.cetteadressecomportecinquantesignes.com/PrimePath.htm Best, É.

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[math-fun] patterns in the ramanujan Tau function
by Simon Plouffe 09 Oct '06

09 Oct '06

Hello there, I am conducting some experiments with sequences mod M, for various M and found this interesting pattern with Ramanujan Tau function with the number 23 and multiples of 23. http://www.lacim.uqam.ca/%7Eplouffe/OEIS/A000594%20mod%2023M/ So what I did is a graph of RamanujanTau[n] mod 23M, where M=1,2,3... on the unit circle to <see> the pattern, and here it is, very nice(!). simon plouffe

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Re: [math-fun] Primes in 2^N +-3
by Daniel Asimov 08 Oct '06

08 Oct '06

<< Integers really are amazing things. What's so amazing about one thing after another with no variation, endlessly? --Dan (:-)>

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[math-fun] FW: Constance Reid, Emma Lehmer's 100th birthday
by Schroeppel, Richard 07 Oct '06

07 Oct '06

This seemed worth passing on. -- Rich -----Original Message----- From: Number Theory List on behalf of John Cosgrave Sent: Fri 10/6/2006 2:00 PM To: NMBRTHRY(a)LISTSERV.NODAK.EDU Subject: Constance Reid, Emma Lehmer In a recent email to me Constance Reid wrote: '...Emma Lehmer, who will be 100 years old on November 6. I and others are suggesting that cards, not just on that day but scattered randomly throughout the month of November, would be very welcome. ... Emma...still goes each day, expectantly, to the mail box. Her address is still 1180 Miller Avenue, Berkeley CA 94708.' Emma Lehmer - along with her husband D. H. Lehmer, and many other renowned number theorists - is in the Oxford 1969 photograph at my web site http://www.spd.dcu.ie/johnbcos/oxford.htm. There is also a lovely photograph of Emma Lehmer in Constance Reid's book 'Julia'. John B. Cosgrave, Mathematics Department, St. Patrick=C2=92s College, Drumcondra, Dublin 9, IRELAND. Office phone: 00-353-1-8842133 Web site: www.spd.dcu.ie/johnbcos

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[math-fun] October update of multimagie.com
by Christian Boyer 07 Oct '06

07 Oct '06

Some October news from www.multimagie.com/indexengl.htm: -Best known 6x6 pandiagonal multiplicative magic square, first seen in [math-fun]. 5 720 160 45 80 1440 4800 12 150 192 300 6 9 400 288 25 144 800 320 180 10 2880 20 90 75 48 2400 3 1200 96 576 100 18 1600 36 50 And other new best known nxn pandiag mult squares. -Nobody knows a 4x4 magic square of cubes, using distinct positive integers. But very interesting step with the first known 4x4 semi-magic squares of cubes (semi-magic means non-magic diagonals), by Lee Morgenstern, USA 16^3 20^3 18^3 192^3 180^3 81^3 90^3 15^3 108^3 135^3 150^3 9^3 2^3 160^3 144^3 24^3 Who will construct a 4x4 magic square of cubes, with 2 magic diagonals? -you will see nice construction methods of 4x4 (used for the above square), 6x6, 8x8, 9x9 semi-magic squares of nth-powers, using Taxicab numbers. I am not sure that magic squares are useful, and not sure that Taxicab numbers are useful, ...but good news: Taxicab numbers are at least useful for magic squares! Christian.

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[math-fun] Pi nut case
by Eugene Salamin 04 Oct '06

04 Oct '06

Yahoo news article: TOKYO - A Japanese mental health counselor recited pi to 100,000 decimal places from memory on Wednesday, setting what he claims to be a new world record. Akira Haraguchi, 60, needed more than 16 hours to recite the number to 100,000 decimal places, breaking his personal best of 83,431 digits set in 1995, his office said Wednesday. He made the attempt at a public hall in Kisarazu, just east of Tokyo. Pi is a physical constant defined as the ratio of a circle's circumference to its diameter. It is usually written out to a maximum of three decimal places, as 3.141, in math textbooks. But the number, which has fascinated scientists for centuries, has no theoretical limit to the number of decimal places it can be written to. It is a constant that appears in the proofs of many equations defining the universe. "What I am aiming at is not just memorizing figures, I am thrilled by seeking a story in pi," Haraguchi said. The Guinness Book of Records currently lists Hiroyuki Goto, also from Japan, as the official record holder for reciting pi from memory. He recited the ratio out to 42,195 decimal places in 1995. Guinness never entered Haraguchi's 1995 feat in its record book. The editors of the book could not be immediately reached for comment regarding Haraguchi's latest attempt. Haraguchi, a psychiatric counselor and business consultant in nearby Mobara city, took a break of about 5 minutes every one to two hours, going to the rest room and eating rice balls during the attempt, said Naoki Fujii, spokesman of Haraguchi's office. Fujii said all of Haraguchi's activities during the attempt, including his bathroom breaks, were videotaped for evidence that will later be sent for verification by the Guinness Book of Records. Two local education officials joined 29 conference hall staff who worked in rotation to monitor Haraguchi. Haraguchi, who began reciting pi at 9 a.m. Tuesday, reached his previous record of 83,431 digits Tuesday night, finishing exactly at 100,000 digits at 1:28 a.m. Wednesday, Fujii said. In 2002, University of Tokyo mathematicians, aided by a supercomputer, set the world record for figuring out pi to 1.24 trillion decimal places. __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com

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